Energy-Efficient Coding and Modulation Methods for
Interference Suppression in Wireless Sensor Network Systems
by
Chun-Hung Liu
B.S. Mechanical Engineering
National Taiwan University, 1997
Submitted to the Department of Mechanical Engineering in Partial
Fulfillment of the Requirements for the Degree of
Master of Science in Mechanical Engineering
at the
BARKEr
Massachusetts Institute of Technology
OCT 2 5 2002
June, 2002
@ Massachusetts Institute of Technology 2002
All rights reserved
Signature of Author
-W,
MASSACHUSEMS INSTITUTJE
OF TECHNOLOGY
-P - - -
F
LIBRARIES
9
Department Of Mechanical Engineering
May 10, 2002
'I
Certified by
Haruhiko Harry Asada
Engineering
Mechanical
Ford Professor of
_oeo<,0rhesisSupervisor
Accepted by
Ain A. Sonin
Students
Graduate
on
Committee
Department
Chairman,
Energy-Efficient Coding and Modulation Methods for
Interference Suppression in Wireless Sensor Network Systems
by
Chun-Hung Liu
Submitted to the Department of Mechanical Engineering on May 10,
2002 in Partial Fulfillment of the Requirements for the Degree of
Master of Science in Mechanical Engineering
Abstract
An Energy-Efficient DS-CDMA communication and modulation technique for reducing
multiple access interference (MAI) as well as for reducing power consumption in DSCDMA wireless sensor LAN systems is presented. Source symbols are represented by a
special coding, termed Minimum Energy coding (ME coding), which exploits redundant
bits for saving power when transmitted via RF links with On-Off-Keying. Since, in OOK,
energy is consumed mostly when high bits are transmitted, the ME coding represents
source symbols with the least number of high bits, given an extended word length. This
ME coding is applied to DS-CDMA sensor network systems in order to reduce MAI as
well as to reduce power consumption. When each channel uses the ME coding combined
with a spreading code and OOK, fewer high bits are transmitted and thereby the
probability of multiple channels sending signals at the same time is lowered. This implies
that the MAI is reduced. It is shown that, with the new low MAI ME coding, signal-tonoise ratio is significantly increased and that the error probability is lowered as well. First,
the architecture of this low MAI DS-CDMA communication system is described,
followed by the principle of interference reduction. Second, a signal model is obtained for
the new source coding and transmission process, and the SNR and error probability are
analyzed. Third, guidelines for designing the optimal length of codeword, the number of
communication channels, and power efficiency are obtained. Finally, a RF sensor
network system is designed and simulation is conducted to verify the theoretical results
and demonstrate the low MAI and low energy features of the sensor network.
Thesis Supervisor: Haruhiko H. Asada
Title: Professor of Mechanical Engineering
2
To My Parents and My Brother
3
Acknowledgement
I would like to thank my thesis supervisor, Professor Haruhiko Asada,
for his guidance and encouragement throughout my research. His profound
insight and splendid wide vision gave me a great chance to get into the
world of new research directions. His valuable support and advice were the
greatest factor that I could write this thesis.
I also would like to thank to all my lab-mates in d'Arbeloff Laboratory
who showed me sincere friendship and care. Also, I would like to express
deep thanks to my best friends at MIT, Chung-Yao Kao and Wen-Hua Kuo,
who made my life more energetic and enjoyable. I also would like to say
thanks to my best female friend, Mei-Feng Chang who always supported me
during my depression.
Finally, I would like to express my best appreciation to my parents and
my brother, Jun-Chieh Liu, who have been watching me with great love.
Their love and care have been the main source of energy that encouraged me
through my life.
4
Contents
9
1. Introduction ..................................................................
2. Minimum Energy Coding Algorithms .................................
12
2.1 RF Transmitter Power Consumption .............................................
13
2.2 Memoryless ME Coding .............................................................
14
2.2.1 M E C oding ........................................................................
14
2.2.2 Fixed-Length ME Coding ......................................................
18
2.2.3 Optimality Bound to ME Coding ..............................................
19
3. Energy Efficient DS-CDMA for RF Transmission ...................
21
3.1 Motivation of Power Saving ........................................................
21
3.2 Energy Efficient Spreading Codes ................................................
24
3.2.1 Auto-correlation and Cross-correlation between PN sequences ..........
24
3.2.2 Ideal pseudorandom (PN) sequences .........................................
25
3.2.3 Finite-Field Arithmetic: Modulo-2 addition and multiplication ..........
26
3.3 Energy-Efficient DS-CDMA Communication Systems .......................
27
3.3.1 Signal recovery method of general DS-CDMA systems ..................
27
3.3.2 Signal recovery for spreading codes taking values of 0 and I ............
29
........
31
3.3.3 Signal recovery for spreading codes taking values of 0, 1 and -1
3.4 Simulation Results ...................................................................
31
3.5 Estimation of SNR for Different Spreading Codes ...........................
34
3.5.1 SNR 1 estimation for +1/-I spreading codes .................................
34
3.5.2 SNR 2 estimation for 1/0 spreading codes ....................................
34
3.5.3 SNR 3 estimation for 1/0/-I spreading codes .................................
35
3.5.4 Comparison of SNRs for different spreading codes ........................
36
3.6 Estimation of Error Probability for Different PN Sequences ...............
38
3.6.1 Error probability for +1/-I spreading codes .................................
38
3.6.2 Error Probability for 0/1 spreading codes ....................................
40
3.6.3 Error Probability for 0/1/-1 spreading codes .................................
40
3.6.4 Comparison of error probability for different spreading codes ............
41
5
4 Suppression of Multiple Access Interference (MAI) in EnergyEfficient DS-CDMA Communication Systems ........................
44
4.1 Principle of MAI Suppression ......................................................
44
4.2 Signal Model ...........................................................................
47
4.3 Evaluation of System Performances ..............................................
48
4.3.1 Signal-to-noise-ratio (SNR) ....................................................
49
4.3.2 Error Probability ..................................................................
50
4.4 Simulation Results .....................................................................
52
5 Communication System Design ...........................................
54
5.1 Critical Codeword Length ..........................................................
54
5.2 System Parameters and General Considerations ...............................
56
5.3 Updating Algorithm of Seeking the Optimal Codeword Length .............
57
5.4 Circuit Design of ME Coding Transmitters ....... ...............................
59
6 Conclusion ....................................................................
63
R eferences .........................................................................
64
A ppendix ...........................................................................
66
6
List of Figures
9
Figure 1.1 Wireless Body LANfor Wearable Computing ...................................
Figure 1.2 FingerRing Sensor with RF Transmitterfor Monitoring Vital Signs ......... 10
Figure2.1 PrincipleofMinimum Energy Coding ..........................................
13
Figure 2.2 DigitalRF Transmitter ............................................................
13
Figure 2.3 FixedLength L-bit Codewords ...................................................
18
Figure3.1 Bi-directionalCommunicationsin The Intelligent Sensor Network .........
22
Figure 3.2 Energy Efficient Spreading Codesfor DS-CDMA .............................
23
Figure3.3 Block Diagramof a DS-CDMA Transmitter ...................................
23
Figure3.4 Block Diagramof a DS-CDMA Receiver .......................................
24
Figure 3.5 Modulo-2 Addition and Multiplication ..........................................
26
Figure3.6 Signal Recovery Processfora GeneralDS-CDMA System ..................
28
Figure3.7 Signal Recovery forSpreadingCodes Taking Values of ] and 0 ..............
30
Figure 3.8 Signal Recovery for Spreading Codes Taking Values of 0, 1 and -1 ......... 31
Figure 3.9 Data Signals and Chipped Data Signals ........................................
32
Figure 3.10 TransmittedSignal and Received Signal ........................................
32
Figure 3.11 DemodulatedSignal Sd(t) and Output of the IntegratorY ................... 33
Figure 3.12 S,(t), ^,(t)G
1 (t)
and d,(t) .................................................
33
Figure 3.13 SNR v.s. Power Saving Rate for 10 Receivers and The Periodof Spreading
Codes N =31 ........................................................................
37
Figure 3.14 SNR v.s. Power Saving Rate for 10 Receivers and The Periodof Spreading
Codes N = 1023 ......................................................................
38
Figure 3.15 ErrorProbabilityv.s. Eb/Nofor Different SpreadingCodes if a] = 0.5 ... 42
Figure 3.16 Errorprobabilityv.s. E/Nofor different spreadingcodes if a] = 0.1 ...... 43
Figure4.1 DS-CDMA Combinedwith ME Source Coding ..................................
44
Figure4.2 Principleof Multiple Access Interference Reduction ............................
45
Figure 4.3 SNR for Energy-Efficient DS-CDMA vs. The Variationof al if E/No = 10 dB
andN =63 ..............................................................................
7
50
Figure 4.4 Error Probabilityper Bit for Energy-Efficient CDMA with the Variation of
a, .......................................................................................
52
Figure 4.5 ME Signal TransmissionforTwo-Sender Case ...................................
53
Figure 4.6 Total Signals in The Channel .....................................................
53
Figure 5.1 Ratio of Lk/Lb with The Variationof a,ifM=50 andN=63 ..................... 55
Figure 5.2 Trade-offProblem of Choosing The Optimal Codeword Length ............... 57
Figure 5.3 UpdatingProceduresof Seeking an Optimal Codeword Length ............... 59
Figure 5.4.1 Basic Architecture of a ME Coding Transmitter ............................
60
Figure 5.4.2 Circuit Design of Analog Switch (1) ........................................
60
Figure 5.4.3 CircuitDesign of Power Switch (2) .........................................
60
Figure 5.5 Basic Architecture of a ME Coding Receiver..................................
61
8
Chapter 1
Introduction
There is an increasing need for short-range, low power, multiple access wireless
communications. Connecting laptop computers, PDA, and mobile phones together with
video cameras, printers, and other peripheral devices, we will soon use wireless links in
our daily life. Furthermore, as the wireless device gets smaller, it can be placed on the
human body and micro machines, places where traditional RF and IR devices cannot be
used. This would open up new possibilities of wireless local area network. Figure 1.1
illustrates a wireless body LAN for wearable computing. Data collected from various
parts of the body are linked to each other. Figure 1.2 shows a finger ring sensor
monitoring vital signs of the patient and transmitting the data to a PDA and mobile phone
24 hours a day. These examples point in the future direction of wireless networking and
distributed sensing.
