In this paper, we study a multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system where one multi-antenna base station (BS) sends information to a user with multiple antennas in the downlink and simultaneously senses the location parameter of a target based on its reflected echo signals received back at the BS receive antennas. We focus on the case where the location parameter to be sensed is unknown and random, for which the prior distribution information is available for exploitation. First, we propose to adopt the posterior Cramér-Rao bound (PCRB) as the sensing performance metric with prior information, which quantifies a lower bound of the mean-squared error (MSE). Since the PCRB is in a complicated form, we derive a tight upper bound of it to draw more insights. Moreover, we analytically show that by exploiting the prior distribution information, the PCRB is always no larger than the CRB averaged over random location realizations without prior information exploitation. Next, we formulate the transmit covariance matrix optimization problem to minimize the sensing PCRB under a communication rate constraint. We obtain the optimal solution and derive useful properties on its rank. Then, by considering the derived PCRB upper bound as the objective function, we propose a low-complexity suboptimal solution in semi-closed form. Numerical results demonstrate the effectiveness of our proposed designs in MIMO ISAC systems exploiting prior information.

中文翻译：

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利用先验信息的 MIMO 综合传感和通信


在本文中，我们研究了一种多输入多输出（MIMO）集成传感与通信（ISAC）系统，其中一个多天线基站（BS）通过下行链路中的多个天线向用户发送信息，并同时感知位置根据 BS 接收天线接收到的反射回波信号来确定目标的参数。我们关注要感测的位置参数未知且随机的情况，对于这种情况，先验分布信息可用于利用。首先，我们建议采用后验 Cramér-Rao 界（PCRB）作为具有先验信息的传感性能指标，它量化了均方误差（MSE）的下界。由于 PCRB 的形式很复杂，我们推导出它的严格上限以得出更多见解。此外，我们分析表明，通过利用先验分布信息，PCRB 始终不大于在没有先验信息利用的情况下在随机位置实现上平均的 CRB。接下来，我们制定传输协方差矩阵优化问题，以在通信速率约束下最小化感测 PCRB。我们获得最佳解决方案并得出其等级的有用属性。然后，通过将导出的 PCRB 上限视为目标函数，我们提出了半封闭形式的低复杂度次优解。数值结果证明了我们在利用先验信息的 MIMO ISAC 系统中提出的设计的有效性。