218002050 J V Pillay
Uplink NOMA system and modulation/demodulation for uplink NOMA
1
Non orthogonal multiple access
Each user in NOMA works in the same band and at the same time, and they may be identified from
one another by their power output. In order for the successive interference cancellation (SIC) receiver
to be able to distinguish between users in both the uplink and the downlink channels, NOMA employs
superposition coding at the transmitter.
We take into account NOMA as the multiple access strategy and orthogonal frequency division
multiplexing (OFDM) as the modulation scheme. Orthogonal frequency division multiple access
(OFDMA), a natural extension of OFDM, is used in standard 4G networks to assign information for
each user to a portion of subcarriers. On the other hand, each user in NOMA has access to every
subcarrier. The spectrum sharing for two users using OFDMA and NOMA is shown in Figure 1. Both
uplink and downlink transmission are included by the idea.
Figure 1
The same spectrum can be used by all users thanks to superposition coding at the transmitter and
successive interference cancellation (SIC) at the receiver. The numerous information signals are
combined into a single waveform at the transmitter location, and the SIC decodes each signal
individually until it locates the desired signal. The idea is demonstrated in Figure 4. The three
information signals marked with various colours in the figure are overlaid at the transmitter. All three
of these signals are included in the signal that the SIC receiver has received. The strongest signal is
the first one that the SIC decodes, and all others are considered interference. If the decoding is
flawless, the waveform with the other signals is precisely derived by subtracting the first decoded
signal from the received signal. SIC repeats the process until the desired signal is discovered.
Figure 2
Figure 3
Figure 4
The complete cancellation of the signals during the iteration steps is essential to the success of SIC.
The power distribution between the user information waveforms by the transmitter should be precise,
and they should be superimposed. For uplink and downlink channels, different power splitting
techniques are used.
2
NOMA via the domains
2.1 NOMA VIA POWER DOMAIN MULTIPLEXING Basic NOMA with a SIC
Receiver:
In order to balance the sum rate of all multiplexed users and the fairness of throughput among
individual users, signals for various users are linearly added up at the BS transmitter under specific
power partitioning. SIC is frequently utilized at the receiver to implement multi-user detection
(MUD). The channel conditions may differ dramatically among users as a result of the near-far effect.
It is recommended to do SIC in descending sequence of SINR for users with a high signal-tointerference-plus-noise ratio (SINR). As we can see, the fundamental NOMA with SIC utilizes the
SINR differences between users, whether as a result of the near-far effect or of the transmitter's nonuniform power distribution. Uplink system capacity can be increased by employing a similar
approach.
2.2 Network NOMA:
Cell edge users encounter more interference from nearby cells when downlink NOMA transmit power
allocation favors far-off users. Using a cellular system with two cells and four users as an example, it
can be seen that, under the assumption of a two-user NOMA scheme, user 1 and user 2 are served by
BS 1, while user 3 and user 4 are supplied by BS 2. Users 1 and 3 are predicted to have significant
interference, which could harm network NOMA, or multicell NOMA, performance. Joint precoding
of NOMA users' signals across adjacent cells is an option to reduce inter-cell interference. It is
necessary for all user data and CSI to be accessible at various BSs, however selecting the best
precoder is not simple. Furthermore, because the precoder for geographically distinct BS antennas
does not actually generate the physical beam that can easily be used for intra-beam NOMA, the multiuser precoding employed for single-cell NOMA may not be practical for the network NOMA
scenario. A complexity-reduced precoding strategy for network NOMA has been described in, where
the multi-cell joint precoder is used exclusively to cell edge users. This is based on the idea that largescale fading would be considerably different between the links to various cells (e.g., user 1 and user
3).
