Non orthogonal multiple access

MASTER OF TECHNOLOGY
in
Communication & Signal Processing Engineering
Engineering
Submitted by
Mr. Shalikram
(1924104)
DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING
NATIONAL INSTITIUTE OF TECHNOLOGY SILCHAR
2019-2020
Non-Orthogonal Multiple Access

INTRODUCTION
Why NOMA introduced ?

Abstract
 In this presentation, I explore the concept of non-orthogonal multiple
access (NOMA) scheme for the future radio access for 5G.
 We first provide the fundamentals of the technique for both
downlink and uplink channels and then discuss optimizing the
network capacity under fairness constraints.
 We further discuss the impacts of imperfect receivers on the
performance of NOMA networks.
 I discuss the spectral efficiency (SE) of the networks that employ
NOMA with its relations with energy efficiency (EE).
 We demonstrate that the networks with NOMA outperform other
multiple access schemes in terms of sum capacity, EE and SE.

 In FDMA implementations, such as orthogonal frequency division
multiple access(OFDMA), information for each user is assigned to a
subset of subcarriers.
 NOMA is fundamentally different than other multiple access schemes
which provide orthogonal access to the users either in time,
frequency, code or space.
 In NOMA, each user operates in the same band and at the same time
where they are distinguished by their power levels.
 NOMA uses superposition coding at the transmitter such that the
successive interference cancellation (SIC) receiver can separate the
users both in the uplink and in the downlink channels.
1.Introduction

2. Non-orthogonal multiple access (NOMA)
 We consider orthogonal frequency division multiplexing (OFDM) as the modulation
scheme and NOMA as the multiple access scheme.
 In conventional 4G networks, as natural extension of OFDM, orthogonal frequency
division multiple access (OFDMA) is used where information for each user is assigned to
a subset of subcarriers.
 In NOMA, on the other hand, all of the subcarriers can be used by each user. the
spectrum sharing for OFDMA and NOMA for two users. The concept applies both uplink
and downlink transmission.
2.1 Spectrum sharing for OFDMA and NOMA for two users
 OFDMA-> Each user is assigned to a
subset of subcarriers.  NOMA->It shows two users as using the
same slots but different powers levels.
Figure 1(a,b)

2.2 Superposition coding & Successive interference cancellation(SIC)
 Superposition coding at the transmitter and successive interference cancellation (SIC) at the
receiver makes it possible to utilize the same spectrum for all users.
 At the transmitter site, all the individual information signals are superimposed into a single
waveform, while at the receiver, SIC decodes the signals one by one until it finds the desired
signal.
 The three information signals indicated with different colors are superimposed at the transmitter.
 The received signal at the SIC receiver includes all these three signals.
 The first signal that SIC decodes is the strongest one while others as interference.
 The first decoded signal is then subtracted from the received signal and if the decoding is perfect,
the waveform with the rest of the signals is accurately obtained.
 SIC iterates the process until it finds the desired signal.
Figure 2

2.3. NOMA for downlink
In NOMA downlink, the base station superimposes the information waveforms for its serviced users.
Each user equipment (UE) employs SIC to detect their own signals.
2.3.1 Power allocation criteria :
 The challenge for base station(BS) is to decide how to allocate the power among the individual
information waveforms, which is critical for SIC. In NOMA downlink, more power is allocated to
UE located farther from the BS and the least power to the UE closest to the BS.
2.3.2 Downlink process :
 In the network, all UEs receive the same signal that contains the information for all users. Each UE
decodes the strongest signal first, and then subtracts the decoded signal from the received signal.
 SIC receiver iterates the subtraction until it finds its own signal. UE located close to the BS can
cancel the signals of the farther UEs. Since the signal of the farthest UE contributes the most to the
received signal, it will decode its own signal first.

Figure 3 Downlink NOMA for K users.

The transmitted signal by the BS can be written as
x 𝑡 = 𝑛=1
𝑘
𝛼 𝑛 𝑃 𝑇 𝑥 𝑛 𝑡 ;Pn= αnPT
𝑥 𝑛 𝑡 =individual information conveying OFDM waveform,
𝛼 𝑛 is the power allocation coefficient for the UEn,
PT is the total available power at the Base Station.
Pn The power allocated to each UEn
The received signal at the UEn is
yn(t)=x(t) gn+ wn(t)
gn = Channel attenuation factor for the link between the BS and the UEn
Wn(t) = the additive white Gaussian noise at the UEn with mean zero and density N0(W/Hz)
The signal to noise ratio (SNR) for UEK
SNRK =
𝑃 𝐾
𝑔 𝐾
2
𝑁0
𝑊+ 𝑖=1
𝐾−1 𝑃𝑖
𝑔2
𝐾
where w is the transmission bandwidth.