Figure 1 Wireless Body LAN for Wearable Computing
Low power, wireless networking is still a challenging problem, however. Bluetooth
is an ambitious technology, but its power consumption, around 30 mA, is too high to
power the device by a small cell battery, needing a regular-size battery that limits its form
factor. Furthermore, Bluetooth still has a major difficulty in multiple access interference
(MAI), causing a serious delay of delivery. i-Bean by Millennial Net is powered by a cell
9
battery, consuming only I mA under normal conditions, but is limited in channel capacity
and interference reduction. MAI reduction has been studied extensively in academia in
conjunction with DS-CDMA. A theoretical analysis has revealed that the average bit
error probability sharply increases as the channel number increases in DS-CDMA
systems with BPSK modulation [1]. In the past decade, numerous methods for MAI
cancellation and reduction have been developed, most of which focus on the design of
effective correlation receivers. [2]-[4] reported a receiver that outperforms the linear
correlation receiver. However, they have a significant increase in complexity. For
example, the computational complexity of the proposed receiver in [2] grows
exponentially with the number of users.
Figure 1.2 Finger Ring Sensor with RF Transmitter for Monitoring Vital Signs
In this thesis we would like to explore a different approach, focusing on source
coding. Instead of merely designing receivers to suppress interferences, our idea is to
represent source symbols using a special codebook so that MAI can be greatly reduced.
The codebook is designed in such a way that the probability of multiple channels sending
RF signals at the same time is substantially lowered than that of a standard source coding.
The remainder of this thesis is organized as follows. Chapter 2 summarizes a special
source coding, called the ME coding [5],[6]. Chapter 3 applies this ME coding to the DSCDMA communication system. In Chapter 4, signal models for ME transmissions are
described, and the principle of reducing interference is explained, and Signal-to noise
10
ratio (SNR) and error probability are evaluated as well; then Chapter 5 discusses the
design issues of energy-efficient communication systems. Finally Chapter 6 summarizes
the major results.
11
Chapter 2
Minimum Energy Coding Algorithms
Wireless networking is enjoying its fastest growth period in history, due to the
enabling technologies that permit wide-spread deployment [7]. However, this growth is
still limited due to the limited battery power at the portable terminals. Since the progress
in battery technology is rather slow to meet the rapidly increasing application demands,
new technology for energy efficient wireless communication must be crated [8-13]. In
attempt to devise new technology for energy efficient wireless communication, this paper
aims to optimize the power consumption in digital RF transmission. Digital RF
transmitters constitute the major power-consuming component in many portable
communication devices. Current efforts on transmitter power optimization aim to
minimize the transmitted power while satisfying some qualify of service constraints.
These efforts aim to achieve optimal transmitter performance via transmitter power
level adaptation [12], error control strategy adaptation [8,13], or a combination of the two
[14] for vary channel conditions. While these efforts are of considerable value, they do
not provide the ultimate optimal performance. In this paper, we propose a formulation of
the energy efficient RF transmission problem, solution of which can be combined with
the previous efforts to yield the ultimate optimal performance. In attempt to solve this
problem, this chapter aims to find special source codes that minimize power consumption
in RF transmission. Here we developed a novel memoryless coding algorithm, that is,
minimum energy coding (ME coding).
ME coding is a low-power coding algorithm that minimizes power consumption
when transmitting the same amount of information through a RF channel. The method
uses On-Off-keying, which is limited in performance, but is simple and energy efficient.
In On-Off keying, power is more consumed when a high bit is transmitted. Therefore the
total power consumption is dominated by the number of high bits to be transmitted. When
a few redundant bits are added to the original codeword, as shown in Figure 2.1, one can
use a set of codewords that contain fewer high bits to represent the same number of
source symbols. Therefore we can use redundant bits for the purpose of power saving.
12
Original Codeword Length
N umber of Redundent Bits
ME Coding
-
New Codeword Length (more zeros)
Figure 2.1 Principle of Minimum Energy Coding
2.1 RF Transmitter Power Consumption
Digital RF transmitter modulates the information to be communicated onto a carrier
waveform, amplify the waveform to the desired power level, and deliver it to the
transmitting antenna [16]. Many digital transmitter components are similar with the major
power consuming component being the oscillator. The oscillator is the circuitry
responsible for the modulation of the message signal (i.e. the bit stream of encoded data)
onto the transmitted waveform.
An attempt to formulate the power consumption optimization problem requires
understanding the oscillator operation. Oscillators are actuated upon the receipt of high
bits only (see Figure 2.2); hence, power consumption in the transmitter occurs only when
high bits are sent and virtually no power is consumed when low bits are sent. Each bit
period tb is assigned
High
Low
Energy
consumed
for Ct tb
transmitting one high bit
Figure 2.2 Digital RF Transmitter
a minimum detectable value that is determined from the channel characteristics. Since
this period is much longer than the oscillator period (a factor of nearly 106), the transient
13
period when the oscillator begins to oscillate is negligible in evaluating the power
consumption. Therefore, the total energy consumed in the RF transmitter in one second,
Eotai, is proportional to the total duration of high bits, namely, the total number of high
bits, nlotal, times the bit period
tb
Ei,, = CItltoal
(2.1)
where Ct is the power consumption coefficient. Let M be the number of symbols
transmitted in one second and n-be the average number of high bits involved in each
codeword. The average power consumption per symbol, C , is therefore given by
C -otal
M
-
tbn
(2.2)
Equation (2.2) suggests several ways of optimizing power consumption. Power
consumption can be optimized by (2.1) improving the transmitter circuitry to minimize
C, , (2.2) minimizing tb, and (2.3) minimizing n-.
The first two are determined by the
physical conditions of the transmitter and the channel, and require modifications to the
physical layer. The third one, on the other hand, is a non-physical factor, which would
allow us to further enhance energy efficiency beyond the physical limit. The average
number of high bits in each codeword
q
n=
Pn,
(2.3)
i=1
where q is the number of source symbols, ni is the number of high bits in i-th codeword,
and Pi is the probability of the i-th symbol. The objective of this paper is to reduce this
average high bit number, W . Next, we introduce Memoryless ME coding, a novel source
coding algorithm optimizing power consumption in RF transmission. At this point we
should note that in our application, noise is not of significant magnitude. Hence, we
consider noiseless source coding on at this stage.
2.2 Memoryless ME Coding
2.2.1 ME Coding
14
ME coding is a source coding algorithm that aims to optimize the energy efficiency
in RF transmission by minimizing the average number of high bits used in coding the
information source. ME coding is generated through two distinct steps: Codebook
Optimality and Coding Optimality. The former is to determine a set of codewords, termed
a codebook, that has fewest high bits, and the latter is to assign codewords having less
high bits to symbols with higher probability. The following two theorems underpin the
theory of ME Coding.
Theorem 1: Coding Optimality. Let S
=
{s1 , s 2 ,...,
qs_1 s
be a source alphabet with
symbol probabilityes
P ={PI
-- Pq- I
P2
(2.4)
Jq
Given a codebook of q codewords, each of which contains ni high bits, I <i < q, the
optimal code that minimizes the average number of high bits n=
n, P is given by
assigningthe codewords to symbols such that
n, :
n2
: ... :
nq_,
!
nq
(2.5)
In this optimal coding, all the codewords are arrangedin the ascending order of the
number of high bits involved in each codeword, and the symbols are assigned these
codewords in the descending order of symbol probabilities. This coding algorithm
provides optimal codes for a given codebook with respect to power consumption.
Proof
i<j
Let i and] be arbitrary integers such that 1
P
q. From equations (2.4) and (2.5),
P and n,
nj
q
Consider the two terms involved in n
n,
=
Old: Pn, +Pnj
Interchanging the codewords for the i-th and j-th symbols yields
New: P,n, + Pn,
15
(2.6)
Subtracting Old from New and using (2.6), the net change in the average number of high
bits due to this re-assignment becomes
New - Old = (P,- P,Xn, - ni) 0
Therefore, the advantage number of high bits, ii, does not decrease for any interchange of
codewords. Hence, this coding algorithm provides optimal codes for a given codebook
with respect to energy consumption.
Let W be a codebook of q codewords arranged in the ascending number of high bits
involved in each codeword. The code C(W,S) assigns the q codewords in codebook W to
q symbols in source S in such a manner that equations (2.4) and (2.5) determine the
minimum -nfor the given W. Hence, the minimum of n- varies depending on properties
of the codebook used. The remaining question is how to obtain a codebook that provides
the overall minimum of n. Let W, = {w1 , w2
that are usable for ME Coding; q
...
,
wq-j,,I
I
be the entire set of codeword
q0 <+oo. We first number each codeword in the
ascending number of high bits involved in it, namely, n,
n2
...
nq,_,
nq., where ni
is the number of high bits in codeword w,. Then, we generate the codebook used for ME
coding by taking the first q codewords having the least high bits.
Definition: Minimum Codebook. Let the codewords of the whole codeword set W,
{WJW2,.,Wq-1,Wq}
be numbered in the ascending number of high bits involved in each
codeword, n, : n 2
...
...
nq
nq, .
A minimum codebook of q codewords, Wmin,
consists of the first q codewords of the whole codeword set W
Wmin = {w,
W2 ,
-Iq-
1, wq IC
(2.7)
Wo
It can be noticed in the previous example that the overall minimum energy codign cannot
be obtained unless the above minimum codebook is used.
Theorem 2: Codebook Optimality. Let S be a q-symbol source with symbol
probabilities P ={P
! P2
.
P-
q
} and W be a code book of q-codewords taken
from the usable codewords set W = {w,w 2 ,...,w-q,wq 1, q
, =
q0 <±+oo; W c W0 . The
, n, P, is that the codebook W is a minimum codebook of Wo.