2.3 NOMA VIA CODE DOMAIN MULTIPLEXING Low-Density Spreading
CDMA:
In order to lessen interference at each chip, LDS-CDMA substitutes sparse spreading sequences for
the dense spreading sequences used in traditional CDMA. LDS-CDMA can thereby enhance system
performance by utilizing CDMA's LDS sequences, which is the primary characteristic that sets it
apart from regular CDMA. With the right spreading sequence design, interference between several
users will be effectively reduced, and overloading can be accomplished. MUD can be implemented at
the receiver using a message passing algorithm (MPA). The factor graph, a bipartite graph with
variable and factor nodes, is extremely effective for MPA. Edges, which can be regarded as the soft
values that indicate the dependability of the symbol associated with each edge, are used to pass
messages between variable nodes and factor nodes. A variable node's marginal distribution can be
thought of as a function of the messages that node has received.
3 Comparison of OMA and NOMA
Table 1:advantages and disadvantages of OMA and NOMA
Advantages
- Simple receiver detection
OMA
NOMA
-
Higher spectral efficiency
Higher connection density
Enhanced user fairness
Lower latency
Supporting diverse Qos
Disadvantages
- Lower spectral efficiency
- Limited number of users
- Unfairness for users
- Increased complexity of receivers
- Higher sensitivity to channel
uncertainty
4 Noma for uplink
Multiple users transmit their individual uplink signals to the BS in the same RB during uplink NOMA
transmission. With the help of SIC, the BS can identify every message sent by users. Please take note
of the following important distinctions between uplink and downlink NOMA:
-
-
-
Transmit Power: Unlike downlink NOMA, uplink NOMA allows users to transmit at a
power that is dependent only on their individual channel conditions. Regardless of their
broadcast strength, if the users' channel conditions are significantly varied, their received
SINR at the BS may be quite different.
SIC Operations: The users' experiences with interference and SIC operations in uplink and
downlink NOMA are also quite dissimilar. For downlink NOMA particularly, the stronger
signal of User m is first detected, remodulated, and then subtracted from the composite signal
to clean the signal of User n from the interference caused by User m. It indicates that SIC
operation is done on a strong user in the downlink to cancel out the interference from the
weak user. By treating User m as interference, SIC is used in uplink NOMA to detect strong
User n first. The recovered signal is then remodulated, and User n's interference is subtracted
in order to identify User m.
Performance Gain: NOMA has a different performance advantage over OMA for uplink and
downlink. Because NOMA's capacity region is outside of OMA's, using it in the downlink
results in better throughput performance. In contrast, NOMA primarily offers fairness gains in
uplink systems, especially when compared to OMA with power control.
4.1 System model
Figure 6 shows the uplink NOMA scheme for K user equipment’s (UEs). User equipment is the
devices that users are currently using to connect to a network e.g., laptops, phones, Internet of things
(Iot) devices. In downlink NOMA successive interference cancellation (SIC) is used for each
individual user, but as can be seen in the diagram, in uplink SIC is applied at the BS to for decoding
all UEs.
Figure 5:diagram illustrating uplink NOMA system for K users
4.1.1 The received signal at the base station (BS) for synchronous uplink NOMA:
(1)
Where:
hi : Channel coefficient of the ith user.
P: Maximum transmission power assumed for all users.
n: Zero mean complex additive Gaussian noise with a variance of σ2 ; that is n~CN(0, σ2 )
In downlink NOMA the power is allocated according to the distance of UEs to the BS. This is
somewhat the same for uplink NOMA, however we assume that users are well distributed in cell
coverage as well as the power levels, the assumption is made since power optimization requires
connection between all UEs which could be difficult to implement. All K users transmit their signals
at equal power P in the same resource block (time slot and frequency band) to the BS which decodes
the user symbols with the stronger magnitude first before dealing with weaker signals. The received
power of each user at the BS is inversely proportional to the square of the distance as shown below.
4.1.2 The received power of each user at the BS:
(2)
Where:
di : Distance of the ith user to the BS
At the receiver the BS implements SIC as mentioned before and the first signal it decodes will be the
one from the nearest user.
