Compressed Sensing-Based Sparse Spatial Channel Estimation under IQ Imbalance

Compressive sensing (CS) enables fast spatial channel estimation in millimeter-wave and terahertz systems by leveraging the sparsity of the channel in the angle-domain. CS measurements, however, are often distorted by in-phase and quadrature-phase (IQ) imbalance at the oscillator, leading to a model mismatch. In this paper, we study how this mismatch impacts the channel estimated with a standard CS algorithm. Next, we develop an augmented CS model to jointly estimate the sparse channel and the IQ imbalance parameter. The sparse vector in our model comprises the channel as well as the IQ imbalance parameter. We show that this vector exhibits group sparsity, which is exploited using our custom paired-support orthogonal matching pursuit (PSOMP) algorithm. Finally, the estimate is decomposed to determine the channel and the IQ imbalance parameter. We provide support recovery guarantees for our PSOMP algorithm, highlighting the impact of IQ imbalance on channel recovery. Numerical results show that our method achieves better support recovery and lower error in the estimated channel than the baselines.