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Achievable Rate Analysis of Millimeter Wave Channels with Random Coding Error Exponent

Millimeter Wave (mmWave) communication has attracted massive attentions, since the abundant available bandwidth can potentially provide reliable communication with orders of magnitude capacity improvements relative to microwave. However, the achievable rate of mmWave channels under latency and reliability constraints is still not quite clear. We investigate the achievable rates of mmWave channels by random coding error exponent (RCEE) with finite blocklength. With imperfect channel state information at the receiver, the exact and approximate analytical expressions of the training based maximum achievable rate are derived to capture the relationship among rate-latency-reliability. Additionally, the relationship between the training based maximum achievable rate and bandwidth is investigated. We show that there exists critical bandwidth to maximize the training based maximum achievable rate for the non-line-of-sight (NLoS) propagation. Numerical results show that the approximate expression of the training based maximum achievable rate are tight and can capture the tendency at low SNRs. In addition, results show that for a given rate, one can reduce both packet duration and decoding error probability by increasing bandwidth. Results also suggest that in some mmWave bands, e.g. 57–64 GHz band, the performance, i.e., Gallager function, is significantly affected by frequency selective power absorption.