Design of a User Spread Spectrum Communication System with Walsh Code DSSS and BPSK Modulation

In this task, we will design a spread spectrum communication system for a single user. The system employs a spreading gain of N=16, utilizing Walsh codes for Direct Sequence Spread Spectrum (DSSS) with BPSK modulation. The entire system operates over an Additive White Gaussian Noise (AWGN) channel.

At the receiver end, we implement despreading, demodulation, and decision operations. Through simulation, we obtain the bit error rate versus signal-to-noise ratio performance results for one user. The implementation involves generating orthogonal Walsh codes using Hadamard matrix transformation and performing correlation-based despreading.

To elaborate our design methodology, let's explain each step in detail.

First, we employ spreading gain N=16 to increase the signal bandwidth using code division multiple access principles. This enhances interference resistance during transmission. The Walsh code generation algorithm creates orthogonal spreading sequences through recursive Hadamard matrix construction, ensuring minimum cross-correlation between codes.

Next, we implement BPSK modulation for the spread spectrum signal. The BPSK modulator maps binary data to phase shifts (0° for '0', 180° for '1') using carrier multiplication. The modulation process can be implemented with I/Q components where I-channel carries the spread signal and Q-channel remains zero.

We then simulate communication over an AWGN channel model. The channel adds white Gaussian noise using random number generation with variance determined by the SNR setting. The noise addition is implemented through mathematical convolution of the transmitted signal with Gaussian-distributed random variables.

At the receiver, we perform three key operations: despreading using correlation detectors, coherent BPSK demodulation with phase recovery, and threshold-based decision making. The despreading operation correlates the received signal with the assigned Walsh code using dot product calculations. Demodulation employs matched filtering and carrier synchronization techniques, while decision circuitry uses zero-threshold comparison for bit estimation.

Finally, we obtain simulation results showing the relationship between bit error rate and signal-to-noise ratio for one user. The BER calculation implements error counting by comparing transmitted and received bits, with SNR sweeps performed through logarithmic scaling. These results enable system performance evaluation and optimization of parameters like spreading factor and modulation scheme.

This explanation outlines our designed spread spectrum communication system with implementation specifics. For further technical clarification or code implementation details, please feel free to inquire.