EM-aided AMP for sparse channel recovery and ranging in nakagami-m fading

Accurate recovery of sparse channels and line-ofsight (LoS) distances is essential for integrated sensing and communications (ISAC). Conventional approximate message passing (AMP) approaches typically adopt Gaussian or Bernoulli– Gaussian priors, which fail to capture realistic fading and lead to biased amplitude estimates. We propose an Expectation– Maximization aided AMP (EM–AMP) framework tailored to the Nakagami-m prior. A closed-form denoiser is derived and embedded in the EM loop, enabling the average path power to be learned directly from data. On top of this, a hybrid estimator combines AMP-based probabilistic support detection with a leastsquares refit, mitigating shrinkage bias and sharpening power– delay profiles for robust ranging. Monte Carlo simulations show that while greedy algorithms like OMP achieve low residual channel errors, they suffer from severe amplitude bias and missed paths under Nakagami-m fading. The proposed EM-AMP framework improves support recall and reduces the ranging meansquared error (MSE) by approximately 3 dB at high SNRs, making it highly robust for practical ISAC deployments.