Robust Design of Widely Linear Pre-Equalization Filters for Pre-Rake UWB Systems

Pre-rake ultra-wideband (UWB) systems are appealing for UWB communications applications which include devices with different processing capabilities so that signal processing complexity need to be shifted from the receiver of one or more devices to the transmitter of another. Recently, basic pre-rake schemes have been extended to include full pre-equalization, multiple-antenna, and multi-user interference processing. All these design approaches for pre-rake UWB systems have relied on the availability of accurate channel state information (CSI) at the transmitter. However, uncertainties in the acquisition of CSI can drastically affect the overall system performance. Therefore, in this paper, we present robust design methods for pre-equalization filters (PEFs) for pre-rake UWB systems that take CSI uncertainties into account. We treat the general case of a broadcast (i.e., multiuser) pre-rake UWB system, which includes single-user communication often considered in literature as a special case. For this general setting, we derive new PEF designs that improve system performance with imperfect CSI. Similar to the literature on robust filter designs for multiple-input multiple output (MIMO) systems, we consider two uncertainty models, namely stochastic and bounded uncertainty, which correspond to different performance optimization paradigms, and we adjust these according to channel estimation of UWB channels. As most of previous work on (pre-rake) UWB, we focus on binary transmission. We argue that widely linear filter design should be applied in this case and thus extend the robust filter design methodology accordingly. Our numerical results for typically UWB test channels demonstrate the efficacy of the proposed design procedures to achieve reliable communication in multiuser pre-rake UWB systems.