16
Proof
Let n,
n2
...
n,
n be the number of high bits in the codeword w, through
...
wq
involved in the minimum codebook Wmin. The proof is given by showing that replacing
an arbitrary codeword wi involved in Wmin with an arbitrary codeword wj not involved in
Wmin
does not decrease the minimum average number of high bits n- . Since
iiq
j
n,,,
qO and n,
n,+1 - n,
..
nq
n1 , the following inequalities hold
0, n,+2 - n,+,.,
nq
,
- n
0 , ni -nq
0
(2.8)
Multiplying P,, P,,..., Pq by the above inequalities individually and summing them yield
P,(ni+ -n,)+...+ P_(nq -nq-
j+ P(nj -nj
)! 0
(2.9)
or
Pnf,
P~n, +...+ P_,n_ +Pnq Pin +... + Pqnq
Adding Pn, +... + P, n, 1 to both sides,
P,n, +...+ P,_n
+...+ P_,nq, + Pnq
Pn, +...+ P,, n- + PI n
<
+...+ P_,nq + P(n1
The left hand side gives the minimum average number of high bits for the minimum
for a non-minimum codebook where wi
codebook, while the right hand side provides Wn
is replaced by wj. The former is always smaller than or equal to the latter. Therefore, the
codebook must be a minimum codebook in order to minimize n- for available WO and
given P. Combining Theorem 1 and 2, the following Corollary is easily obtained.
Corollary 1: ME Coding. Let S be a q-symbol source with symbol probabilities
P={P,
P2
high bits i =(
-P--
,q
n=
, andW={w,w
2
,--,
wq- 1 ,Wq I
be the average number of
where ni is the number of high bits involved in the codeword wi, is
given by
(z) Using the minimum codeword Wmin of Wofor the codebook; W= Wmin c WO, and
(ii) Assigning the q codewords of Wmin in the ascending order of number of high bits to
the q-symbols of the descending order ofsource probabilities.
This optimal coding is referredto as ME Coding.
17
Consider a special case equals the total number of high bits in the codebook divided by q.
Therefore, the following Corollary holds.
Corollary 2: A minimum codebook contains the minimum number of high bits;
MinE n 2.2.2. Fixed-Length ME Coding
Of practical importance is ME Coding with fixed-length codewords. Hence, the
rest of this paper will concentrate on fixed-length ME Coding and extensions of fixed
length ME Coding. As shown by Theorem 2 and Corollary 1, use of a minimum
codebook is the necessary condition for obtaining ME Coding. Thus, we must first
generate a minimum codebook. For L-bit fixed-length codewords, Figure 2.3 shows the
entire set of usable codewords sorted by the number of high bits; W = {w
... ,
Note
Wq.
that the total number of usable codewords is q, = 2' .
W1
Codeword
Number of
C12
Codewords
L
W2'''"W1,4
..~
-''
3
L
L
I
'22'*
2L
L-1
L
L
L
-
Codeword
Pattern
flr-----I
Discard
Figure 2.3 Fixed Length L-bit Codewords
The first column has only
has
1
=
1 codeword with zero high bit, the second column
= L codewords with one high bit, the third column has
2
codewords
containing two high bits and so on. All the codewords are number I through
2L
in the
ascending order of the number of high bits. The last codeword, w2 consists of all high
18
bits. Selecting the first q codewords from this exhaustive list of 2 L codewords yields the
minimum codebook needed for ME Coding.
It is clear from Figure 3 that, as the codeword length L becomes longer, the total
number of high bits involved in the first q codewords becomes smaller. An extreme case
is the unary coding, where L is long enough to express all q symbols with only high bit
per codeword, e.g., 00010000. Since a longer codeword takes a longer transmission time
if the bit period
tb
is kept constant, transmission rate decrease. Hence, this constitutes the
trade-off between energy efficiency and transmission rate.
2.2.3. Optimality Bound to ME Coding
In section 2.2.1 and 2.2.2, we proved the optimality of ME coding and introduced
fixed-length ME coding. Since a closed form solution for the optimal performance of
fixed-length ME Coding is not available, we derive the following optimality bound
(2.11)
1
k(kl
Bk
where Hk is the source entropy and Bk is the codebook capacity defined as
Bk
(2.12)
=Lk-'
1=1
where k is an arbitrary constant greater than 1. Inequality (2.11) suggests that source
entropy Hk and codebook capacity Bk provide a lower bound on the optimal energy
performance. As the entropy Hk decreases and the codebook consisting of q codewords of
fixed-length L, the maximum codebook capacity Max(Bk) can be obtained from Table 1.
Namely, the minimum codebook consisting of the first q codewords in the table provides
the maximum codebook capacity given by
Max(Bk
)=
(L+-kI j+ko0
+(L)
k'a
+b
k a+1
(2.13)
where a and b are positive integers shown in Table 1. In the (a+1) column, the q-th
codeword exists at the b-th position. In other words, q =
19
+ b. Note that any
exchange of the first q codewords with the other (2L-q) codewords decreases the value of
codebook capacity unless exchanging codewords within the (a+I)st column. Note also
that, as the codeword length L increases, maximum codebook capacity Max(Bk) tends to
increase, hence a longer codeword tends to lower the average number of high bits and the
energy consumption.
20
Chapter 3
Energy Efficient DS-CDMA for RF Transmission
Direct-sequence code-division multiple access (DS-CDMA) has recently generated
increasing interest, particularly for cellular mobile and wireless communication. Energy
Efficient DS-CDMA is a power-saving communication technique we exploited in the
wireless sensor network by performing special modulation algorithms. Multiple access
property is basically achieved by assigning a unique code sequence that each receiver
uses to encode its information-bearing signal. In our research we have to design a set of
energy efficient spreading codes to achieve the multiple access property and save power
at the same time. An ideal spreading sequence would be an infinite random sequence of
equally likely random binary digits. However, the use of an infinite random sequence
implies infinite storage in both the transmitter and receiver, which is impossible in
practice. Having a deterministic, periodic spreading code which has very similar
attributes inherently coming from a real random sequence can make a huge improvement
in signal recovery. In order to be able to spread and despread data signals successfully we
have to devise a new signal recovery process different from that of general DS-CDMA
communication systems. We will take a combined algorithm including Modulo-2
addition and multiplication on the receiver side to recover the intended data signal.
Finally we can evaluate the system performance by means of estimation of error
probability and signal-to-noise ratio (SNR) via on-off keying signal transmission, and
further seek an effective means to improve it.
3.1 Motivation of Power Saving
According to the previous description for ME coding principle, one can know that
we already exploited redundant bits for saving power and correcting errors, and proposed
a new source coding and modulation techniques with the feature of minimizing power
consumption when transmitting signals. Nonetheless, the future problem we will deal
with is a wireless communication network containing a couple of smart sensors in which
21
we need multiple access techniques to achieve the goal of bi-directional communications
between smart sensors, the PDA and cell phone.
SSensor
B i-d irec tional
W ireless
C o m m u n ic a tio n s
Figure 3.1 Bi-directional Communications in The Intelligent Sensor Network
The most important issue of the multiple access capability is how to make each icoin receive its own signal and discard those signals that do not belong to it and noise.
Direct Sequence Code Division Multiple Access (DS-CDMA) is an attractive modulation
technique for solving our problem. If multiple transmitters convey a spread-spectrum
signal at the same time, the receiver will be able to distinguish between the transmitters,
provided that each transmitter has a unique spreading code (pseudorandom code, or PN
code) that has a sufficient low cross-correlation with the other codes. The classic
spreading code is basically not designed under the power saving condition. In order to
save more power, we should design a new energy-efficient spreading code to minimize
energy consumption for short-range RF transmission. The new spreading code is
basically to use the 1 and 0 sequence instead of the traditional ±1 to modulate the data
signal. Since the oscillator is the circuitry responsible for the modulation of the data
signal onto the transmitted waveform and is actuated on the receipt of high bit only,
power consumption in the transmitter occurs only when high bits are sent and virtually no
power is consumed when low bits are sent. The function of energy-efficient spreading
codes is to partition the high bit signal into small high bit chips as less as possible. Then
we take a new signal process of recovery to receive the intended data signal.
22
C(t): 1/0 spreading code
C(t) : 1/0/-l spreading code
L t
-
t
6
T: chip duration
-1
T :chip duration
Figure 3.2 Energy Efficient Spreading Codes for DS-CDMA
In the DS-CDMA systems the modulated information-bearing signal (the data signal)
is directly modulated by a digital code signal. The data signal can be either an analog
signal or a digital one. In most cases it will be a digital signal. What we often see in the
case of a digital is that the data modulation is omitted and the data signal is directly
multiplied by the code signal and the resulting signal modulates the wideband carrier. It is
from this multiplication that the direct-sequence CDMA get its name. In Figure3.3 a
block diagram of a DS-CDMA transmitter is given. The binary data signal modulates an
RF carrier. The modulated carrier is then modulated by the code signal. This code signal
consists of a number of code bits or "chips" that can be either +1
or -I. To obtain the
desired spreading of the signal, the chip rate of the code signal must be much higher than
the chip rate of the information signal.
Data Signal
Wide-Band
Data
0
01Modulator
code
-
Modulator
Carrier
Code
Generator
Generator
Figure 3.3 Block Diagram of a DS-CDMA Transmitter
23
After transmission of the signal, the receiver (which can be seen in Figure 3.4) uses
coherent demodulation to despread the spread spectrum (SS) signal, using a locally
generated code sequence. To be able to perform the despreading operation, the receiver
must not only know the code sequence used to spread the signal but also the codes of the
received signal and the locally generated code must also be synchronized. This
synchronization must be accomplished at the beginning of the reception and maintained
until the whole signal has been received. After despreading the modulated data signal and
after demodulation the original data can be recovered.
Code
Data
Demodulator
Demodulator
Data Signal
Carrier
Code Synchr.
Code
Tracking
Generator
Generator
Figure 3.4 Block Diagram of a DS-CDMA Receiver
In the previous paragraphs a number of advantageous properties of spread-spectrum
signals were mentioned. The most important of those properties from the viewpoint of
DS-CDMA is the multiple access capability, the multipath interference rejection, the
narrowband interference rejection, and with respect to secure/private communication, the
low probability of interception.
