Generalized mutual information (GMI) is used to compute achievable rates for fading channels with various types of channel state information at the transmitter (CSIT) and receiver (CSIR). The GMI is based on variations of auxiliary channel models with additive white Gaussian noise (AWGN). One variation is based on reverse channel models that give the largest rates but are challenging to optimize. A second variation is for receivers unaware of the CSIT where adaptive symbols achieve capacity. The GMI is then based on forward models with inputs that are linear functions of the adaptive symbol's entries. For scalar channels, the maximum GMI is achieved by a conventional codebook, and where the amplitude and phase of each channel symbol are modified based on the CSIT. A third variation partitions the channel output alphabet and has a different auxiliary model for each subset of the partition. The partitioning helps to determine the capacity scaling at high signal to noise ratios. A class of power control policies is described for partial CSIR, including a truncated minimum mean square error policy for full CSIT. Several examples for fading channels with AWGN illustrate the theory, with a focus on on-off fading and Rayleigh fading. The capacity results generalize to block fading channels with in-block feedback, including capacity expressions based on mutual information and directed information.

翻译：广义互信息（GMI）被用于计算在发射端（CSIT）与接收端（CSIR）具有不同类型信道状态信息时衰落信道的可达速率。该GMI基于含加性高斯白噪声（AWGN）的辅助信道模型的变体。一种变体基于逆向信道模型，该模型能提供最大速率但优化困难；第二种变体适用于接收端未知CSIT的场景，其中自适应符号可实现容量。此时GMI基于前向模型，其输入为自适应符号分量的线性函数。对于标量信道，最大GMI由传统码本实现，且每个信道符号的幅度与相位可根据CSIT进行调整。第三种变体对信道输出字母表进行划分，并为每个子集建立不同的辅助模型。这种划分有助于确定高信噪比下的容量标度律。针对部分CSIR情形，本文提出一类功率控制策略，包括针对完全CSIT的截断最小均方误差策略。通过多个含AWGN的衰落信道实例（重点分析通断衰落与瑞利衰落）对理论进行验证。容量结果可推广至含块内反馈的块衰落信道，包括基于互信息与定向信息的容量表达式。