4.1.3 The power allocation to maximize sum rate is given by:
(3)
when K users access a shared channel for uplink transmission. If we add a constraint for a total
transmit power, i.e. ∑𝑘𝑘=1 𝑝𝑘 ≤ 𝑝, where P is the total transmit power, the optimal allocation of
maximizing the sum rate becomes:
(4)
4.1.4 SINR analysis
The BS decodes the signals of the users orderly according to the power coefficients of users, and then
the SINR for the lth user l ≠ 1
(5)
Where γ = P ∕ σ2
4.1.4.1
SINR for the first user
𝑆𝐼𝑁𝑅1 = 𝑎1 𝛾|ℎ1 |2
(6)
Assuming the descending decoding order with SIC. Then the SINR is given by:
(7)
In order to support all users at an equal rate, the same SINR threshold, 𝛤 is applied to all the users.
Therefore, when there is 2 users (K=2):
(8)
Resulting in the following satisfying transmit powers:
(9)
For K >= 2, for convenience:
(10)
Where 𝛤(0) = 0, thus giving….
(11)
Example 1
Suppose that there are K = 3 users. For simplicity, let N0 = 1.
In addition, let |h1|2 = 1, |h2|2 = 2, and |h3|2 = 10.
WhenΓ = 2, it can be shown that Γ(1) = 2, Γ(2) = 6, and Γ(3) = 18.
For the descending decoding order, from (11), we have P1 = 2/1 = 2, P2 = 6/2 = 3, and P3 =
18 /10 = 1.8.
Thus, the total transmit power becomes 6.8, while other decoding orders result in higher total
transmit powers.
4.1.5 Sum rate analysis
The sum rate for uplink NOMA can be written as
(12)
When γ → ∞ the sum rate of uplink NOMA becomes:
(13)
4.1.6 SNR for UE1 (this formula includes others as noise):
𝑆𝑁𝑅1 =
𝑃𝑔12
𝑁 + ∑𝐾
𝑖=2 𝑃𝑔𝑖 2
(14)
Where:
P : Power transmission of UEs
N : N=N0W
4.1.7 SNR for UEk (assuming perfect cancellation):
𝑆𝑁𝑅𝑘 =
𝑃𝑔𝑘 2
𝑁
(15)
4.1.8 SNR for UEk (without perfect cancellation):
𝑆𝑁𝑅𝑘 = 1 +
𝑃𝑔𝑘 2
𝑁 + ∑𝐾
𝑖=𝑘+1 𝑃𝑔𝑖 2
(16)
4.1.9 BPS (throughput) for each UE:
(17)
5 NOMA uplink fading and noise
5.1 Performance analysis of NOMA uplink transmission over generalized-K fading
channels
Most of the previous studies on NOMA systems only consider the impact of fading in the
transmission medium; however, more realistic channel models include both fading and shadowing.
Outage probability (OP), average channel capacity, and symbol error rate (SER) for uplink NOMA
over generalized-K fading are derived analytically for the arbitrary number of users and then verified
by Monte Carlo simulations.
All derivations are performed according to M users. First, the OP is obtained by finding the CDF from
the derived PDF above. Second, AVC is obtained by averaging the capacity for a fixed SINR over the
SINR distribution. Finally, the SER of the system is analysed.
5.1.1 Outage probability (OP)
OP is a commonly used performance statistic that sheds light on the system's availability. It can rely
on the desired degree of quality of service or receiver sensitivity, and is defined as the chance of the
received SINR dropping below a threshold value (γth):
(18)
Figure 6
OP results are illustrated in Figure 7 where theoretical results are plotted by using the expression. The
SINR threshold is selected as 4*10^(-4) dB. As can be seen, theoretical and simulation results match
perfectly. OP of Un is lower than that of other users because its received power at the BS is strongest.
Un, Um, and Uf reach 10^(-3) OP value at -23 dB, -9 dB, and 7 dB, respectively. On the other hand,
theoretical and simulation results of Um are also plotted by selecting multipath fading and shadowing
parameters as 2 and 3, respectively. As expected, OP increases since channel distortions increase. It
reach 10^(-3) OP value at -1 dB.