In general, for nth UEn, the SNR becomes
When NOMA is used, the throughput (bps) for each UE can be written as
Rn=Wnlog2(1+
𝑃 𝑛
𝑔2
𝑛
𝑁0
+ 𝑖=1
𝑛−1 𝑃𝑖
𝑔2
𝑛
)
• UEs are assigned to a group of subcarriers in order to receive their information. When the total bandwidth and power are shared
among the UEs equally,
• the throughput for each UE for OFDMA becomes
Rn=Wnlog2(1+
𝑃 𝑛
𝑔2
𝑛
𝑁 𝑛
)
Where Wn=
𝑊
𝐾
𝑎𝑛𝑑 Nn=N0Wn
SNRn =
𝑃 𝑛
𝑔2
𝑛
𝑁0
𝑊+ 𝑖=1
𝑛−1
𝑃𝑖
𝑔2
𝑛
The sum capacity for both OFDMA and NOMA can be written as
RT = 𝑛=1
𝐾
𝑅 𝑛
• We further define fairness index
F =
𝑅 𝑛
2
𝑘 𝑅2
𝑛
• which indicates how fair the system capacity is shared among the UEs, that is, when F gets close to 1, the capacity for each
UEs gets close to each other.

Figure 4. Uplink NOMA for K users.
2.4. NOMA for uplink
Uplink implementation of NOMA is slightly different than the downlink. Figure 4 depicts a
network that multiplexes K UEs in the uplink using NOMA. This time, BS employs SIC in order
to distinguish the user signals.

 In the uplink, the received signal by the BS that includes all the user signals is written as This assumption
is more natural from practical point of view, since power optimization requires connection between all
the UEs.
which may be difficult to implement. At the receiver, the BS implements SIC. The first signal it decodes
will be the signal from the nearest user. The SNR for the signal for the UE1 can be written as, including
others as interference.
SNR1=
𝑃𝑔2
1
𝑁+ 𝑖=2
𝐾 𝑃𝑔2
𝑖
P is the transmission power of UEs and N=N0W
 The last signal that the BS decodes is the signal for the farthest user UEK. Assuming perfect
cancellation, the SNR for UEK can be written as
SNRK =
𝑃𝑔2
𝐾
𝑁
 Generally, for the nth UE, the SNR becomes,
SNRn= 1+
𝑃𝑔2
𝑛
𝑁+ 𝑖=𝑛+1
𝐾 𝑃𝑔2
𝑖

The throughput (bps) for each UE can be written as
Rn= Wlog2 (1+
𝑃𝑔2
𝑛
𝑁+ 𝑖=𝑛+1
𝐾 𝑃𝑔2
𝑖
)
 In OFDMA, on the other hand, UEs are allocated orthogonal carriers in order to receive
their information.
 When the total bandwidth and power are shared among the UEs equally,
 throughput for each UE for OFDMA becomes.
Rn = Wnlog2 (1+
𝑃 𝑛
𝑔2
𝑛
𝑁 𝑛
)
 Where Wn =
𝑊
𝐾
and Nn = N0Wn
 The sum capacity for both OFDMA and NOMA can be written as
RT= 𝑛=1
𝐾
𝑅 𝑛

3. Imperfectness in NOMA
 Our discussions so far in the previous sections assume perfect cancellation in the SIC receiver.
 In actual SIC, it is quite difficult to subtract the decoded signal from the received signal without
any error.
 In this section, we revisit the NOMA concept with cancellation error in the SIC receiver.
Here, we consider the downlink only;
SNRn =
𝑃 𝑛
𝑔2
𝑛
𝑁0
𝑊+ 𝑖=1
𝑛−1 𝑃𝑖
𝑔2
𝑛
+𝜀 𝑖=𝑛+1
𝐾 𝑃𝑖
𝑔2
𝑛
where ε is cancellation error.

