Geometry-Based Bounds on the Capacity of Peak-Limited and Band-Limited Signals over the Additive White Gaussian Noise Channel at a High SNR

We present a new computable geometry-based upper bound on the capacity of peak-power-limited and band-limited signal over the Additive White Gaussian Noise Channel. The peak limit applies at continuous time. The bound is a function of the volume and shape of the transmitted signal set, namely the body, in the space of Nyquist-rate samples, comprising all of the points the transmitted signal can reach. At a high SNR, the bound is tight, better than previously known upper bounds and, together with a known lower bound, provides the capacity at an asymptotically high SNR. We found, using a numerical evaluation, the high-SNR capacity of signals with the structure used in Cyclic Prefix assisted Frequency Domain Equalization (CP-FDE) and OFDM for sequence length of up to 100 Nyquist intervals, and we present a conjecture that this result is correct for any sequence length and does not depend on the CPA-FDE structure. This paper extends the methodology developed in previous works. The penalty in power efficiency at a high SNR due to the peak power constraint relative to an average power constraint is about 7.5 dB in the low-pass case and about 5.4 dB in the band-pass case.