5.1.2 Average channel capacity (AVC)
Channel capacity gives information about the limits on error-free transmission rates, and it depends on
SINR as C=W log2(1+ γ).
(19)
Figure 7: channel capacity comparison of OMA and NOMA in an AWGN channel: a) uplink AWGN channel; b) downlink
AWGN channel
Figure 8
The AVC curves are presented in Figure 5 where theoretical results from the expression (25) and
simulation results match perfectly where the bandwidth is taken as 1 kHz. This figure shows that as
the distance of the user from BS increases, the AVC also increases. For example, AVCs for Un, Um,
and Uf are approximately 11.2 b/s/Hz, 48.5*10^(-2) b/s/Hz, and 11.2*10^(-3) b/s/Hz, respectively, at
SNR = 9 dB. Furthermore, when multipath and shadowing parameters increase, AVC also increases
since the channel degradation is less.
5.1.3 Symbol error rate (SER)
(20)
Figure 9
The SER performance where the theoretical results are plotted by using the SER expression. One can
see that there is a little bit of discrepancy between simulation and theoretical results. It stems from the
truncation used in the summation of the SER expression. As more terms are added, simulation results
approach to theoretical ones. Un, Um, and Uf reach 10^(-1) SER value at approximately 3 dB, 15 dB,
and 30 dB, respectively. SER values of Un are lower than the others since it is the nearest to the BS
and its received power is the strongest. SER results of Un for mm =2 and ms = 3 are also shown where
the SER reach 10^(-1) value to 5 dB.
5.2 Effect of Impulsive Noise on Uplink NOMA Systems
We consider an uplink NOMA network consisting of an AP and M SUs, with transceivers equipped
with a single antenna. Let hi represent the instantaneous Rayleigh fading gain between the ith SU and
the AP. Since the basic idea behind power domain NOMA is to superimpose the signals in the power
domain and assuming that the AP utilizes the instantaneous CSI to determine the decoding order, the
received signal is given by
(21)
the probability distribution function (PDF) of the combined noise n is given by
(22)
Hence, assuming perfect cancellation and perfect CSI, the instantaneous SNR per symbol of the jth
sorted SU’s message is given by
(23)
6 Modulation and Demodulation
In this section a study of the bit error rate (BER) performance of a two-user uplink NOMA using
BPSK, QPSK and 16-QAM with SIC receiver is introduced. The simulations will be done over a
perfect channel estimation and a channel with estimation error as a function of the modulation error.
Figure 10
Throughout this section we will consider a two-user uplink NOMA system as shown in figure 11. The
first user transmits signal X1 scaled by power coefficient P1 to the BS over a channel with the scalar
coefficient h1. The second user transmits signal X2 scaled by power coefficient P2 to the BS over a
channel with the scalar coefficient h2. The received (y) signal by the BS is represented as:
(24)
Where n is the additive white gaussian noise with zero mean and 𝜎 2 .
For the perfect scenario, the methodology assumes that the two-users signals have been generated
each 10^6 bits in duration to create the BPSK, PSK and 16-QAM signals. In addition, AWGN noise
has been generated and then it is added to the two transmitted signals at the receiver side.
Figure 11:SIC signal detection for two-user uplink NOMA
The simulation results for perfect channel estimation of BPSK uplink NOMA system with two users
is shown in Fig. 13. As expected, the figure shows that user 2 has better BER performance than user
1. In this case, the parameter that affects the performance of SIC detection is the ratio of user 2’s
power to the combination of user one’s power plus the noise power. As assumed, the SIC detector will
detect user 2 signal first from the superimposed received signal plus noise. The noise power will have
a significant effect on the detection of user 1 since the receiver first performs subtraction of the
detected user 2’s signal in addition to processing the noise. After detecting user 2’s signal with the
SIC receiver, the remaining signal, assuming correct detection of user 2, is user 1’s signal in addition
to the noise. So that, the subtraction of user 2’s signal makes the detection of user’s 1 signal more
vulnerable to noise than user 2 and this leads to a larger BER for this user as compared to user 2. As
shown in Fig. 13, the BER for user 2 at SNR = 0 dB is equal to 0.0123 compared to 0.15 for user 1 at
the same SNR of 0 dB. Furthermore, for SNR = 5 dB, user 2 has a BER of 0.0007 and user 1 has a
BER of 0.10.
