# Location Information-Assisted Robust Beamforming Design for Ultra-Wideband Communication Systems
## 1 Introduction
proposed a time-domain beamforming algorithm that adaptively guides the array beam by estimating the direction of arrival of the signal and adjusting the corresponding time delay. Considering the nanosecond duration of the UWB pulse signal in the time domain, a least-squares-based beamforming achieved by taking full advantage of frequency invariance was proposed in [15]. Based on the geometry of the UWB antenna array, a new pointing beam was proposed to eliminate other interferences in the same frequency [16]. However, for multi-user communication systems, the performance of the proposed directional beamforming (OBF) technology was seriously degraded. A nonlinear OBF technique based on an improved radial basis function neural network was proposed in [17], which could effectively eliminate the interference caused by directional UWB. However, the array elements of the two antennas needed to be matched one by one; consequently, the implementation complexity of the system was high. It is still worth pointing out that most of the systems designed in the literature implement communication and location functions independently, which leads to a waste of spectrum resources. At present, some researchers have paid more and more attention to location information-assisted communication, namely the use of location estimation information to improve the system capacity, thus improving the Quality of Service (QoS) of communication services [18]. The joint optimization problem of maximizing the total rate under the localization constraint and minimizing the localization error under the communication constraint was presented in a large-scale MIMO system, and the results showed that high data rate communication and mobile 3D localization can be achieved simultaneously [19]. A joint location and beamforming scheme was proposed to jointly estimate the user's position and instantaneous CSI, and then to optimize the beamforming vector according to the estimated results [20]. The existing research mainly use the estimated user location information to assist the communication process and then improve the communication quality. The common method is to take the location estimation as a constraint in order to maximize the communication rate. However, the coupling relationship between communication and location has not been considered in the existing research, and the impact of the location estimation error on CSI estimation and the communication rate has not been taken into account. In this paper, we will make use of the inherent coupling relationship between communication rate and positioning accuracy, robust beamforming is designed by introducing CSI estimation error in the presence of multipath interference. The mechanism mainly consists of two key components. For the location, a weighted least squares (WLS) localization algorithm using reference point coordinate information is proposed. Combined with Taylor expansion and multipath information, an approximate CSI estimation error distribution is derived from the user position error distribution constructed by the Cramer-Rao Lower Bound (CRLB). On this basis, a robust beamforming optimization problem to minimize the total transmit power is formulated. Since the non-convex optimization problem is difficult to solve, a suboptimal method based on the Bernstein-type inequality and SDR is proposed. More specifically, robust beamforming is accomplished by converting the SINR probability constraint into a deterministic constraint and by transforming the unsolvable nonconvex problem into a solvable convex problem.