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How Beamforming Improves SNR

The mathematical [↗] and theoretical aspects of beamforming [↗] have already been covered. We'll talk about coding in MATLAB in this tutorial so that you may generate results for different beamforming approaches. Let's go right to the content of the article.

In analog beamforming, certain codebooks are employed on the TX and RX sides to select the best beam pairs. Because of their beamforming gains, communication created through the strongest beams from both the TX and RX side enhances spectrum efficiency. Additionally, beamforming gain directly impacts SNR improvement.

Wireless communication system capacity = bandwidth*log2(1+SNR) bits/s.

Thus, the capacity or overall throughput of the system increases.

MATLAB Script

%Written by Salim Wireless %Visit www.salimwireless.com for study materials on wireless communication %or, if you want to learn how to code in MATLAB clear all; close all; clc; % System paramters Num_TX = 16; % number of Tx antennas Num_RX = 16; % number of Rx antennas Num_DataStream = 1; % no of simultaneous data streams Num_Cluster = 8; % no of scattering cluster Num_Ray = 10; % propagation paths in a cluster %Typically, angular spread covers the whole zone of communication thru beamsteering %For example, for first instinct of time it covers 0 to 10 degree angular area %Then covers 10 degree to 20 degree and so on. Angular_spread = 10 * pi / 180; % angular spread of 10 degrees j = sqrt(-1); % k * d (By using mathematics we get that relation of wave number) kd = pi; % k*d = 2*pi/lambda*d = 2*pi/lambda * (0.5*lambda) = pi % tx angle range % Azimuth angular coverage is similar to horizontal angular coverage % Evevation angular coverage is similar to verticle angular coverage azimuth_angle_tx_min = 0; azimuth_angle_tx_max = 60*pi/180; % azimuth (horizontal) angle range : [0~60] elevation_angle_tx_min = 0; elevation_angle_tx_max = 20*pi/180; % elevation (verticle) angle range : [0~20] % rx angle range azimuth_angle_rx_min = 0; azimuth_angle_rx_max = 360*pi/180; % azimuth angle range: [0~360] elevation_angle_rx_min = 0; elevation_angle_rx_max = 360*pi/180; % elevation angle range: [0~360] % SNR range SNR_dB = -40:5:0; % SNR range in dB SNR_inRatio = 10.^(SNR_dB/10); % SNR range in linear power N = 5000; % number of random channel realizations % As channel matrix H equivalent to % Normalization factor for adding contributions from multi-paths % AOA, AOD, and their normalized vector gain % H = gamma * alpha(i,r) * ar * at'; % alpha denotes normalized angular vector gain gamma = sqrt((Num_TX*Num_RX)/(Num_Cluster*Num_Ray)); % normalization factor % Tx/Rx antenna array response vector ygv=0:sqrt(Num_TX)-1; zgv=0:sqrt(Num_TX)-1; [Yt,Zt] = meshgrid(ygv,zgv ); % replicates the grid vectors ygv and zgv to produce the coordinates of a rectangular grid (Yt,Zt) [Yr,Zr] = meshgrid(0:sqrt(Num_RX)-1, 0:sqrt(Num_RX)-1); % Spectral Efficiency Spectral_Efficiency = zeros(length(SNR_dB),N); % for SNR loop for SNRLoop = 1 : length(SNR_dB) SNR = SNR_inRatio(SNRLoop); % random channel realization for n = 1 : N % Generate random angle mean azimuth_angle_tx_mean = azimuth_angle_tx_min + (azimuth_angle_tx_max - azimuth_angle_tx_min)*rand(Num_Cluster,1); % uniform random in [min, max] % 'rand' generates random values from 0 to 1 % e.g., 0.5, 0.833, 0.936, etc. elevation_angle_tx_mean = elevation_angle_tx_min + (elevation_angle_tx_max - elevation_angle_tx_min)*rand(Num_Cluster,1); azimuth_angle_rx_mean = azimuth_angle_rx_min + (azimuth_angle_rx_max - azimuth_angle_rx_min)*rand(Num_Cluster,1); elevation_angle_rx_mean = elevation_angle_rx_min + (elevation_angle_rx_max - elevation_angle_rx_min)*rand(Num_Cluster,1); azimuth_angle_tx = zeros(Num_Cluster,Num_Ray); elevation_angle_tx = zeros(Num_Cluster,Num_Ray); azimuth_angle_rx = zeros(Num_Cluster,Num_Ray); elevation_angle_rx = zeros(Num_Cluster,Num_Ray); alpha = zeros(Num_Cluster,Num_Ray); At = []; Ar = []; H = zeros(Num_RX,Num_TX); % Nr x Nt matrix H for i = 1:Num_Cluster % for each cluster i azimuth_angle_tx(i,:) = laprnd(1,Num_Ray,azimuth_angle_tx_mean(i),Angular_spread); % tx elevation_angle_tx(i,:) = laprnd(1,Num_Ray,elevation_angle_tx_mean(i),Angular_spread); azimuth_angle_rx(i,:) = laprnd(1,Num_Ray,azimuth_angle_rx_mean(i),Angular_spread); % rx elevation_angle_rx(i,:) = laprnd(1,Num_Ray,elevation_angle_rx_mean(i),Angular_spread); alpha(i,:) = (randn(1,Num_Ray) + j*randn(1,Num_Ray))/sqrt(2); % gain for r = 1:Num_Ray % for each ray r % array response vector for UPA at = 1/sqrt(Num_TX)*exp(j*kd*(Yt(:)*sin(azimuth_angle_tx(i,r))*sin(elevation_angle_tx(i,r))+Zt(:)*cos(elevation_angle_tx(i,r))));%tx ar = 1/sqrt(Num_RX)*exp(j*kd*(Yr(:)*sin(azimuth_angle_rx(i,r))*sin(elevation_angle_tx(i,r))+Zr(:)*cos(elevation_angle_tx(i,r))));%rx At = [At at]; % A matrix at tx Ar = [Ar ar]; % A matrix at rx H = H + gamma * alpha(i,r) * ar * at'; % adding all rays end end %%% 2. Beam Steering based on maximum ray gain azimuth_angle_tx_col = azimuth_angle_tx(:); % make it as column vector elevation_angle_tx_col = elevation_angle_tx(:); % make it as column vector azimuth_angle_rx_col = azimuth_angle_rx(:); % make column vector elevation_angle_rx_col = elevation_angle_rx(:); % make column vector [~,idx] = sort(abs(alpha(:)), 'descend'); % largest first F_beamsteer = []; W_beamsteer = []; for s=1:Num_DataStream % max Ns of alpha f_beamsteer = 1/sqrt(Num_TX)*exp(j*kd*(Yt(:)*sin(azimuth_angle_tx_col(idx(s)))*sin(elevation_angle_tx_col(idx(s)))+Zt(:)*cos(elevation_angle_tx_col(idx(s))))); F_beamsteer = [F_beamsteer f_beamsteer]; w_beamsteer = 1/sqrt(Num_RX)*exp(j*kd*(Yr(:)*sin(azimuth_angle_rx_col(idx(s)))*sin(elevation_angle_rx_col(idx(s)))+Zr(:)*cos(elevation_angle_rx_col(idx(s))))); W_beamsteer = [W_beamsteer w_beamsteer]; end %%% Calculation of Spectral Efficiency % Rn is noise variance Rn = W_beamsteer'*W_beamsteer; % Similar to C=log2(1+SNR) % Although here 'SNR' is dependent on varoius gain factors Spectral_Efficiency(SNRLoop,n) = real(log2(det(eye(Num_DataStream)+SNR/Num_DataStream*inv(Rn)*W_beamsteer'*H*F_beamsteer*F_beamsteer'*H'*W_beamsteer))); end end figure; plot(SNR_dB, mean(Spectral_Efficiency,2), 'g.-'); hold on; grid on; xlabel('SNR (in dB)'); ylabel('Spectral Efficiency (bits/s/Hz)'); legend('Beam Steering / Analog Beamforming'); web('https://www.salimwireless.com/search?q=beamforming', '-browser'); function r = laprnd(m, n, mu, b) %LAPRND generate Laplacian random numbers % r = laprnd(m, n, mu, b) returns an m-by-n matrix of Laplacian random numbers % with mean mu and scale parameter b. % Uniform random numbers u = rand(m, n) - 0.5; % Laplacian distributed random numbers r = mu - b * sign(u) .* log(1 - 2 * abs(u)); end
 

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