3.2 Energy Efficient Spreading Codes
3.2.1 Auto-correlation and Cross-correlation between PN sequences
24
The spreading signal c(t) is deterministic, so that its autocorrelation function is defined by
[17]
R, (r)= -
c(t)c(t - r)dt
(3.1)
Since c(t) is periodic with period T, it follows that Ra(T) is also periodic with period T.
Consider two different spreading signals cj(t) and c2(t). The cross-correlation function of
these two deterministic signals is
Re (')=-
fC1(t)- C2(t
T
- r)dt
(3.2)
where it has been assumed that both signals have the same period T. The cross-correlation
function is also periodic with period T.
3.2.2 Ideal pseudorandom (PN) sequences
There are two major objectives of the pseudorandom noise sequences used in wireless
digital or personal communication DS-CDMA system. One is spreading the bandwidth of
the modulated signal to the larger transmission bandwidth. The other is to distinguish
between the different user signals utilizing the same transmission bandwidth in a
multiple-access scheme. An ideal PN sequence is not random; it is deterministic, periodic
sequences. The following are the three key properties of an ideal PN sequence [18]
1. The relativefrequencies of minus one and one are each 1/2.
2. For minus ones or ones, half of all run lengths are of length 1; one quarter are of
length 2; one eighth are of length 3; and so on.
3. If a PN sequence is shifted by any nonzero number of elements, the resultingsequence
will have an equal number of agreements and disagreements with respect to the
originalsequence.
To achieve the spreading objective, the power spectrum of a PN sequence should be
like white Gaussian noise in order to make the spreaded signal occupy the transmission
band equally. The second and more difficult objective of the PN sequence for a multiuser
CDMA system is to distinguish between the signals of the different users utilizing the
same transmission bandwidth. The PN code is the key of each user to his or her intended
25
signal in the receiver. For this reason the complete set of PN sequences has to be chosen
with a small cross-correlation between the several sequences. This keeps the adjacent
channel interference small. Theoretically, a zero cross-correlation is maintained by every
set of orthogonal spreading signals. However, in practical wireless systems one has to
design for easy, coherent generation of the PN sequences, on both the transmitter and the
receiver sides.
As a matter of fact, an energy efficient spreading code is a PN sequence of taking
one and zero values. For a general purpose, we can just use a linear feed back shift
register to generate a sequence which has those three properties just mentioned in the
previous section. However, the energy-efficient spreading code cannot provide the same
signal-to-noise ratio (SNR) at receiver as the traditional ±1 spreading code. The signal
power is lowered by the spreading code but the decreased noise energy could not be
proportional to the signal power reduction. General speaking, SNR will become a little bit
worse if we use energy efficient spreading codes.
3.2.3 Finite-Field Arithmetic: Modulo-2 addition and multiplication
Some of the manipulations that will be performed on the code sequences introduced
later require an understanding of the mechanics of finite-field arithmetic, especially,
Modulo-2 addition. Here we only summarize the main properties for Mdoulo-2 addition.
Consider the set S={O, } with addition and multiplication defined in Figure 3.5. It can
easily be verified that this set, with the operations defined in Figure 3.5 satisfies closed,
communicative, distributive over addition and associative properties. There also exist an
additive identity element, an additive inverse element, multiplicative identity element and
multiplicative inverse element in S. This field is a binary number of field that will be used
extensively in what follows. Observe that addition can be accomplished electronically
using an Exclusive-OR gate and multiplication can be accomplished using an AND gate.
Multiplication
Addition
S1
1
0
0
1
0
1
Ii
0
1
110
0
0
0
0
Figure 3.5 Modulo-2 Addition and Multiplication
26
3.3 Energy-Efficient DS-CDMA Communication Systems
Before we discuss the energy-efficient DS-CDMA system, we have to briefly
reminisce the signal transmission model at the transmitter side. Consider a general DSCDMA with channel delay and let S,(t) denote the transmitted signal which consists of M
receivers. Then
S, (t) = JJ1%dk (t - rkc, (t - Tk,)cos(oct + pk)
(3.3)
k=I
where Pkis the signal power, oic is the carrier angular frequency, dk (t) is the data signal
for the kth receiver,
#
and
'rk
Ck
(t)
is the spreading signal corresponding to the kth data signal and
are the signal phase and delay for the kth receiver, respectively.
The data signal dk (t) can be expressed as follows
(3.4)
dd)=)n(jT, (i+ )T)
dk(
The spreading signal can be expressed
()3.c
5)
ck
where
a
I1(t,,t 2 ) is
Pr(dk) = 0)>> Pr(dk)
()
e f-1,1} with C
)
=
unit rectangular
pulse
on
[t ,t 2 )
,
d k) e
{0,1}
where
1) because of using ME coding to code our data and
()N
for all j and k and for some integer N. The integer N is the
minimum period of the spreading sequence. The chip length Tc will be assumed to be
given by T, = Tb/N where Tb is the bit interval duration.
3.3.1 Signal recovery method of general DS-CDMA systems
The signal recovery process of a DS-CDMA system is shown in Figure 3.6. After we
send our spreading modulated signal to the channel, the signal could be contaminated by
some noise. For the convenience of analysis, we will view noise in the channel as
additive white Gaussian noise (AWGN). Thus the received signal at the receiver can be
27
expressed as
S, (t = I
2Pkcd/k (t -
-k )ck
(t -
k
)cos(ot +
Without loss of generality, we will restrict our consideration to the
Ok
)+ n(t)
1s'
(3.6)
user and assume
that r, =#, = 0. Furthermore, there is no loss in generality in assuming that -Ck e [0,T)
and
bk
e [-5,.)
since we are only interested in time delays modulo T and phase delays
modulo 2n. Then the despreaded demodulated signal Sd(t) can be easily described as
M
Sd W)=
2Pkdk(t -r k
k(t -1k)cos(ot +$kcosC
k=2(3.7)
(37
+ 2Jd,(t)cos2 coj + n(tc,(t)coscoct
Sampling
C,(t)COS ct
t = nT)
S,(tW
Bit Detection
)/
d,(t )
Figure 3.6 Signal Recovery Process for a General DS-CDMA System
The major objective here of using the integrator (or called correlator) is to find the signal
autocorrelation and crosscorrelation and make the noise become much smaller. Let Y
denote the output of the correlator receiver matched to user I at t=T. Then
Y=
T d() + N + k"
w2 h
I()(T,,d)
2
where
28
(3.8)
dk =(d(k),d k))
Ng=
I (k)
f
n(tc, (t)cos ot dt
k)R
Ccosk d
R,(k)(r)
= fC 1 (ck
r =
k)
(t- 1k
C1 ()ck (t -
+ d()k)(k) (k)
)dt
Trk
The second term Ng in Y is a Gaussian random variable due to integration of the
Gaussian channel noise and the third sum of terms in Y is referred to as multiple access
noise. The final step to recover the data signal di(t) is the bit detection that is to detect
which time slot signal is one or zero. The bit detection process could fail if the total noise
energy is pretty high. Hence it is very crucial to maintain a low crosscorrelation between
different spreading codes. Usually our approach is to make the spreading signals have a
long period to improve the crosscorrelation and autocorrelation properties. Of course we
need more memories to storage the spreading pattern. If the bit detection process is
successful we can get the data signal from transmitter 1, i.e.
d, (t)= d, (t)
(3.9)
3.3.2 Signal recovery for spreading codes taking values of 0 and 1
If we use the spreading code taking values of 0 and I the process of recovering the
data signal d1 (t) should be modified as shown in Figure 3.7. Then the despreaded and
demodulated signal Sd(t) is
Sd(t) =
2Pkd1
d (t -
1k
1 ()ck
(t -rk )cos(ot + $ )cos
(.t
k=2(3.10)
+ 2pd, (t)c1 (t)cos 2 ayt + n(t)c, (t)cos oct
where c(t) has the same form of (3.3) but c .) e {0,1} and note c 2 (t)= c(t).
The integrator in Figure 3.7 has an upper limit Tc that is different from that in Figure
3.6.
29
c,
Sampling
t = nT1,
(t)cosa't
(-t
S,(t)
Chip Detection
Pass
d (Low
(t)
W
Filter
C1
(
)
c, (t)
Figure 3.7 Signal Recovery forSpreading Codes Taking Values of I and 0
This is because we want to reduce the noise influence on the data signal in the chip
duration. The sampled output of the integrator is sent to a chip detection mechanism used
to recover the chipped data signal. Let Y be the output of the integrator, then we have
Y=
2
Td(')c()+N +
g'0 k=2
2
I,(')(rk,#k d)
(311
where
dk
Ng
(d(k),d (k)
=
=
f n(t)c, (t)cos ow dt
(k) = cos Ok
R,(k)(r)=
R
=
[d
±) d
Rk ) -
c1 (t)ck (t -
k)Rd )(k) )
rkdt
C1 (tck (t -r-k
kit
If there is no error occurring in the following chip detection process we can have S, (t) as
follows
Afe= , (ti
After performing the modulo-2 Addition, we get
30
(t)
d,A(td,
t od(t)u=
(3.12)
S1,I
@ -(t) = d,(t) + (I- d,()).1(t)
(3.13)
The second term in (3.13) is a high frequency signal. It can be filtered out by a low pass
filter. Therefore, the output signal of the low pass filter should be the same as the data
signal di(t).
3.3.3 Signal recovery for spreading codes taking values of 0, 1 and -1
The third case we will discuss here is to use an energy efficient spreading code
taking values of 0, 1 and -l when chipping the data signal. The signal recovery process is
very similar to the previous one described in Section 3.2. The only difference is that we
have to use .2 (t) to perform the Modulo-2 addition. Since c, (t) is not equal to c, (t) but
c, (t1. Thus the output of chip detection S, (t) equals to d, (t)cl (t). After performing the
Modulo-2 addition we know
5,(t)@2 (t)=d, (tc2(t)@j (t)=d,(t)+(I-d,(t))j2(t)
Similarly, we can find the data signal d, (t) by filtering out the high frequency term.
