A communication setup is considered where a transmitter wishes to convey a message to a receiver and simultaneously estimates the state of that receiver through a common waveform. The state is estimated at the transmitter by means of generalized feedback, i.e., a strictly causal channel output, and the known waveform. The scenario at hand is motivated by joint radar and communication, which aims to co-design radar sensing and communication over a shared spectrum and hardware. For the case of memoryless single receiver channels with i.i.d. time-varying state sequences, we fully characterize the capacity-distortion tradeoff, defined as the largest achievable rate below which a message can be conveyed reliably while satisfying some distortion constraints on state sensing. We propose a numerical method to compute the optimal input that achieves the capacity-distortion tradeoff. Then, we address memoryless state-dependent broadcast channels (BCs). For physically degraded BCs with i.i.d. time-varying state sequences, we characterize the capacity-distortion tradeoff region as a rather straightforward extension of single receiver channels. For general BCs, we provide inner and outer bounds on the capacity-distortion region, as well as a sufficient condition when this capacity-distortion region is equal to the product of the capacity region and the set of achievable distortions. A number of illustrative examples demonstrate that the optimal co-design schemes outperform conventional schemes that split the resources between sensing and communication.
翻译:在发送者希望通过共同波形向接收者传递信息并同时估计该接收者状态的情况下,即考虑通信设置;在发送者希望通过共同波形向接收者传递信息时,即通过一般反馈,即纯粹因果通道输出和已知波形,对接收者状况进行估计;在手边的情景是联合雷达和通信,目的是共同设计共享频谱和硬件的雷达感应和通信;对于无记忆的单一接收者渠道,即:d.时间变化状态序列,我们充分将能力扭曲交易完全定性为一个相当直接的单一接收渠道的延伸;在满足对州感的某些扭曲限制的同时,可以可靠地传递信息;我们提出了一个数字方法,用以计算最佳投入,实现能力扭曲交易;然后,我们处理无记忆状态的广播频道(BCs),目的是共同设计一个共享频谱和时间变化状态序列,我们把能力扭曲能力扭曲区域描述为单一接收器频道的一个相当直接的扩展点;对于一般的 BCs,我们提供了一种计算方法,用以计算最佳投入最佳投入的内、外向区域展示该可实现的变现产区。