Spreading Code Generation in CDMA and Its Auto-correlation and Cross-correlation Properties

In wireless communication systems, spreading codes serve as a vital component of CDMA (Code Division Multiple Access) systems. These codes determine the uniqueness of CDMA signals and are essential for mitigating mutual interference among users in CDMA networks. Spreading codes can be generated using methods based on channel encoders or pseudorandom code generators, with the latter being the most commonly employed approach in practice. Pseudorandom code generation typically utilizes Linear Feedback Shift Registers (LFSRs) with specific polynomial configurations to produce sequences like Gold codes or Walsh codes. The performance of spreading codes is primarily evaluated through their auto-correlation and cross-correlation properties. Auto-correlation measures the similarity between a code and its time-shifted version, while cross-correlation quantifies the similarity between different codes. For optimal CDMA system performance, spreading codes should exhibit low auto-correlation sidelobes (except at zero shift) and minimal cross-correlation values. This ensures reliable signal separation, reduces interference, and maintains system stability. Implementation typically involves calculating correlation values using algorithms that perform bitwise XOR operations followed by summation, or by employing Fast Fourier Transform (FFT) methods for efficient computation in frequency domain implementations.