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）被用于计算存在各类发射端信道状态信息（CSIT）和接收端信道状态信息（CSIR）的衰落信道的可达速率。GMI基于具有加性高斯白噪声（AWGN）和循环对称复高斯输入的辅助信道模型的变体。一种变体使用基于最小均方误差（MMSE）估计的反向信道模型，该类模型能提供最大速率但优化难度较大；另一种变体使用基于线性MMSE估计的前向信道模型，其优化相对容易。两类模型均适用于接收端未知CSIT且自适应码字可实现信道容量的场景。为简化分析，前向模型输入被选取为自适应码字元素的线性函数。对于标量信道，最大GMI可通过常规码本实现，其中每个信道符号的幅度和相位均基于CSIT进行调整。通过划分信道输出字母表并对每个划分子集采用不同辅助模型，可提升GMI。这种划分还有助于确定高信噪比与低信噪比下的容量缩放特性。针对部分CSIR场景，本文描述了一类功率控制策略（包括适用于全CSIT的MMSE策略），并通过多个含AWGN的衰落信道示例（重点讨论开关衰落和瑞利衰落）阐释理论。容量结果可推广至含块内反馈的块衰落信道，其容量表达式涉及互信息和有向信息。