Sampling
c. (t)cos aOit
S,()
Sr)
-)
Sd)0
d
Chip Detection
--
Low Pass
Filter
1 0
c71
(t=leC2 (t)
Figure 3.8 Signal Recovery for Spreading Codes Taking Values of 0, 1 and -l
3.4 Simulation Results
31
(3.14)
We use Figure 3.9-3.12 to present the whole signal recover process. Figure 3.12 shows
that we successfully recover the data signal d (t).
2
1.5
1.5
0.5
0.5
0
0
-0.5
-0.5
-1
0
6
4
2
10
8
-
-1
)
2
4
tim e(m s)
6
8
10
8
10
time(m s)
2
1.5
1.5
a0.5
0
0
-0.5
-0.5
-1
2
0
8
6
4
-1
10
0
2
4
6
time(ms)
time(ms)
Figure 3.9 Data Signals and Chipped Data Signals
ill
S0
-1
0
1
2
3
4
1
2
3
4
5
tme(ms)
6
7
8
9
10
5
6
7
8
9
10
3
2-
S,
0
-1-2
0
ime(ms)
Figure 3.10 Transmitted Signal and Received Signal
32
4-
2 INi*i0'i
1i
0
-2 -I
0
3
2
1
4
I
II
5
6
9
8
7
10
time(ms)
.5
0.5
-
0 (,
-0.5 --11
0
2
1
4
3
7
6
5
10
9
8
time(ms)
Figure 3.11 Demodulated Signal Sd(t) and Output of the Integrator Y
2
I
I
I
I
1
2
3
4
I
I
I
I
I
5
6
7
8
9
I
I
I
I
I
5
6
7
8
9
5
6
7
8
I
5
6
7
8
9
0
0
1
time(ms)
9-'
I
1
I
I
3
4
0
'5 -1
0 0
1
2
10
time(ms)
0
0
-1
0 1
4I
12
2
3
4
time(ms)
Figure 3.12 S,(t), ,(t) E,(t) and d (t)
33
10
0
3.5 Estimation of SNR for Different Spreading Codes
The signal-to-noise ratio (SNR) is an efficient index to evaluate the quality of the
received signal. We can realize the variation of SNRs by means of the output of the
correlator under using different spreading codes. Here we analyze SNRs for three
different cases.
3.5.1 SNR, estimation for +1/-1 spreading codes
Recall the output of the integrator Y in Figure 3.6 is as follows
Id
Y = -- T
L+N+
I
)
We can calculate the signal power by the following definition:
2
PdI
T
fT
2
dt = aP'T2
d
2
if d')e{0,1}
(3.15)
where a, is the percentage of high bits for di(t) during the transmission duration of T
seconds. Then the noise power can be shown to be
NOTb
"
4
k=2
kPk
2
(3.16)
2
The detailed procedures of deriving (3.15) and (3.16) can be proved in Appendix.
Therefore, the SNR for this case can be found as
SNR1 =
P,
NOTb
4
(3.17)
k=2
,P
2
3.5.2 SNR2 estimation for 1/0 spreading codes
We already obtained the output of the integrator Y in Figure 3.7 as
34
Yd
-
2k~)~jd
)c') +Ng +~
The signal power is
2
Pd2
where
dt - al A PI
2
f-T d(')c(l)
F2 '
T
Th2
(3.18)
p, is the percentage of chipped high bits of c, (t) in a bit duration.
Then the noise power is
P2
=
I)(kk,dkj2
N9+1
dt=
+
4
Mak/k P
k=2
2
(3.19)
The detailed procedures of deriving (3.18) and (3.19) can be proved in Appendix
Therefore, the SNR for this case can be found as follows
SNR2 2_
2
/2
_
P0 T,,/3
N
(3.20)
2
Ma/PI
4
k=2
2
where pI, is the percentage of chipped high bits of c, (t)ck (t -
17k)
in a bit duration.
3.5.3 SNR3 estimation for 1/0/-1 spreading codes
Similarly, we can show the output of the integrator Y in Figure 3.8 is as follows
Y=
2T d
+Ng+
k
(3.21)
I( )
where Ng and I,(k)(rk,$,, dk) are the same as those in (3.8).
The signal power can be found as
Pd3
where
$, +)/i
=21
Td(c
dt =
2
(#, + y, )T;)
is the percentage of chipped high bits of c2(t) in a bit duration.
35
(3.22)
The noise power can be computed as follows
2d
P
IN +Y'
T
\
I('rk,',dk)Idt
(3.23)
k=2
(=/+y,)NoT
4
k=2
a
2
2
The detailed procedures of deriving (3.22) and (3.23) can be proved in Appendix.
Therefore, the SNR for this case can be found as follows
(A +r,)PiT
SNa,
SNR
_
3
d3
P
_/2
NOT (6+y)
4
where
,+
71k
a (
k=2
(3.24)
+y)P
2
2
'
is the percentage of chipped high bits of c, (t)ck (t -
rk)
in a bit duration.
3.5.4 Comparison of SNRs for different spreading codes
According the equations (3.17), (3.20) and (3.24) derived above we can plot Figure
3.13 and 3.14 to show the discrepancies between different SNRs. In Figure 3.13 we
assume there are ten receivers in the communication system and the period of each
spreading code is 31; that is, the data signal will be chipped 31 times in one single bit
duration. We have to notice several key points when taking a look at these diagrams. The
power saving rates on the vertical axis for SNR, SNR2 and SNR3 are equal to (1ai)xlOO%, (1-ci
pi)
xl00% and (1-ixi(3 1+71)) x100% respectively. For example, assume
all SNRs are 2 dB, 81 = 0.5 for SNR2 and /3+y; = 0.5, then we can calculate in Figure
3.13 al=0.75, (1-ai Pi)xlOO%=(1-ax(@3i+y)) x]00%=62.5%. Check SNR2 and SNR3 lines
at 62.5%, we found the corresponding SNR1 and SNR2 are about 0.4 and I dB,
respectively. This means although we sacrifice some SNR the power saving rate is largely
increased. Then for the BPSK (Bi-Phase Shift Keying) case without saving any power,
we can find its SNR is equal to
2
/2
BIK =PPTT2K
SNR SN]
BPK
NOT
A4
4
36
k=1
2 ~
PM= 1, Tb= I ms and No = 0.00015 as the
Here we adopted M= 10, P1 = P2 = ....
calculating conditions and found SNRBPSK =6.02 dB if the period of spreading codes is 31.
It is the merging point of these three curves in Figure 3.13.
Figure 3.14 shows the discrepancy of taking spreading codes with different periods.
It is obvious that the SNR for each case is increased at the same power saving rate if
compared to Figure 3.13. Although using a spreading code with a very long period can
improve SNRs, it makes the chip detection process become difficult. Thus how long the
period we should use is also another important issue in practice.
90
80
70
SNR2
600)
C
.5
Cu
(I,
G)
0
0~
SNR3
SNR,
50
40
U30
20-
N=31
M=10
10-
01
-1 1
-10
-8
-6
-4
-2
0
2
4
6
SNR (dB)
Figure 3.13 SNR v.s. Power Saving rate for 10 receivers and
the period of spreading codes N=31
37
8
90
I
I
I
I
80-
SNR2
70-
SNR 3
60-
SNR
> 50I
40-
30 -20-
N =1023
10-
0
-8
M =10
-6
-4
-2
2
0
SNR (dB)
4
6
8
10
Figure 3.14 SNR v.s. Power Saving Rate for 10 Receivers and
The Period of Spreading Codes N= 1023
3.6 Estimation of Error Probability for Different PN Sequences
The estimation of error probability in a communication system is very important since
we can realize whether the communication performance is good or not based on the
relation between SNR and error probability. The performance is related to the correlation
properties of the unique spreading code used. We usually evaluate the performance of a
CDMA system by calculating it transmission error probability. A communication system
has a good system performance, which means its error probability is lower than that of
other systems under the same SNR. Here what we are concerned with is whether taking
the energy efficient spreading codes to spread the data signals instead of traditional
spreading codes results in an increase of error probability or not. We start to formulate
the problem from a general DS-CDMA system.
3.6.1 Error probability for +1/-1 spreading codes
38
A bit detection error usually occurs in misjudging a high bit signal into a low bit
signal or vice versa. The average error probability of receiver I for transmitting one bit
can be denoted as
P(O= (I) Pr(Y
61d'
=O)+p')Pr(Y <S d(' =i)
where p() is the probability of transmitting zero signals for
probability of transmitting one signals for
Jst
(3.25)
transmitter, p') is the
transmitter, 6 is the threshold for bit
1 st
detection
(1) If d') = 0, we can know the output of the integrator from (3.8) can be simplified to
YO=N +M
k=2
(2) If d('
,
I (
(3.26)
2
1, we can know the output of the integrator from (3.8) can be also simplified
to
Y, = N +
(I,,
2IT
,d
(3.27)
T where a > 0, we have
Substitute (3.26) and (3.27) into (3.25) and let o= a
=2
P(])=p ')Pr(YO
6)+p0'Pr<6
PO) Pr Ng
,dka
2L
b+
(3.28)
A0)Pr Ng +k
L
k=2
2
IW)(rk,$O ,d)+
IT, <a
T,
A straightforward application of the central limit theorem then indicates that Pj') goes to
p1)Q(a SNR, ) as long as SNRI approaches constant [19].
