FFT reconstruction of signals from MIMO sampled data

This paper introduces an innovative approach for signal reconstruction using data acquired through multi-input-multi-output (MIMO) sampling. First, we show that it is possible to perfectly reconstruct a set of periodic band-limited signals $\{x_r(t)\}_{r=1}^R$ from the samples of $\{y_m(t)\}_{m=1}^M$, which are the output signals of a MIMO system with inputs $\{x_r(t)\}_{r=1}^R$. Moreover, an FFT-based algorithm is designed to perform the reconstruction efficiently. It is demonstrated that this algorithm encompasses FFT interpolation and multi-channel interpolation as special cases. Then, we investigate the consistency property and the aliasing error of the proposed sampling and reconstruction framework to evaluate its effectiveness in reconstructing non-band-limited signals. The analytical expression for the averaged mean square error (MSE) caused by aliasing is presented. Finally, the theoretical results are validated by numerical simulations, and the performance of the proposed reconstruction method in the presence of noise is also examined.