Figure 12: BER vs SNR for two BPSK uplink NOMA users with perfect channel estimation
On the other hand, for the same modulation of BPSK but with channel estimation errors, the
simulation results are shown in Fig. 14. In this figure, two channel estimation errors, 0.15 and 0.25,
are assumed. In addition to the affecting parameters of the perfect case, adding an estimation error
degrades the SIC detection process and the BER performance. Assuming detection of user 2’s signal
first by the SIC detector, the remaining signal after detection user 2’s signal is user 1’s signal with an
added estimation error in addition to the noise. This degrades signal reception and, as expected, leads
to a degraded BER compared to the perfect case. For example, at SNR = 15 dB, the BER for user 1 is
equal to 0.01 for 0.15 channel estimation error compared to a BER of 0.007 for perfect estimation at
the same SNR value. As the estimation error value increases, the BER is increased. In the same way,
as shown in Fig. 14, at SNR = 15 dB, the BER for user 1 is equal to 0.32 for 0.25 channel estimation
error which is higher than the BER of 0.007 for perfect estimation and 0.01 for 0.15 channel
estimation error at the same SNR value.
Figure 13: BER vs SNR for two BPSK uplink NOMA users with different channel estimation errors
Approximately, the same analysis for the two scenarios can be followed for higher modulation
schemes, QPSK and 16- QAM, as shown in Fig. 15 and Fig. 16, respectively. In these figures, the
results for various channel estimation errors are demonstrated. For the perfect case, at SNR = 5 dB,
the BER of user 2 for QPSK modulation is equal to 0.005 compared to 0.14 for user 1 at the same
SNR. On the other hand, for 16-QAM, the BER for user 2 at SNR = 5 dB is equal to 0.04 compared to
0.20 for user 1 at the same SNR. As a result, the BER performance of user 1 becomes worse for the
same reason discussed in the perfect BPSK case and at the same time increasing the modulation level
increases the degradation of the BER. For the channel estimation error scenario, 16-QAM has a higher
BER than QPSK BER which is expected as discussed above. For example, at SNR = 15 dB and 0.15
channel estimation error, Fig. 15 shows that the QPSK BER of user 1 is equal to 0.028 compared to
0.017 for the perfect estimation at the same SNR value. In addition, for the same SNR value of 15 dB,
Fig. 16 shows that 16-QAM of user 1 has a BER of 0.17 for 0.15 channel estimation error compared
to 0.07 for the perfect estimation at the same SNR value. Furthermore, for a QPSK with 0.25 channel
estimation error, the BER of user 1 is equal to 0.058 at SNR = 15 dB compared to 0.017 for perfect
estimation and 0.028 for 0.15 channel estimation error at the same SNR. For 16-QAM, the BER at
SNR = 15 dB is 0.20 for 0.25 channel estimation error compared to 0.07 for perfect estimation and
0.17 for 0.15 channel estimation error at the same SNR. As a result, with increased channel estimation
error, the BER is also increased and further increases with increased modulation order. An interesting
observation is that, at high channel estimation error, the results for the three modulation schemes
indicate a very high BER and a flattened performance as compared to the perfect estimation and the
given channel estimation errors results. This is due to the degradation in the SIC receiver that results
in high BER.
Figure 14: BER vs SNR for two QPSK uplink NOMA users with different channel estimation errors
Figure 15: BER vs SNR for two 16-QAM uplink NOMA users with different channel estimations