Dr. Bradley J. Bazuin
Assistant Professor
Department of Electrical and Computer Engineering
College of Engineering and Applied Sciences

Chapter 11: Multichannel and Multicarrier Systems
11.1
737
Multichannel Digital Communications in AWGN Channels 737
11.2
11.3
Multicarrier Communications
Bibliographical Notes and References
743
759
Problems 760
ECE 6640
Notes and figures are based on or taken from materials in the course textbook:
J.G. Proakis and M.Salehi, Digital Communications, 5th ed., McGraw-Hill, 2008 .
2

• In some applications, it is desirable to transmit the same information-bearing signal over several channels simultaneously. This mode of transmission is used primarily in situations where there is a high probability that one or more of the channels will be unreliable from time to time.
– For example, radio channels such as ionospheric scatter and tropospheric scatter suffer from signal fading due to multipath, which renders the channels unreliable for short periods of time.
– As another example, multichannel signaling is sometimes employed in wireless communication systems as a means of overcoming the effects of interference of the transmitted signal.
• By transmitting the same information over multiple channels, we are providing signal diversity, which the receiver can exploit to recover the information.
• Another form of multichannel communications is multiple carrier transmission, where the frequency band of the channel is subdivided into a number of subchannels and information is transmitted on each of the subchannels. These involve current OFDM systems, which will be introduced.
ECE 6640 3

• Multichannel signaling over fixed channels that differ only in attenuation and phase shift.
– Narrow bandwidths are assumed; therefore, equalization can be performed using a simple gain and phase adjustment.
– Coherent or non-coherent combining of one or more channels that contain identical symbol information.
ECE 6640 4

x
0 x
1 x
2
Forming Wideband and Reforming Narrowband
Filters narrower than the Nyquist regions are used for generating FDM waveforms.
A guard band between adjacent frequencies is typically used h
0 h
0 y
0
FFT h
1 h
2 y x h
1 h
2
IFFT y
1 y
2 x
M
 1
ECE 6560 h
M
 1 h
M
 1
Synthesis
Multirate Signal
Processing
Implementation Analysis
Notes and figures are based on or taken from materials in the course textbook: fredric j. harris,
Multirate Signal Processing for Communication Systems, Prentice Hall PTR, 2004. ISBN 0-13-
146511-2.
y
M
 1
 
5

• The waveforms are assumed to have equal energy and to be equally probable a priori.
• The waveforms transmitted over the L channels are scaled by the attenuation factors {α n
}, phase-shifted by {φ n
}, and corrupted by additive noise. (Note n=1:L) r l
  n
 e j
  n
 s lm
 
 z n
 
, n
 1 :
L and m
 1 :
M
• Coherent decision metric sum multichannel summation
CM m
 n
L 
 1
Re


 conj

 ˆ n
 e j
  ˆ n



T
0 r l
   
 conj
 s
  lm
  



, m
 1 : M
ECE 6640 6

• Non coherent combining may also a performed.
– The analysis multiply defines the same variables, Xn and Yn, with different values that are not the same. One refers to non-coherent, the other to coherent detection of simultaneous waveforms.
• A performance analysis is discussed … and a combining loss estimate described.
ECE 6640 7

• Using the concepts defined for multichannel signaling and processing, the concept of independent, orthogonal subcarriers existing within the broader bandwidth has been embraced and extended.
• Therefore, we consider the transmission of information on multiple carriers contained within the allocated channel bandwidth. The primary motivation for transmitting the data on multiple carriers is to reduce ISI and, thus, eliminate the performance degradation that is incurred in single carrier modulation.
ECE 6640 8

• For a non-ideal linear filter channel, one option is to employ a single-carrier system in which the information sequence is transmitted serially at some specified rate R symbols/s. In such a channel, the time dispersion is generally much greater than the reciprocal of the symbol rate, and, hence, ISI results from the non-ideal frequency response characteristics of the channel.
• An alternative approach to the design of a bandwidthefficient communication system in the presence of channel distortion is to subdivide the available channel bandwidth into a number of subchannels, such that each subchannel is nearly ideal.
ECE 6640 9

• The frequency band allocated is divided into multiple narrowband subchannels with the following goals:
– orthogonal waveforms on each subchannel
– multipath mitigating or tolerant
– optimal utilize each subchannel based on the noise, interference, etc.
– maintain an average power per “multichannel symbol” transmission
ECE 6640 10

• Shannon-Hartley Capacity Theorem for AWGN is
C

W
 log
2



1 
N
P
Avg
0

W
• If we define subchannels capacity as



C i
  f
 log
2




1 
 f

P
 f
   
 i
S nn
  i i
2




– where the power is the subchannel power times the subchannel filter power and the noise is the noise power spectral density
• Summing
C
 i
L 
 1
C i
  f
 i
L 
 1 log
2




1 
 f

P
 f
   
 i
S nn
  i i
2




ECE 6640 11

• In the limit of small channels, the summation becomes and integral and
C

W
 log
2




1 
P
   
S
  f nn
 2




 df
• Choosing P(f) to maximize C, using Lagrange methods,
P

– for f in the band of interest
K

S
C nn f
 
  2
– Interpretations: K is the average power level being used across the band. The other term defines the frequency domain noise floor.
Valid communications may occur based on the distance between the two.
ECE 6640
– This gives rise to a “water filling” analogy as shown on the next page.
12

