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) and circularly-symmetric complex Gaussian inputs. One variation uses reverse channel models with minimum mean square error (MMSE) estimates that give the largest rates but are challenging to optimize. A second variation uses forward channel models with linear MMSE estimates that are easier to optimize. Both model classes are applied to channels where the receiver is unaware of the CSIT and for which adaptive codewords achieve capacity. The forward model inputs are chosen as linear functions of the adaptive codeword's entries to simplify the analysis. For scalar channels, the maximum GMI is then achieved by a conventional codebook, where the amplitude and phase of each channel symbol are modified based on the CSIT. The GMI increases by partitioning the channel output alphabet and using a different auxiliary model for each partition subset. The partitioning also helps to determine the capacity scaling at high and low signal-to-noise ratios. A class of power control policies is described for partial CSIR, including a MMSE policy for full CSIT. Several examples of fading channels with AWGN illustrate the theory, focusing on on-off fading and Rayleigh fading. The capacity results generalize to block fading channels with in-block feedback, including capacity expressions in terms of mutual and directed information.

翻译：广义互信息（GMI）被用于计算在发射机（CSIT）和接收机（CSIR）具备不同类型信道状态信息时衰落信道的可达速率。GMI基于加性高斯白噪声（AWGN）和循环对称复高斯输入的辅助信道模型变体。一种变体采用基于最小均方误差（MMSE）估计的反向信道模型，该模型能实现最大速率但优化困难。第二种变体采用基于线性MMSE估计的前向信道模型，更易于优化。两类模型均应用于接收机不知晓CSIT且自适应码字可达容量的信道。为简化分析，前向模型输入被选为自适应码字条目的线性函数。对于标量信道，最大GMI可通过传统码本实现，其中每个信道符号的幅度和相位根据CSIT进行调整。通过划分信道输出字母表并对每个分区子集使用不同的辅助模型，GMI得以提升。这种划分还有助于确定高、低信噪比下的容量标度。针对部分CSIR，描述了一类功率控制策略，包括全CSIT下的MMSE策略。多个AWGN衰落信道（重点包括通断衰落和瑞利衰落）的实例验证了该理论。容量结果可推广至带块内反馈的块衰落信道，包括基于互信息和有向信息的容量表达式。