4. Spectral efficiency and energy efficiency
In addition to spectral efficiency (SE) of NOMA, we analyze the energy efficiency (EE) of NOMA systems.
 we incorporate the static power consumption of the network.
 due to the power amplifiers in addition to the power consumed for the information waveform. The total
power consumption at the transmitter can be represented as the sum of the information signal power and
the power consumed by the circuits (mainly by power amplifiers).
 Considering the downlink, the total power consumed by the BS can then be written as
P total = PT + P static
 where , PT is the total signal power and
 Pstatic is the power consumed by the circuitry.
Energy efficiency (EE) is defined as the sum rate over the total consumed power of the base
station
EE =
𝑅 𝑇
𝑃𝑡𝑜𝑡𝑎𝑙
= SE
𝑊
𝑃𝑡𝑜𝑡𝑎𝑙
(bits/joule)
where SE is the spectral efficiency (RT/W) in terms of bps/Hz.

5. Result
5.1Rate pairs
• We assume that there are two users in the network for the sake of discussion and analyze the boundaries of the achievable rate regions for these
two users.
• We consider a symmetric downlink channel so that the users are at equal distance to the BS. Lets SNR1= SNR2=10dB shows the boundaries of
the achievable rate regions R1 and R1 for NOMA and OFDMA.
• NOMA achieves higher rate pairs than the OFDMA except at the corners points (where the rates are equal to the single user capacities).
• When the fairness is high, both users experience 1.6 bps/Hz throughputs with both NOMA and OFDMA.
• However, when the fairness is lower, both sum capacity and individual throughputs are higher with NOMA. when the channel is asymmetric,
that is, SNR1= 20dB, SNR2=10dB. NOMA achieves much higher rate pairs than OFDMA, particularly for the farther user, UE2.
Figure 5(a,b)

5.2 SE-EE trade-off with NOMA
• we compare the EE and SE of NOMA with OFDMA. We again consider the downlink.
• The system bandwidth is taken as W=5MHz
• The channel gains for UE1 and UE2 are taken respectively, taken as g1
2 =-120dB & g2
2 =-140dB
• Noise density is taken asN0 = −150 dBW/Hz
• We assume that the static power consumption at the BS is Pstatic=100W
• the obtained EE-SE curves for this setup. It is seen that NOMA achieves higher EE and SE than OFDMA system. The green-points occur for
NOMA and OFDMA when PT at 17W and 18W, respectively. At these points, both systems achieve their maximum EE.
• NOMA clearly outperforms OFDMA at green point and beyond for both EE and SE.
Figure 6

MATLAB
Programming
codes
Coding for figure 5(b):
%%% NOMA parameters
P = 1;
G1 = 20;
G2 = 10;
count = 1;
for alpha = 0:0.01:1 %power splitting factor
P1 = P*alpha;
P2 = P - P1;
R1(count) = log2(1 + P1*G1);
R2(count) = log2(1 + P2*G2/(P1*G2 + 1));
count = count + 1;
end
hold on;
plot (R1,R2,'r');
grid on;
count = 1;
for alpha = 0:0.01:1 %bandwidth splitting factor
P1 = P/2;
P2 = P/2;
R1(count) = alpha*log2(1 + P1*G1/alpha);
R2(count) = (1-alpha)*log2(1 + P2*G2/(1-alpha));
count = count + 1;
end
hold on;
plot(R1,R2,'k');
xlabel('Rate of user 1 (bps/Hz)');
ylabel('Rate of user 2 (bps/Hz)');
grid on;
box on;
legend('NOMA','OFDMA'); title(‘Asymmetric downlink
channel rate pairs with OFDMA & NOMA’);
Coding for figure 5(a):
%%% NOMA parameters
P = 1;
G1 = 10;
G2 = 10;
count = 1;
for alpha = 0:0.01:1 %power splitting factor
P1 = P*alpha;
P2 = P - P1;
R1(count) = log2(1 + P1*G1);
R2(count) = log2(1 + P2*G2/(P1*G2 + 1));
count = count + 1;
end
hold on;
plot (R1,R2,'r');
grid on;
count = 1;
for alpha = 0:0.01:1 %bandwidth splitting factor
P1 = P/2;
P2 = P/2;
R1(count) = alpha*log2(1 + P1*G1/alpha);
R2(count) = (1-alpha)*log2(1 + P2*G2/(1-alpha));
count = count + 1;
end
hold on;
plot(R1,R2,'k');
xlabel('Rate of user 1 (bps/Hz)');
ylabel('Rate of user 2 (bps/Hz)');
grid on;
box on;
legend('NOMA','OFDMA');
title(‘symmetric downlink channel rate pairs with OFDMA & NOMA’);

