Impact of Multipath on Passband BPSK Modulated Signal Using MATLAB

Multipath Propagation in Wireless Communication

Multipath propagation, a common phenomenon in wireless communication, occurs when transmitted signals reach the receiver via multiple paths due to reflections, diffraction, or scattering from obstacles like buildings, mountains, or trees. These multiple paths result in multiple copies of the same signal, each with a different time delay and potentially varying amplitude, due to the different distances and obstacles encountered.

The constructive interference increases the signal's amplitude, while destructive interference can cause attenuation or fading of the signal. This interference phenomenon is often characterized by a fading channel, where the signal's strength varies unpredictably due to the combined effect of the multipath components.

Furthermore, the channel impulse response (CIR) captures the effects of multipath on the signal, including delays and amplitude variations caused by different propagation paths. The convolution of the transmitted signal with the CIR introduces a time-spread effect, where the received signal is stretched in time, often referred to as delay spread. This can lead to inter-symbol interference (ISI), where symbols interfere with one another, degrading the quality of the received signal.

At Receiver Side:

y(t) = h(t) * x(t) + n(t)

Where:

• y(t): The received signal (distorted due to multipath and noise).
• h(t): The channel impulse response (which models the effect of the channel).
• x(t): The transmitted signal.
• n(t): The noise term, typically assumed to be Gaussian noise.

This convolutional distortion is a key challenge in communication systems, requiring techniques like equalization and diversity to mitigate the effects of multipath propagation.

Impact of Multipath on Passband BPSK Modulated Signal with Continuous Channel Impulse Response (CIR)

% The code is developed by SalimWireless.com clc; clear; close all; L = 3; tau = [0 1e-6 3e-6]; alpha = [1.0 0.6 0.3]; Rb = 1e6; Tb = 1/Rb; fc = 10e6; fs = 100e6; samples_per_bit = fs / Rb; samples_per_bit = round(samples_per_bit); Nbits = 10; Ns = Nbits * samples_per_bit; t = (0:Ns-1)/fs; bits = randi([0 1],1,Nbits); symbols = 2*bits - 1; s_bb = repelem(symbols, samples_per_bit); fd = 50; M = 16; theta_m = 2*pi*(1:M)/M; g = zeros(L, Ns); for k = 1:L psi = 2*pi*rand(1,M); gk = zeros(1, Ns); for m = 1:M gk = gk + exp(1j*(2*pi*fd * t * cos(theta_m(m)) + psi(m))); end gk = gk / sqrt(M); gk = gk / sqrt(mean(abs(gk).^2)); g(k, :) = alpha(k) * gk; end y_bb = zeros(1, Ns); n_delays = round(tau * fs); for k = 1:L d = n_delays(k); if d >= Ns continue; end s_shifted = zeros(1, Ns); s_shifted((d+1):end) = s_bb(1:(end-d)); y_bb = y_bb + g(k, :) .* s_shifted; end s_pass = real(s_bb .* exp(1j*2*pi*fc*t)); r_pass = real(y_bb .* exp(1j*2*pi*fc*t)); SNR_dB = 20; r_pass_noisy = awgn(r_pass, SNR_dB, 'measured'); n0 = round(Ns/4); sigma = 0.05e-6; t_h = -0.5e-6 : 0.01e-6 : 5e-6; h_snapshot = zeros(size(t_h)); for k = 1:L h_snapshot = h_snapshot + g(k, n0) * exp(-((t_h - tau(k)).^2)/(2*sigma^2)) / (sigma*sqrt(2*pi)); end figure('Name','Passband BPSK Through Time-Varying Multipath'); subplot(3,1,1); plot(t*1e6, s_pass, 'LineWidth', 1.0); xlim([0 min(10, t(end))*1e6]); xlabel('Time (\mus)'); ylabel('Amplitude'); title('Transmitted Passband BPSK'); grid on; subplot(3,1,2); plot(t_h*1e6, abs(h_snapshot), 'LineWidth', 1.3); xlabel('Delay (\mus)'); ylabel('|h(\tau)|'); title(sprintf('Instantaneous CIR magnitude (t = %.3f ms)', t(n0)*1e3)); grid on; subplot(3,1,3); plot(t*1e6, r_pass_noisy, 'LineWidth', 1.0); xlim([0 min(10, t(end))*1e6]); xlabel('Time (\mus)'); ylabel('Amplitude'); title(sprintf('Received Passband (Rayleigh + AWGN, SNR = %d dB)', SNR_dB)); grid on; figure; plot(t*1e6, r_pass_noisy, 'LineWidth', 1); xlim([0 6]); ylim([-1.5 1.5]); xlabel('Time (\mus)'); ylabel('Amplitude'); title('Received passband (zoom 0–6 µs)'); grid on; web('https://www.salimwireless.com/search?q=fading', '-browser');  

Output

Impact of Multipath on Passband BPSK Modulated Signal with Discrete Channel Impulse Response (CIR)

% The code is developed by SalimWireless.com clc; clear; close all; % -------- Parameters -------- L = 3; % Number of multipaths tau = [0 1e-6 3e-6]; % Path delays (seconds) alpha = [1.0 0.6 0.3]; % Average path gains Rb = 1e6; % Bit rate (1 Mbps) Tb = 1/Rb; % Bit duration fc = 10e6; % Carrier frequency (10 MHz) fs = 100e6; % Sampling frequency (100 MHz) Ts = 1/fs; samples_per_bit = round(fs / Rb); Nbits = 10; Ns = Nbits * samples_per_bit; % -------- BPSK Modulation -------- bits = randi([0 1], 1, Nbits); symbols = 2*bits - 1; % Map 0→-1, 1→+1 s_bb = repelem(symbols, samples_per_bit); t = (0:Ns-1)*Ts; s_pass = s_bb .* cos(2*pi*fc*t); % Passband BPSK % -------- Discrete Multipath Channel -------- phi = 2*pi*rand(1,L); % Random phases n_delay = round(tau / Ts); % Sample delays max_delay = max(n_delay); h = zeros(1, max_delay + 1); for k = 1:L h(n_delay(k)+1) = alpha(k) * exp(1j*phi(k)); end h = h / norm(h); % Normalize channel energy % -------- Convolution (Channel Effect) -------- r_pass = conv(s_pass, real(h), 'same'); % -------- Add AWGN -------- SNR_dB = 20; r_pass_noisy = awgn(r_pass, SNR_dB, 'measured'); % -------- Plot Results -------- figure('Name','Passband BPSK with Discrete CIR'); subplot(3,1,1); plot(t*1e6, s_pass, 'LineWidth', 1.1); xlabel('Time (\mus)'); ylabel('Amplitude'); title('Transmitted Passband BPSK'); grid on; subplot(3,1,2); stem((0:length(h)-1)*Ts*1e6, abs(h), 'filled'); xlabel('Delay (\mus)'); ylabel('|h[n]|'); title('Discrete Channel Impulse Response Magnitude'); grid on; subplot(3,1,3); plot(t*1e6, r_pass_noisy, 'LineWidth', 1.1); xlabel('Time (\mus)'); ylabel('Amplitude'); title(sprintf('Received Passband BPSK After Channel + AWGN (SNR = %d dB)', SNR_dB)); grid on; web('https://www.salimwireless.com/search?q=fading', '-browser');

Output

Further reading

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