Closed-Form Approximation for Performance Bound of Finite Blocklength Massive MIMO Transmission

It is supposed that ultra-reliable low latency communication (uRLLC) would continue to evolve in the future sixth generation (6G) network, to provide enhanced capability towards extreme connectivity, with the aid of well established multiple-input multiple-output (MIMO) technology. Since the latency constraint can be represented equivalently by the blocklength of a codeword, channel coding theory at a finite blocklength plays an important role in theoretic analysis of uRLLC. Based on Polyanskiy’s and Yang’s asymptotic results on maximal achievable rate, we first derive the proximate closed-form expressions for the expectation and variance of channel dispersion. Then, the upper bound of average maximal achievable rate is obtained for massive MIMO systems under ideal independent and identically distributed fading channels. Since almost all the fundamental parameters, including the spatial degree-of-freedom (DoF), are considered, this expression can be viewed as a performance bound of the spatiotemporal two-dimension channel coding to some extent. Moreover, it is shown by simulation and analysis, as the DoF goes to infinity, MIMO systems reveal a nature of deterministic transmission, since the average maximal achievable coding rate per antenna can be achieved at each transmission. In this case, the inversely proportional law observed therein implies that the blocklength in the time domain can be further shortened at the expense of spatial DoF. This exchangeability of space and time, to support a given coding rate, paves a solid and feasible road for us to further reduce latency in 6G uRLLC.