Estimation of Wideband Dynamic mmWave and THz Channels for 5G Systems and beyond

Millimeter wave (mmWave) wideband channels in a multiple-input multiple-output (MIMO) transmission are described by a sparse set of impulse responses in the angle-delay, or space-time (ST), domain. These characteristics will be even more prominent in the THz band used in future systems. We consider two approaches for channel estimation: compressed-sensing (CS), exploiting the sparsity in the angular/delay domain, and low-rank (LR), exploiting the algebraic structure of channel matrix. Both approaches share several commonalities, and this paper provides for the first time i) a comparison of the two approaches, and ii) new versions of CS and LR methods that significantly improve performance in terms of mean squared error (MSE), computational complexity, and latency. We derive the asymptotic MSE bound for any estimator of the ST-MIMO multipath channels with invariant angles/delays and time-varying fading, with unknown angle/delay diversity order: the bound also accounts for the degradation introduced by sub-optimal separable channel models. We will show that in the considered scenarios both CS and LR approaches attain the bound. Our performance assessment over ideal and 3^{rd} generation partnership project (3GPP) channel models, suitable for the fifth-generation (5G) and beyond of cellular networks, shows the trade-off obtained by the methods over various metrics: i) CS methods are converging faster than the LR methods, both attaining the asymptotic MSE bound; ii) the CS methods depend on the array manifold, while LR methods are independent of the array calibration; iii) CS solutions are more complex than LR solutions.