Vandermonde invariance transformation

In this article we introduce a novel multiple-input-multiple-output (MIMO) spatial filter (SF) which can be applied as a preprocessing scheme to uniform linear arrays, preserving the Vandermonde structure of the steering vectors while changing the amplitude and the phase gradient of the steering vector in a nonlinear fashion. The new scheme is therefore titled Vandermonde Invariance Transformation. The introduced degrees of freedom due to this preprocessing transformation can be used to beneficially influence the properties of the channel to achieve an enhanced performance of the subsequent signal processing algorithm. 1. INTRODUCTORY MOTIVATION Some years ago the application of antenna arrays has been proposed for mobile communication systems to attain an increase in capacity and interference reduction by additionally exploiting the spatial separation of the mobile users. Using more then one antenna for the receiver and/or sender provokes a noticeable increase of the system performance by achieving antenna gain, enhanced interference cancellation, and also transmitreceive diversity. Exploiting these properties requires the knowledge of the channel. Therefore channel estimation has to be applied to determine the parameters of the channel. These channel estimation schemes work better for higher signal-to-noise ratios (SNR). To this end preprocessing schemes can be applied to the antenna output to amplify the user signal over the noise and interference. The most commonly used structure of an antenna array is the Uniform Linear Array (ULA). In this case M antennas are arranged in a line with equal distance to their neighboring antennas. Assuming L different propagation paths impinging at a ULA with M antennas under the influence of additive, possibly colored noise produces the data model