Subbands have communications capacity in the “water-filled” regions.
Band dynamic range
(E b
/N o
) defines the type of
“symbol” and bits-persymbol available for a subband.
ECE 6640
P. P. Vaidyanathan, "Filter banks in digital communications," in
IEEE Circuits and Systems Magazine, vol. 1, no. 2, pp. 4-25, 2001.
13

• Frequency based noise floor across a wide-bandwidth channel.
• By subdividing into multiple narrowband channels, what is available can be “fully” utilized.
ECE 6640 14

• Discrete Fourier Transform based symbol placement, modulation and demodulation.
ECE 6640 15

• Multiple simultaneous DFT spaced carriers with defined magnitude and phase (related to the symbol) are transmitted for 1+CP IDFT time, where CP is a cyclic prefix.
– Since the IDFT outputs “perfect periods” for each of the carrier waveforms. A time segment from the end of the time period can be
“pre-pended” onto the front of the waveform and it will be a smooth continuation of the IDFT time period.
– The cyclic prefix provides a “preamble” of sorts for the 1 IDFT time period that must be collected and DFT transformed by the receiver.
– It effectively provides a “burst” to “burst” transition time interval while maintaining the nominal power in the symbols transmission.
ECE 6640 16

• With each subband (or subchannel), we associate a sinusoidal carrier signal of the form s k
 
 cos

2   f k
 t

, k
 0 :
N
 1
• By selecting the symbol rate 1/T in each of the subchannels to be equal to the frequency separation f of the adjacent subcarriers, the subcarriers are orthogonal over the symbol interval T , independent of the relative phase relationship between subcarriers.
T

0 cos

2   f k
 t
  k

 cos

2   f j
 t
  j




0
1
2
,
, j
 k j
 k
ECE 6640 17

• With narrowband subchannels, the transmission time for the simultaneous “bins” is N time the single channel system … significantly longer.
– Multipath mitigating as the period is significantly greater than the
“channel dispersion”. This is related to the “time-delayed” signal paths all expected to be occurring during the received symbol time instead of partially in one symbol and partially in the next.
– This makes each channel appear to have simple phase and gain offsets do to the channel and the summation of all the multipath rays.
ECE 6640 18

• Suppose that each subcarrier is modulated with M-ary
QAM. Then the signal on the kth subcarrier may be expressed as
• With C(f) channel effects, the received symbol is
ECE 6640 19

• By periodically transmitting known “pilot tones” as QAM symbols, gain and phase equalization for each “bin” can be determined and applied prior to detection.
• Standard coherent QAM detection can be applied to each bin to determine the data contained in the OFDM symbol.
ECE 6640 20

• It is convenient to view the multicarrier modulation as consisting of “N” independent QAM channels, each operating at the same symbol rate 1/T , but each channel having a distinct QAM constellation; i.e., the i th channel will employ M = 2 bi signal points.
– If 16-QAM symbols used in a 256-pt IDFT, 1024 bits per OFDM symbol could be transmitted.
– However, (1) not all bins would be used, a guard band at the top and bottom of the IDFT is present. (2) Pilot tones may be sent as the entire symbol occasionally or periodic pilot tones may be placed in each OFDM symbol.
– Don’t forget that there is a cyclic prefix that occurs before the desired T OFDM symbol period.
ECE 6640 21

• Each of the OFDM “bins” may operate with a different
E b
/N
0 capability. If the bins “dynamic range” or “noise floor” can be estimated. The QAM symbol with the highest bits-per-symbol may be transmitted in the bin.
– “Bin” dynamic range could be time varying.
– Instantaneous OFDM symbol capacity could vary in time!
ECE 6640 22

• The sinc function characteristic of a time limited period.
ECE 6640 23

• Frequency offset in the received signal can result in a loss of orthogonality resulting in intersymbol interference.
– Doppler shift, offset transmit and receive clocks,.
• If “subchannel filtering” is applied, limited amounts of clock offset and Doppler shift can be allowed.
– The filter adds complexity to the received system and may require
“matched” transmitting and receiving filters!
– Mathematically a window is applied to the DFT data prior to DFT processing. Alternately a “precombiner” operating at a multiple of the DFT sample rate can be applied. (see MRSP class)
ECE 6640 24

ECE 6640 25

• Peak-to-Average Power Ratio
– If all OFDM “bins” are statistically random, a smooth average power could be transmitted during the T x (1+CP) symbol period.
– However, the coherent summation of sinusoidal waveforms can cause a significant voltage peak in the transmitted waveform.
Large peaks will require higher power to be transmitted and could causing clipping in the Tx DAC (and non-linearities).
– Hundreds (if not thousands) of people with Matlab have and continue to propose ways to minimize PAPR.
• The central limit theorem may be used to model the combined signal on the N subchannels, when large, as a zero-mean Gaussian random process. In such a model, the voltage PAR is proportional to sqrt(N).
ECE 6640 26

• To avoid intermodulation distortion, it is common to reduce the power in the transmitted signal and thus operate the power amplifier at the transmitter in the linear operating range. This power reduction or “power backoff” results in inefficient operation of the communication system. For example, if the PAR is 10 dB, the power backoff may be as much as 10 dB to avoid intermodulation distortion.
– Various methods have been devised to reduce the PAR in multicarrier systems. One of the simplest methods is to insert different phase shifts in each of the subcarriers. These phase shifts can be selected pseudorandomly, or by means of some algorithm, to reduce the PAR.
ECE 6640 27

• OFDM is prevalent in many communications systems
• I expect that must broad bandwidth communications systems are either already OFDM based or seriously considering it.
• There is much more to learn about …
ECE 6640 28