Bit error probability and capacity bound of OFDM systems in deterministic doubly-selective channels

Doubly-selective channels, such as those that occur when the transmitter and the receiver move relative to each other at high speeds, are a key scenario for fifth generation (5G) cellular systems, which are mostly based in the use of the orthogonal frequency-division multiplexing (OFDM) modulation. In this paper, we consider an OFDM system using quadrature amplitude modulation (QAM) symbols and we show that, when transmitting over deterministic doubly-selective channels, the inter-carrier interference (ICI) affecting a symbol can be well approximated by a complex-valued normal distribution. Based on this, we derive a lower bound for the link capacity using the Shannon-Hartley theorem. Finally, we provide an approximation of the bit error probability (BEP) using the well-known BEP expressions for Gray-coded QAM constellations over additive white Gaussian noise (AWGN) channels, and show numerical results that confirm that the proposed BEP expression approximates accurately the bit error ratio (BER) of the OFDM system for standardized channel models. The proposed closed-form analytical expressions for the capacity and the BEP do not only allow for discarding the need of computationally-costly Monte-Carlo system simulations, but also provide a theoretical framework to optimize the system parameters directly impacting on the achievable performance.