-k
P
k=2
2
-- oo as M -> oo and p1) >> p()
1
Under these conditions, we can simplify (3.28) into
39
P(') ~ pQ(aSNRj =(I-a,Q(a S-NR,j
(3.29)
2
where Q(x)=
e 2du
3.6.2 Error Probability for 0/1 spreading codes
According to (3.11), we know the output of the Integrator in Figure 3.7 is
N
id(')c(l)
2=
0O+
2
I
+
(1) If d(')c(' =0 , then Y becomes
YO =N +
Z
k=2
I
(k)(k,,d,)
(3.30)
2
(2) If d')c() =1, then Y becomes
At g2
L= T +N +
,
2 f(k)(r1,#bd)
(3.31)
Although Y is sampled by each chipping rate T~, the error probability we estimate is
based on one bit signal transmitted. Hence, the average error probability for one bit can
be expressed as
)]Pr(Y
P,' =[(I1-ai)(1 - A)+ai(I-#A)+ (I-aJA
! 9)+ (a,,)Pr(Y; < 9)
Using the same approach and conditions in Section 3.6.1, we can get a more concise form
of Pe :
PV
(-a,#A)Q(a SNR2 )
3.6.3 Error Probability for 0/1/-1 spreading codes
According to (3.21), we know the output of the Integrator in Figure 3.8 is
40
(3.32)
Y=
Tdo(
(C(
kI I()(zk,
2+N],Z+
$kd,
k=22
(3) If d()
(c'))
=0, then Y becomes
(3.33)
)(r,k d)
2
PI
YO =N9 +
k=2
(4) If d
(C
=
=1,
then Y becomes
Y,=
Te+N, +
=2 Tk=2k
k I(k)(rk,,#k
2
dk)
(3.34)
Although Y is sampled by each chipping rate Te, the error probability we estimate is
based on one bit signal transmitted. Hence, the average error probability of receiver I for
transmitting one bit can be expressed as
P(') = [(I -a,)(] -,)+a, (I- ,)+ (I -aj), +a, (I -,)]Pr(Yo
+ [a.(A + r, )] Pr(Y, < 9)
Using the same approach in Section 5.1, we can also get a concise form of P<
Pe(') ~ 1- Cr (A, + r.)]QWTNa
)
>!9)
as
(3.35)
3.6.4 Comparison of error probability for different spreading codes
We use (3.29), (3.32) and (3.35) to demonstrate the relationship between error
probability and SNR. As you can see in the following figures, the three curves for SNR1 ,
SNR2 and SNR3 almost overlap together, but SNRBPSK is greatly different from them.
Actually there are some small differences between these three curves. This feature tells us
a very important result; that is, the error probability in the energy-efficient DS-CDMA
system is barely influenced by using different energy efficient spreading codes.
Nevertheless, it is much worse than that in the BPSK DS-CDMA system and we cannot
expect the error probability would not increase if excessively saving the transmitting
41
power since the above example is an ideal case. It just tells you the error probability
would not alter abruptly in a reasonable power-saving range.
There is also an interesting feature we can find if we compare Figure 3.15 with
Figure 3.16. That is, if we save more power (decrease a1 ) the differences between error
probability cures for three cases are getting smaller and smaller and the error probability
become worse and worse. Therefore, the error probabilities by using different energyefficient spreading codes will approach the same value and the signal communication
performance becomes bad if a keeps decreasing.
10
10
02
SNRI,
>. -4
.$ 10-0
-L
2
10-6
SNR BS
M=10
N =511
a, =0.5
A, =0.5 for SNR 2
pA +y, =0.5 for SNR 3
10-8
0
5
10
15
Eb/No (dB)
20
25
30
Figure 3.15 Error Probability v.s. EJ/No for Different Spreading Codes if ai = 0.5
42
100
10
SNR,
11.
>.
S10
-4
CU
SNR13,S
M=10
10-
N=511
a, =0.2
A =0.5 for SNR 2
A, +y, =0.5 for SNR 3
I
1
10
0
5
10
15
Eb/No (dB)
20
25
30
Figure 3.16 Error Probability v.s. E/No for Different Spreading Codes if (X= 0.1
In this chapter, we investigated the problem of energy efficient DS-CDMA
communications in the wireless sensor network. We can learn there are three important
findings in this research:
(1) New signal recovery methods for energy efficient spreading codes are proposed
here.
(2) Although SNRs for energy efficient spreading codes become a little bit worse, we
can save a lot of power.
(3) Error Probability almost does not alter if using energy efficient Spreading codes.
In the future research work, we would like to figure out a good method to generate
energy efficient spreading codes based on how much power we want to save. The
traditional linear feed back shift register to generate a PN sequence is not suitable for
our case. Then we will discuss the synchronization problem for the energy efficient
DS-CDMA system.
43
Chapter 4
Suppression of Multiple Access Interference (MAI) in
Energy-Efficient DS-CDMA Communication Systems
4.1 Principle of MAT Suppression
The ME Coding described above is effective for reducing MAI, when it is used for
DS-CDMA. MAI is reduced due to the low overlap probability of transmitting high bit
signals to multiple receivers. Since ME coding decreases the number of high bits, it not
only reduces power consumption but also reduces the chance of signal interference
among multiple channels. As a result, MAI is significantly reduced.
Pseudorandom
Pattern
Generator
Modulator
Cobn
ME Coding
of
ME Coding
Modulator
cNo(t)
Channel
ataSorc M
Dat Surc
I
ME Coding
d
Noise
Modulator
MED ---- der kt
Demodulator
4----
-
Receiver
Pseudorandom
Pattern
Generator
Figure 4.1 DS-CDMA Combined with ME Source Coding
Figure 4.1 represents the configuration of an Energy- Efficient DS-CDMA system
combined with the ME source coding. Data sources, I through M, are coded with the ME
44
coding having sufficient redundant bits. Each channel of signal di(t) is spreaded with a
unique pseudorandom (PN) sequence. The PN sequence, however, applies only to high
bits of source code d,(t); for low bits, no spread signals are produced. All the channel
signals are superimposed and modulated with a carrier frequency. At a receiver, the
transmitted signal is demodulated, and then decoded to recover the original source
symbol.
Figure 4.2 shows how multiple sources of signals are mixed and modulated. The
data signal to j-th receiver, dj(t), is coded with the ME Coding and thereby it contains
fewer high bits, as shown in the figure. Note that a PN sequence is generated only for the
high bits, and that no signal is generated for low bits. Unlike the standard CDMA using
Binary Phase Shift Keying (BPSK), which generates signals for both high and low bits,
the proposed method superimposes multiple channels of signals that are very sparse.
Therefore the probability of superimposing multiple channels of non-zero signals is low.
d, (t)c,(t)cosox
0o
Signal
No
Signal
No
Signal
I
No
Signal
Time
d
No
Signal
(t)c,(t)cosn
0~IX~
No
Signal
Signal
Highly Chipped Signal
No
IIVl~~
o
Signal
Time
d" (t)c,(t)coscd
No
Signal
No
Signal
No
Signal
*
I
No
Signal
No
Signal
Time
Figure 4.2 Principle of Multiple Access Interference Reduction
45
Figure 4.2 illustrates that multiple non-zero signals are seldom superimposed; all
the time slots except the second slot are occupied by one or zero channel. The system can
send multiple non-zero signals at the same time, since unique PN sequences are assigned
to individual channels, but the chances of such superimposition are lowered in the
proposed method. As the number of channels increases, the chances of interference may
increase. This can be overcome simply by increasing the word length in ME coding. As a
longer word length is used, the number of high bits decreases in the ME codebook, and
individual channels may have sparser non-zero signals to send together. In consequence,
the probability of interference gets lower. In the standard CDMA with BPSK, MAI
rapidly increases as the number of channels increases. The proposed method resolves this
rapid increase of MAI by adding a few redundant bits to source coding.
Two conventional methods for reducing MAI at the transmitter side are to increase
the system processing gain and to boost the signal power. Increasing the processing gain
often entails a longer PN sequence for spreading the signal. This leads to the increase of
memory size, computational complexity, and difficulty in designing spreading sequences.
Boosting the signal power is not desirable for mobile applications and others where
available power is limited. High output power is often prohibited by regulations in some
countries as well. At the receiver side, on the other hand, efficient correlation filters have
been developed to lower MAI, as described previously. Sophisticated correlation filters,
however, add complexity and increase cost. Our source coding approach would
supplement those downstream filter designs, so that effective MAI reduction may be
accomplished with minimum complexity and cost along with substantial power saving.
The salient feature of the proposed method is that the more power the system saves, the
more the MAI is reduced, however, at the expense of sacrificing transmission rate.
In the following sections, we will analyze the system performance with respect to
signal to noise ratio, error probability, and transmission rate. Since we use primitive OOK
instead of BPSK and other modulation methods, the processing gain is lowered for that.
Nevertheless the overall performance would be better, since MAI is significantly lowered.
Also important to note is that, when too many redundant bits are added to the ME
codebook, they not only lower the transmission rate but also increase the error probability
in the whole word. In the following sections we will analyze the relationship among
46
transmission rate, error probability, S/N ratio, and power consumption to address design
trade-offs among word length, channel number, and output power.
4.2 Signal Model
A signal transmission model is developed in this section in order to analyze the
system characteristics. Consider a general DS-CDMA with M receivers. The transmitted
signal consisting of M receivers is given by
St )=
2Pkdk(t - k)ck(t -r
(4.1)
)cos(Wt+ k)
k=1
where Pk is the signal power, oic is the carrier angular frequency, dk(t) is the data signal
for the kth receiver,
Ck
(t) is the spreading signal corresponding to the kth data signal and
# and rk are the signal phase and delay for the kth receiver, respectively. The data signal
dk (t)
can be expressed as follows
dk(t)=
d )H (jTh, (j +)T)
(4.2)
J=-*
The spreading signal is given by
C' (t)=
where
l(t1 ,t2 ) is
a
unit
rectangular
(4.3)
c(+&
C (ck,)j
pulse
on
[tdt 2 )
e {0,1}
,
where
Pr(dk) =0) >>Pr(d(k) = 1) because of using ME coding to code the data and
C() E
{1,1
with
for all j and k and for some integer N. The integer N is the
C k) = Ck)
minimum period of the spreading sequence. The chip length Tc is given by
Tc = T /N where Tb is the bit interval duration.
