QPSK offers double the data rate of BPSK while maintaining a similar bit error rate at low SNR when Gray coding is used. It shares spectral efficiency with 4-QAM and can outperform 4-QAM or 16-QAM in very noisy channels. QPSK is widely used in practical wireless systems, often alongside QAM in adaptive modulation schemes [Read more...]
Gray code is a binary numeral system where two successive values differ in only one bit. This property is called the single-bit difference or unit distance code. It is also known as reflected binary code.
Let's convert binary 111 to Gray code:
Binary bits:
B = 1 1 1Apply the rule:
G[0] = B[0] = 1
G[1] = B[1] XOR B[0] = 1 XOR 1 = 0
G[2] = B[2] XOR B[1] = 1 XOR 1 = 0Gray code:
G = 1 0 0
MATLAB Code
clear all;
close all;
% Set parameters for QAM
snr_dB = -20:2:20; % SNR values in dB
qam_orders = [4, 16, 64, 256]; % QAM modulation orders
% Loop through each QAM order and calculate theoretical BER
figure;
for qam_order = qam_orders
% Calculate theoretical BER using berawgn for QAM
ber_qam = berawgn(snr_dB, 'qam', qam_order);
% Plot the results for QAM
semilogy(snr_dB, ber_qam, 'o-', 'DisplayName', sprintf('%d-QAM', qam_order));
hold on;
end
% Set parameters for QPSK
EbNoVec_qpsk = (-20:20)'; % Eb/No range for QPSK
SNRlin_qpsk = 10.^(EbNoVec_qpsk/10); % SNR linear values for QPSK
% Calculate the theoretical BER for QPSK using the provided formula
ber_qpsk_theo = 2*qfunc(sqrt(2*SNRlin_qpsk));
% Plot the results for QPSK
semilogy(EbNoVec_qpsk, ber_qpsk_theo, 's-', 'DisplayName', 'QPSK (Theoretical)');
hold on;
% Set parameters for BPSK
EbNoVec_bpsk = (-20:20)'; % Eb/No range for BPSK
% Calculate the theoretical BER for BPSK using the provided formula
ber_bpsk_theo = (1/2) * erfc(sqrt(10.^(EbNoVec_bpsk/10)));
% Plot the results for BPSK
semilogy(EbNoVec_bpsk, ber_bpsk_theo, 'x-', 'DisplayName', 'BPSK (Theoretical)');
hold on;
% Add labels, legend, and grid
title('BER vs SNR for Various Modulation Schemes');
xlabel('SNR (dB)');
ylabel('Bit Error Rate (BER)');
grid on;
legend('Location', 'best');
% Set y-axis limits
ylim([1e-6, 1e0]);
Copy the MATLAB Code from here
Output
Are QPSK and 4-PSK same?
QPSK (Quadrature Phase Shift Keying) and 4-PSK (4-Phase Shift Keying) are related but not exactly the same.
QPSK (Quadrature Phase Shift Keying): In QPSK, each symbol represents 2 bits of data. It modulates the carrier signal by changing its phase with four possible values (0°, 90°, 180°, 270°) corresponding to four different states. These four states can be represented in a constellation diagram with points at (1,1), (-1,1), (-1,-1), and (1,-1). Each symbol represents a combination of two bits, where one pair of bits represents the in-phase component and the other pair represents the quadrature component.
4-PSK (4-Phase Shift Keying): 4-PSK is a more general term that refers to any Phase Shift Keying modulation with 4 different phase shifts. This could include QPSK as a specific case. However, 4-PSK might also refer to modulation schemes where each symbol represents only one bit of data, unlike QPSK where each symbol represents 2 bits. In a 4-PSK constellation, there are still four points, but they might not correspond to the same bit combinations as in QPSK.
So, while QPSK is a specific form of 4-PSK, not all 4-PSK schemes are QPSK. The distinction lies in how many bits each symbol represents and how the phase shifts are utilized.