How to simulate a simple NOMA system (AWGN) using MATLAB?

Simulation of BER of Non orthogonal multiple access (NOMA) in AWGN channel - MATLAB code with explanation

You can download the MATLAB code directly here.

In the previous two posts, we took a toy example to understand the concept of NOMA and to prove to ourselves that NOMA indeed works as expected. As we said before, NOMA uses superposition coding at the transmitter end and successive interference cancellation at the receiver end.
In this post, we will see how to simulate a simple two user NOMA system using MATLAB. We will be plotting the BER performance of NOMA in an additive white gaussian noise (AWGN) channel. The AWGN assumption here is made to keep things simple so that we can pay more attention to the actual skeleton of NOMA implementation. We will improve on this model and do the similar exercise over a Rayleigh fading channel in the next post. The MATLAB code used in this example is available for download here.
See this post on How to do power allocation in NOMA?

Assumptions

Here are the assumptions we are going to make:

1. Let us do downlink transmission from base station (BS) to two users.
2. We are not using any path loss models and we assume that both users are located at equal distances from the BS.
3. We are assuming an AWGN channel
4. We are going to use BPSK modulation for both users
5. Since we are using BPSK, we are going to consider only the in-phase/real component of complex AWGN.

A few pointers about these assumptions: (i) In real time systems, NOMA performs better when one of the users is closer to the BS (also called the near/strong user) and the other user is far away (far/weak user). But in our case, for the sake of simplicity, let's assume users are equidistant from the base station. We will see that NOMA works even under this assumption. (ii) The AWGN assumption is not valid in real time applications. The wireless channel is more complicated due to multipath propagation and fading. We will see how to simulate NOMA for Rayleigh fading channel in a later post. (iii) It is also possible to use different modulation schemes for different users.

System Model

Our network will look like this:

We have a base station (BS) at the center. It is transmitting simultaneously to two users, user 1 and user 2, using the same frequency carrier by applying NOMA.

Notation

• x₁ - data to be sent to user 1
• x₂ - data to be sent to user 2
• a₁ = 0.75 - power weight given to user 1
• a₂ = 0.25 - power weight given to user 2

Implementation in MATLAB

We will dive in directly to the implementation part here. To understand the working of NOMA, please refer the previous posts on superposition coding and successive interference cancellation

1. Generate random binary data for user 1 and user 2. For random binary data generation, we can use the inbuilt MATLAB function called randi(). randi([0 1],1,N) will generate a binary sequence of length N
2. Do BPSK modulation to the above generated data. The operation 2*k-1 will give the BSPK modulated symbol for data bit k
3. Do superpostion coding. That is, compute x = √a₁x₁ + √a₂x₂
Iterate steps 4 to 7 for every SNR
4. Add AWGN. The awgn(x,SNR_dB,'measured') function can be used here. After addition of awgn, we have the received signal, y₁ = x + n₁ for user 1 and, y₂ = x + n₂ for user 2.
5. For user 1, perform direct BPSK demodulation of y₁ to get x₁.
6. For user 2, first perform direct BPSK demodulation of y₂ to get x₁.
7. Remodulate x₁ into a BPSK signal as x'₁ = 2x₁ - 1
8. Multiply the estimate obtained in the previous step by √a₁ and subtract it from y. That is, do rem = y - √a₁x'₁
9. Perform direct BPSK demodulation of rem to obtain x₂
10. Compare the decoded bits with the transmitted bits to estimate BER using the inbuilt biterr() function of MATLAB.
    
11. Plot the BER vs SNR curves.
    
    The BER curves look like this:
    
    
    
    We can observe the waterfall trend. Also, we observe that user 2 has slightly higher BER than user 1, especially in the low SNR regime. This is because user 2 has to do SIC. While performing SIC, user 2 must first estimate user 1's data from y. If this estimate is wrong, then, this error will reflect in the decoding of its own information because the wrong data would be subtracted from y. In other words, user 2 must decode both user 1's data and its own data correctly. Any error in decoding user 1's data or its own data will impact its BER. That is why user 2 experiences higher BER than user 1.
    
    

    MATLAB code

    Here is the MATLAB code used in this example. You can also download it as a .m file here.
    clc; clear variables; close all;
    
    N = 10^5; %Number of monte carlo simulations
    SNR = 0:30; %SNR range in dB
    snr = db2pow(SNR); %SNR range in linear scale
    
    %Generate random data bits for transmission
    x1 = randi([0 1],1,N); %Data bits of user 1
    x2 = randi([0 1],1,N); %Data bits of user 2
    
    %Do BPSK modulation of data
    xmod1 = 2*x1 - 1;
    xmod2 = 2*x2 - 1;
    
    %Set power weights for users
    a1 = 0.75; a2 = 0.25;
    
    %Do superposition coding
    x = sqrt(a1)*xmod1 + sqrt(a2)*xmod2;
    
    %Add AWGN to x (Transmit x through an AWGN channel)
    for u = 1:length(snr)
    y1 = awgn(x,SNR(u),'measured'); %Received signal at user 1 corrupted by AWGN
    y2 = awgn(x,SNR(u),'measured'); %Received signal at user 2 corrupted by AWGN
    
    %AT USER 1
    %Direct decoding of x from y1
    x1_hat = ones(1,N); %just a buffer
    x1_hat(y1 < 0) = 0; %AT USER 2 %Direct decoding of x from y2 x11_est = ones(1,N); %just a buffer x11_est(y2 < 0) = 0; %Estimate user 1's signal first x11_est(x11_est == 0) = -1; %Remodulate user 1's signal %Subtract remodulated x11_est component from y2 rem = y2 - sqrt(a1)*x11_est; %Decode x2 from rem x2_hat = zeros(1,N); x2_hat(rem>0) = 1;
    
    %Estimate BER
    ber1(u) = biterr(x1,x1_hat)/N;
    ber2(u) = biterr(x2,x2_hat)/N;
    end
    
    %plot BER curves
    semilogy(SNR, ber1, 'linewidth', 1.5); hold on;
    semilogy(SNR, ber2, 'linewidth', 1.5); grid on;
    legend('User 1 \alpha_1 = 0.75','User 2 \alpha_2 = 0.25');
    xlabel('SNR (dB)');
    ylabel('BER');
    title('BER graph for NOMA in AWGN channel');
    
    In our next post, we will see BER simulation of NOMA in a Rayleigh fading channel, where the users have different channels and are located at different distances from the BS, which is a more realistic case. Thank you!