Assuming that the channel noise is additive white Gaussian (AWGN), we can write
the received signal at the receiver as
S,(t )= I
2Pkdk (t -
1k )ck
k=1
47
(t - rk )cos( owt +
k
)+
n(i)
(4.4)
Without loss of generality, we consider the
1 St
user and assume that r, =
Furthermore, there is no loss in generality in assuming that rk e [0, T) and #k e [-
00
,)
since we are only interested in time delays modulo T and phase delays modulo 27r. Then
the de-spread demodulated signal Sd(t) is given by
Sd (t) =
d2Pkck (t -
Tk
)cI (tck (t - Tk
)cosot +
'k
)cos
k=2
WOLt
(4.5)
+ 2J d, (t)cos wot + n(t)c, (t)cosat
2
Following [20] and [21], let Y denote the output of the correlation receiver matched to
transmitter I at t = Tb. We have
Y =
2
Td() + N +
M
kI()(r'
A ,d )
(4.6)
k=22
where
(dlk), d (k))
dk =
Ng =
b
n(t)c, (t)cos coj dt
J(k) = cosAdd(k)R()( )+ d
R, )(r
=
R )= f
c, (t)ck (t -
Tdt
C,(t)ck (t -
kt
(k)(-k)
The second term Ng in Y is a Gaussian random variable due to integration of the
Gaussian channel noise and the third sum of terms in Y is referred to as multiple access
noise. The final step to recover the data signal di(t) is the bit detection that is to detect
which time slot signal is one or zero. The bit detection process could fail for a
conventional CDMA communication system if Y is very high. Therefore, it is very
essential to maintain a low cross-correlation between different spreading signals.
Conversely, the request of the cross-correlation property between spreading codes for an
energy-efficient DS-CDMA system can be relaxed since Y is always maintained at a
small magnitude.
4.3 Evaluation of System Performances
48
4.3.1 Signal-to-noise-ratio (SNR)
The signal-to-noise ratio (SNR) is an efficient index to evaluate the quality of the
received signal. To calculate SNR, first the signal power of d](t) can be found by the
following definition:
N2
=(T1e)
d
22
T
dt -
1,P
T1,
if dfl c= {0,1}
(4.7)
where a, is the percentage of high bits for di(t) during the transmission duration of T
seconds. Then the MAI and AWGN powers can be shown to be
ccki
aaP
cNjj;,h
P, aNOT,,
4
2(k
(4.8)
2
=2
Therefore, the SNR in the energy-efficient DS-CDMA system can be found as
SNR =
PT(4.9)
a,NoT +m
2
In the BPSK case, a,
=
k=2
a 2 =-=ak =1 , then the SNR reduces to
SNR
=
lsK=
IT
2
NoTh
2
k=2
Several means for calculating the error probability of a CDMA receiver have been
published in the literature over the past couple of decades. If we take a similar simplistic
approach that first appeared in [23], in that MAI is assumed sufficiently well represented
by an equivalent Ganssian random process. In addition, we make the usual assumption
that power control is used so that all transmitters' signals arrive at the receiver of
transmitter I with the same power and the probability of transmitting high bits for each
transmitter is the same, i.e., a, = a2
=-=
a,.
Under these conditions we can show that
Eq. (4.9) can further be simplified as
1+ Nj
SNRn=raI
(3N
49
2Eb
or
SNRBPSK
=LM-1
3N
+Ebi
2Eb
(4.10)
Figure 4.3 plots SNR against power saving coefficient a, for different numbers of
transmitter s M. Note that SNR increases with saving more power.
4
10
N=63
3
10
2
10
M=5
z
M=25
10
M=100
-
=200
10
0
M=500
-
0-11
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
a1
Figure 4.3 SNR for Energy-Efficient DS-CDMA vs. The Variation of a, if E/No = 10 dB
and N=63
4.3.2 Error Probability
A bit detection error usually occurs in misjudging a high bit signal into a low bit signal or
vice versa. The average error probability of receiver 1 for transmitting one bit can be
denoted as
P,, = p() Pr(Y > 9 1d()
0)+ p() Pr(Y < 9 1d()
where p(O is the probability of transmitting zero signals for
1 st
1)
(4.11)
transmitter, p(') is the
probability of transmitting one signals for Ist transmitter and S is the threshold for bit
detection.
If d(') = 0 we can know the output of the integrator from (4.6) can be simplified to
50
O=Ng
+31
(4.12)
2dIk)
If d(') = 1, we can know the output of the integrator from (6) can be also simplified to
Y=Ng +L
Substitute (4.12) and (4.13) into (4.11) and let g
P,, = p ') Pr Y >
As SNRME approaches constant,
k=2
T +
2
(4.13)
k ~ rk Ipk,dk +IT
2
9 we have
Pr Y, <
as
k
ak-><x>
M
-+
T
(4.14)
oo and p!') >> p'), under
these conditions, we can simplify (4.13) into
=IP-(1
- a,)Q SNRME)
where Q(x)=
(4.15)
fe 2du
Figure 4.4 below presents the results of (4.15) for different (xi cases and we can find the
error probability can be decreased largely with saving more power if compared to the
BPSK case (a, =1).
51
0
10-
10
a1=1(BPSK)
10 -2
_
10
-
a1=0.7
Z
(D
CC1=0.3
10
0.
-5
CL
--
1c
- 10
10
10
-1-
-8
10
-
M=50
a=.
1-9
0
2
4
6
8
10
Eb/N, (dB)
12
14
16
18
20
Figure 4.4 Error Probability per Bit for Energy-Efficient CDMA with the Variation of cc
4.4 Simulation Results
In the following simulation example, we use a two-transmitter case to verify the
SNR and error probability are improved if using ME transmission. Figure 4.5 presents the
BPSK signals and ME coding signals at the transmitter side. We have to notice that the
transmitted information in the same period for BPSK and ME coding cases are usually
not equal. The objective here is just to show the signal interference in the same time
period. As you can see in Figure 4.6, the signal interference in ME transmission case is
much less than that in the BPSK case. The computational results can prove the SNR in
the ME case can be augmented up to 5dB better than that in the BPSK case. Hence, we
can facilitate the signal detection process at the receiver end.
52
BPSK Signal Transmission
ME Coding Signals
2
2
1
*0
-o
.-1
U
J-
t--
0)
-l - -L
0
0
20
10
time (ms)
)
-1
30
0
10
20
time (ms)
30
0
20
10
time (ms)
30
2
2
.JU
04
N
_ .L
1
CD
0
cc)
C5
cc
-1
-2
10
0
30
20
time (ms)
0
Figure 4.5 ME Signal Transmission for Two-Sender Case
BPSK Signal Transmission
2
164
iii.. I
I,I I 1.,.. 11j 1111
_0
0
-1
---1irij
-jI.rI
7 ,- 111
i
-9
0
5
10
,
F ' r'1'' 1
15
time(ms)
1
ji*1
-1- I I I.
11
20
25
30
Signal Transmission Using ME Coding
3
2
-
1
-I
-
0
-1
All
I"
I
-2
-3
0
5
10
15
time(ms)
20
Figure 4.6 Total Signals in The Channel
53
25
30
Chapter 5
Communication System Design
In the previous chapter, we already knew the communication system has a good
signal transmission quality because of MAI reduction. However, the information
transmission could become worse if the codeword is excessively extended. The ensuing
problems include a low transmission rate, a high average error probability per codeword
and a increasing difficulty in synchronization. Therefore, we devised an algorithm for
how to decide the codeword length under some system requirements. The first step is to
find the upper bound of the codeword length.
5.1 Critical Codeword Length
The error probability per bit was derived in the previous chapter. Suppose a
codeword having a length L. Define Ek as the event that no error is made at time k. Then
the event &that no error is made in the entire block is the union of the events Ek. If each
event is independent, the probability of event &is as follows
Pr (e)= (1 where Pr(Ec)
=
(5.1)
P)
(1- P) and Pb is the error probability per bit as shown in (4.15).
The error probability of a codeword P, can be represented as
P, = I - Pr(e)
(5.2)
If LPb <<1, (5.2) can be approximated by
P,, = L -P
(5.3)
To find the critical length of a codeword for ME transmission compared to the BPSK
case, we can start from the condition PE >
pBifSK
, that is
K
r
r lQns
whereLadLbarete
an ME t(5.4)
where L,, and Lb are the codeword lengths for BPSK and ME transmission, respectively.
54
Although Q(x) function cannot be expressed as a explicit form it can be bounded by
exp(x 2/2). Thus the critical length L, for ME transmission can also be rewritten as
4 = exp
-
SNRHPSK
2
SNRM
-)
(5.5)
L
I -a,
Substitute (4.10) into (5.5), and then we can obtain a simpler form of L, as
L =
(5.6)
Lb exp[( -a, )SNRml]
1-a,
108
aC =0.1
10
aCq=0.15
n
-J
C)
04
a 1=0. 3
102
5
a =0 . 7
I
100
0
5
I
10
1
15
Eb/NO (dB)
20
25
30
Figure 5.1 Ratio of L,/Lb with The Variation of a,if M=50 and N=63
Therefore, the ME codeword length L.. must be smaller than L, and its exact value can
be obtained on the basis of the given system performance and transmission rate. Figure
5.1 depicts the relationship between the ratio of Lc to Lb and Eb/No , and we can see the
ratio of La/Lb increases as a I increases. The reasonable value of L,, can be determined
from Figure 4.4. For example, we can know Lc=10 4Lb if a, = 0.15 and E/No= 10 dB. If
55
the minimum transmission rate Rmin is also given, the length of a ME codeword can be
determined based on this rule: Lm
min(O'Lh, Rmi.Tb) where T is the bit duration.
5.2 System Parameters and General Considerations
The optimal codeword length of ME coding is related to many system parameters.
We can usually group system parameters into two categories: Given and Design
parameters. Generally speaking, the optimal codeword length could not be expressed as a
close form equation since many parameters couple together. The given system parameters
can be nearly learned as follows:
(1) Number of Channels: M
(2) Power of AWGN: N,
(3) Number of the source symbols to be encoded: q
(4) Minimum transmission rate to be maintained:
(5) Time required to transmit one symbol:
2 min
treq
(6) Maximum allowable error probability per codeword: 1',
In addition, there are only two design parameters to be considered: Signal power pi and
the processing gain Gp.
