Reference-Based Recursive Least-Squares Mitigation of Real Interference in Stereo Audio Recordings

Reference-based adaptive interference cancellation is evaluated for stereo audio recordings corrupted by real train noise and environmental background. The observed signal is modeled as a clean stereo program contaminated by an additive disturbance generated by an external acoustic source through unknown propagation paths. A second stereo recording, representing another filtered observation of the same physical noise source, is used as the reference input of a multi-reference recursive least-squares (RLS) estimator. The estimated train-interference component is subtracted from the noisy audio and followed by a finite-impulse-response low-pass postfilter. Three 74.01 s real audio sequences sampled at 11.025 kHz are processed under identical algorithmic parameters. Since clean ground truth is not available, performance is assessed with no-reference indicators: waveform behavior, Welch spectral estimates, RMS change, and residual normalized correlation with the reference. With 30 taps per reference channel, 15 anti-causal taps, and forgetting factor 0.999, the maximum reference correlation is reduced from 0.386--0.832 before processing to 0.011--0.016 after processing. The corresponding correlation-ratio reduction is approximately 30.6--34.1 dB, while the output RMS decreases by 1.8--4.8 dB depending on section and stereo channel. The results demonstrate that real train interference, including environmental acoustic effects, can be substantially attenuated when a correlated reference recording is available.

Pilot-Aided MIMO Channel Identification and Linear Deconvolution in Correlated Gaussian Noise

This paper presents a pilot-aided study of multiple-input multiple-output (MIMO) channel identification and linear deconvolution under spatially correlated Gaussian noise. A real-valued $4\times4$ baseband model is analyzed for both memoryless and finite-impulse-response channels. The noise process is generated from a Toeplitz covariance matrix, the channel is estimated from pilot symbols through maximum-likelihood/least-squares formulations, and the empirical mean-square error is compared with the Cramer--Rao bound. The estimated channel is then used for data-symbol recovery through maximum-likelihood zero-forcing and linear minimum-mean-square-error deconvolution. The results show that sufficiently long and well-conditioned pilot blocks allow the channel estimator to approach the theoretical lower bound, whereas short training intervals cause rank and conditioning limitations, especially for the four-tap model. The deconvolution experiments further show that MMSE regularization provides a more stable inverse than unregularized zero forcing at low signal-to-noise ratios and for inaccurate channel estimates.