Channel Estimation Using Compressed Sensing with Comparative Analysis

This simulation code demonstrates channel estimation using compressed sensing methodology, with comprehensive comparisons against traditional Least Squares (LS) and Minimum Mean Square Error (MMSE) algorithms. The implementation incorporates sparse signal recovery algorithms such as orthogonal matching pursuit (OMP) or basis pursuit for compressed sensing reconstruction. Key functions include measurement matrix generation (typically random Gaussian/Bernoulli matrices), sparse channel modeling in transformed domains (DCT/Wavelet), and performance metrics calculation (MSE, BER). The simulation framework evaluates compressed sensing performance under various sparsity levels and signal-to-noise ratio conditions, analyzing computational complexity and estimation accuracy trade-offs between the three algorithms. Results include comparative plots of estimation error versus pilot numbers and SNR, demonstrating compressed sensing advantages in under-sampled scenarios where traditional methods require more training symbols.