We investigate the Peak-Power Limited (PPL) Additive White Gaussian Noise (AWGN) channels in which the signal is band-limited, and its instantaneous power cannot exceed the power P. This model is relevant to many communication systems; however, its capacity is still unknown. We use a new geometry-based approach which evaluates the maximal entropy of the transmitted signal by assessing the volume of the body, in the space of Nyquist-rate samples, comprising all the points the transmitted signal can reach. This leads to lower bounds on capacity which are tight at high Signal to Noise Ratios (SNR). We found lower bounds on capacity, expressed as power efficiency, higher than the known ones by a factor of 3.35 and 8.6 in the low pass and the band pass cases respectively. The gap to the upper bounds is reduced to a power ratio of 1.5. The new bounds are numerically evaluated for FDMA-style signals with limited duration and also derived in the general case as a conjecture. The penalty in power efficiency due to the peak power constraint is roughly 6 dB at high SNR. Further research is needed to develop effective modulation and coding for this channel.

翻译：本文研究了峰值功率受限的加性高斯白噪声信道，其中信号带宽受限且瞬时功率不得超过功率P。该模型适用于多种通信系统，但其容量至今未知。我们采用一种基于几何学的新方法，通过评估奈奎斯特采样率空间中传输信号可达点集构成的体积，来计算传输信号的最大熵。由此导出的容量下界在高信噪比条件下是紧致的。研究发现，在低通与带通情形下，以功率效率表示的容量下界分别比已知结果提高了3.35倍和8.6倍。与容量上界的差距缩小至功率比1.5倍。新边界针对有限持续时间的频分多址类信号进行了数值计算，并在一般情形下以猜想形式给出理论推导。在高信噪比条件下，峰值功率约束导致的功率效率损失约为6分贝。未来需进一步研究适用于此类信道的有效调制与编码方案。