.
clc;
Close all; clear all;
B = 5*10^6; %bandwidth Hz
N0 = 10^-21; %-150 dBw/Hz
N = N0*B; % dBW
G1 = 10^-12; %-120 dB
G2 = 10^-14; %-140 dB
Pcircuit = 100; %watt
count = 1;
for p = 1:1:100 %W
P1 = p*0.1; %allocate less power to UE1
P2 = p - P1;
R1 = B*log2(1 + P1*G1/N);
R2 = B*log2(1 + P2*G2/(P1*G2 + N));
R = R1 + R2;
SE(count) = R/B; % bit/sec/Hz
EE(count) = (R/(Pcircuit + p)); % bit/watt.sec
count = count + 1;
end
hold on;
plot(SE,EE,'k');
xlabel('SE (bit/sec/Hz)');
ylabel('EE (bit/joule)');
grid on;
% OFDMA
count = 1;
greenpoint = 0;
maxEE = -1000;
for p = 1:1:100 %Watt
P1 = p/2;
P2 = p/2;
R1 = (B/2)*log2(1 + P1*G1/(N0*B/2));
R2 = (B/2)*log2(1 + P2*G2/(N0*B/2));
R = R1 + R2;
SE_line(count) = R/B; % bit/sec/Hz
EE_line(count) = (R/(Pcircuit + p)); % bit/watt.sec = Mbit/joule
count = count + 1;
end
hold on;
plot(SE_line,EE_line,'g-');
xlabel('SE (bit/sec/Hz)');
ylabel('EE (bit/joule)');
grid on;
MATLAB code for Figure 6

References
[1] D. Tse and P. Vishwanathan, Multiuser Capacity and Opportunistic Communication, Fundamentals of Wireless
Communication, Cambridge University Press, 2005.
97
[2] Y. Saito et al, System Level Performance Evaluation of Downlink Non-Orthogonal Multiple Access (NOMA), in Proceedings
of IEEE Symposium on Personal, Indoor and
Mobile Radio Communications (PIMRC), Sept. 2013.
[3] Y. Saito et al, Non-Orthogonal Multiple Access (NOMA) for Future Radio Access, in Proceedings of IEEE Vehicular
Technology Conference (VTC Spring), pp. 1–5, Sept.
2013.
[4] Jain, Raj, Dah-Ming Chiu, and William R. Hawe. A Quantitative Measure of Fairness and Discrimination for Resource
Allocation in Shared Computer System. Vol. 38.
Hudson, MA: Eastern Research Laboratory, Digital Equipment Corporation, 1984. pp.
20–21.
[5] J.G. Andrews and T.H. Meng, Optimum Power Control for Successive Interference Cancellation with Imperfect Channel
Estimation, IEEE Trans. Wireless Comm., vol. 2,
no. 2, pp. 375–383, 2003.
[6] C. Xiong, G.Y.Li, S. Zhang, Y.Chen, and S. Xu, 2011. Energy-and Spectral-Efficiency Tradeoff in Downlink OFDMA
Networks. IEEE transactions on wireless communications,
10(11), pp.3874–3886.
.

[9] Z. Ding, F. Adachi, and H. V. Poor, The Application of MIMO to Non-Orthogonal Multiple Access, IEEE Trans. Wireless
Communication ., vol. 15, no. 1, pp. 537–552, 2016.
[10] Z. Ding and H. V. Poor, “Design of Massive-MIMO-NOMA with Limited Feedback,” IEEE Signal Processing Letters, vol.
23, no. 5, pp. 629–633, 2016.
[11] Q. Sun, S. Han, C.-L. I, and Z. Pan, “On the Ergodic Capacity of MIMO NOMA Systems,” IEEE Wireless Communications
Letters, vol. 4, no. 4, pp. 405–408, 2015.
[12] Z. Yang, Z. Ding, P. Fan, and G.K. Karagiannidis, “On the Performance of Non- Orthogonal Multiple Access Systems with
Partial Channel Information,” IEEE Trans.
Commun., vol. 64, no. 2, pp. 654–667, 2016.
Thank you Sir

Non orthogonal multiple access

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