Asymptotics of Multi-fold Vandermonde Matrices with Applications to Communications and Radar Problems

We study the performance of signal estimation and reconstruction systems, that exploit the linear minimum mean square error (LMMSE) technique. This model often occurs in signal processing and wireless communications; some examples are radar applications, MIMO communications, or sensor networks sampling a physical field. Our performance analysis implies the characterization of a random matrix product, involving a multifold Vandermonde matrix with complex exponential entries. We therefore derive the LMMSE by computing the eta-transform of this matrix product, which can be evaluated either by implicit as well as by explicit expression, using the matrix asymptotic moments. Finally, we show how our results can be applied in some cases of practical interest.