There are several facts that should be addressed before we precede the procedures
of seeking the optimal codeword length. In general, the communication system is
requested to have a transmission rate f which is higher than a minimum rate, i.e. 7 min, at
most of the communication time to avoid serious transmission
delay occurring in the
system. We can find an upper limit of an ME codeword L0 based on the minimum
transmission rate. According to the previous discussion we apprehend the SNRME and
error probability Pb are both affected by some given parameters such as M, No, a 1and Eb,
etc. Moreover, the error probability of a ME codeword Pc, is just the function of the
codeword length Lm and Pb as shown in Eq. (5.3). In other words, Pc, can be determined
if SNRME and Lm are lucid. As we already knew from Eq. (5.6), the critical codeword
length L, is the allowable longest value of a ME codeword length if compared to the
BPSK transmission mode. Thus, the upper bound of a ME codeword length can be
suggested to determine through using the following relationship:
56
Lr = max (Le,L.)
(5.7)
Furthermore, we are very concerned about the power consumption problem in this
wireless sensor network. We can find another codeword length Lp merely according to
the power saving consideration if the number of source symbols q is known. Finally we
are looking forward to seeing the following result:
(5.8)
Lr > Lm > L,
Figure 5.2 presents the possible optimal codeword position. After the upper and lower
limits are determined, we have to evaluate saving more power or increasing more
transmission rate, which one is more beneficial in the practical communication. Once
how much augmented power or rate
the optimal is verified the optimal codeword
position can be easily located.
Lm
Lr
Save Power LMincrease Y
LP
Lopt
Trade-off ?
Figure 5.2 Trade-off Problem of Choosing The Optimal Codeword Length
5.3 Updating Algorithm of Seeking the Optimal Codeword Length
Since power consumption in the system is the most important issue, we can start
with the ME coding part to find an average codeword length. For simplicity, we here
assume all source symbols are equally probable. Then each symbol is performed by
unuly coding which means the longest codeword length is adopted and each codeword
has at most one high bit. The codeword length by this coding method is denoted as Lp.
Then we can calculate the average of power coefficient a. The next step is to try to
calculate SNRME by using Eq. (4.10) if we plug in the first initial guess of E/No. We
have mentioned in the preceding section that the maximum allowable error probability
57
(per bit or codeword) should be provided by the system designer. We are able to examine
the error probability obtained from (4.15) or (5.3) once SNRME is available. If the error
probability were not satisfactory, we would keep increasing E/No until it meets the
requirement. Afterwards, the signal power can be acquired from the final value of Eb/No.
The following phase is to find the upper limit of a codeword.
Assume the
minimum required transmission rate Ymnin has the unit of bit per second and the required
time to transmission one symbol
treq
is given, then the maximum codeword length Lr on
the basis of Ymin and treq is capable of being expressed as
Lr =
V
, )mrq
(5.9)
where [x] is the smallest integer not less than x. The upper limit value can be determined
as follows
Lma
= min(Lr, Li)
(5.10)
The final step we have to do is to check whether Lm, is greater than L, or not. If Lp
exceeds Lm., which means the error probability and transmission rate could not be
attained, we have to abridge Lp and go back to rerun all the previous steps until you can
find an appropriate Lp making the following parameter relationship valid:
L.
(5.11l)
> L,, > L*
Where L*, is the final updated value of L4 and Lm is the candidate codeword length for
ME coding. As for the optimal value of Lm, we suggest to use the following equation to
compute it instead of another better solution we can come up with at present
LOP,=
L max + AL*
2p
(5.12)
(.2
where X, and X2 are constants which satisfy kl+X 2 = 1. If we are more concerned about
the power consumption, for instance, we can let
k2
procedures of seeking Lopt are presented in Figure 5.3.
58
be greater than X1. The entire flow
Output E orpA
Yrnin
-
mm
req
Yes
No
C.4L
No-'
R
L
9MF
--
ngNo-
Chec~k
Lm
>
Find
Yes
,, > L,
'
-
adjust
Figure 5.3 Updating Procedures of Seeking an Optimal Codeword Length
5.4 Circuit Design of ME Coding Transmitters
The most important issue for the circuit of a ME transmitter is how to turn off the
power of the oscillator while the low bits are transmitting. Figure 5.4.1 shows the basic
architecture of the special transmitter. Basically it contains a spreading code generator
which is based on the coming ME data to generate the PN sequence for each different
data source, a BPSK modulator, filters, oscillator of generating the carrier frequency,
power amplifier, a analog switch and a power switch. The power switch as shown in
Figure 5.4.2 is used to turn off the power of the oscillator as low bits come in. We
adopted some CMOS transistors because of high-speed response considerations.
Moreover, we need an analogy switch to avoid the noise or distortional signals flowing
out from the modulator from entering the following power amplifier and antenna circuit.
59
Antenna
BPSK
Minimam Energy
AL
Switch (1)
DC
4-
Switch (2)
Jim-t
Spreading Co de
Generator
Figure 5.4.1 Basic Architecture of a ME Coding Transmitter
60
Filter
Amplifier
R2
RI
+V.
Figure 5.4.2 Circuit Design of Analog Switch (1)
/RN
+Vcc
R2
I
01
Figure 5.4.2 Circuit Design of Power Switch (2)
61
Chapter 6
Conclusion
In the previous descriptions, we comprehend how an energy efficient DS-CDMA
communication system can greatly reduce the multiple access interference. There are two
important findings in this research. First, the system capacity can be largely increased
because of the MAI reduction. Second, it will be capable of saving lots of power and
improving the system performances, i.e. SNR and error probability, at the same time.
Besides, we can develop a time-division based ME coding for signal transmission and
design a new correlation receiver to further reduce and suppress the MAI. In other words,
MAI reduction and suppression in the energy-efficient DS-CDMA system can be
achieved by an upstream coding technique and a downstream processing signal recovery,
as shown in Figure 6.1.
Upstream
Optimal
Codeword
Length
--------------------------------
----------------------------------------
Downstream
Figure 6.1 MAI Reduction and Suppression : Upstream and Downstream Strategies
62
The performances of an energy-efficient DS-CDMA communication are much
better than those of a traditional DS-CDMA communication because of the extension of
the codeword length. The simulation and experimental results both verify that SNR and
error probability are largely increased and reduced, respectively. Nonetheless, in order to
acquire a good transmission quality, the ME codeword length cannot be extended
arbitrarily since the error probability will increase with it. An optimal codeword length
can be found if the system requirements are given such as, SNR, bit error probability and
transmission rate, etc. Once we can make a good trade-off based on the system needs, the
optimal codeword length can be determined by the proposed updating algorithm
described in Section 5.3. In the future research work, we would like to figure out how to
design a good correlation receiver that can further suppress the received noise and solve
the synchronization problem.
In summary, we investigated the problem of suppressing MAI in energy efficient
DS-CDMA sensor network in this thesis. We can learn there are three important findings
in this research. First, the MAI problem is not so significant in the energy-efficient DSCDMA communication system if compared to a regular DS-CDMA communication
system. Second, although SNR for energy efficient spreading codes becomes a little bit
worse, we still can compensate this loss by MAI suppression and largely reduce the error
probability; of course, we are able to achieve the objective of saving a lot of power as
well. Third, the error probability almost does not alter if using energy efficient Spreading
codes.
63
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65
Appendix
A.1 Proof of (3.15)
d P1 2 r
=
-d
2dt+r
(d'))2dt+...+
(d'))2dtl=
LV'LII,
2T
, -L
.
dt
Td
f(
-.- P
a, PT
2
if a]=
Lb
where T = LTb and Lb is the number of ones in T seconds.
A.2 Proof of (3.16)
-
Cos wj dt
n(t)- c,(t)-
Ng =
.
n(t
)c, (t, )coso t1 dt,
No 6(t, -t2
Jn(t
2
)c(t 2 )cos
t
2
dt2
) dt dh 2
NOTb
4
I f(Ng )2dt-N~
2
k
T f'
k=2
V2
dt
I I(k)
T
[fb' (.)2dt +
LTb
k=2
Pn,
T f'(Ng
)2dt
+
f
Ik
k2
2
fl,
LLT
2
k Pka 2
I
L7 T
2LTh
h
+ f'4
dt
( 1 ())2
(.)2d,
=4 aP
dt
Z2
k=2
21',,
k
\
I' T
k
2'
) dt]
2 1 )(-
(k
Af FLk I
k=2
A.3 Proof of (3.18)
66
N+
4
M
k=2
akPk
2
2
2
dt
0 0
I-T d(')c(l)
f r2
Pd2
,9;
AT2L
-fb ()2dt +
Tf2d')dt=
2
L T
fib (-)2dt
+
f
(.)2dt]
2
T
2
b
2LTb
f' T 2d(')4')dt
0C
T S2
A.4 Proof of (3.19)
n(t, )n(t 2 )c (t
N
n2
2(Ca)(c
sa)2(t -t2)dt
Idt2
n2(t)dt =fIN,
=Q
2
Te
4
d=
4
f(Ng )2dt =N~
Then I
Mk
T
k2F2
=n IAN
=JN 0 T
4
,N
2
I
2
)c (t 2 )cos eOtO coswt t I dt2
2
(k)
dt =
Af
kI
dt=
akfikPk
k=2
+'
$ dk
fk Ik
Ma
dt =
T
2
2
[
k
Uh
N
dt +
k
y
k=2
F2
-) 2
dt
2
k=2
A.5 Proof of (3.22)
2
)2
(c(1)
d3
T
r2
=1Lj20c6 +y
Lb
+
dt -
d(l)
0 0
c
1
)T,2d()di
2T
T dl)( c1
ITb2
2L
8 +y)TFd(I)dt+ fd(')dt
0L,
b 11
L
2
A.6 Proof of (3.23)
67
)2dt
d(')dt]
.
2
=
fh
f
n(t 1 )n(t 2)c,(t 1)c1 (t 2 )cos cot, cos Cot
fb (,
+
y) 2 (t )(cos C&)2S
=b +
t 2)dt
-
2
dt dh 2
dt 2
n(t)dt = il + r, )NO T
2
and
T
fI
k=2F
2 Adt=k
~~~~2~=
+
k~(
M +f I
-
(N4gy)N
(+ r
0I+~ck
dt
I
k=2
~
j
,d) (1k
I
(8k
=
d
2dt
2d2
Ik)ak
)NO T
68
+
2i~~
2
2
Oh1()