Energy Efficiency of Massive Random Access in MIMO Quasi-Static Rayleigh Fading Channels with Finite Blocklength
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This paper considers the massive random access problem in MIMO quasi-static Rayleigh fading channels. Specifically, we derive achievability and converse bounds on the minimum energy-per-bit required for each active user to transmit J bits with blocklength n and power P under a per-user probability of error (PUPE) constraint, in the cases with and without a priori channel state information at the receiver (CSIR and no-CSI). In the case of no-CSI, we consider both the settings with and without knowing the number K_a of active users. The achievability bounds rely on the design of the “good region”. Numerical evaluation shows the gap between achievability and converse bounds is less than 2.5 dB in the CSIR case and less than 4 dB in the no-CSI case in most considered regimes. When the distribution of K_a is known, the performance gap between the cases with and without knowing the value of K_a is small. For example, in the setup with blocklength n=1000, payload J=100, error requirement ϵ=0.001, and L=128 receive antennas, compared to the case with known K_a, the extra required energy-per-bit when K_a is unknown and distributed as K_a∼Binom(K,0.4) is less than 0.3 dB on the converse side and 1.1 dB on the achievability side. The spectral efficiency grows approximately linearly with L in the CSIR case, whereas the growth rate decreases with no-CSI. Moreover, we study the performance of a pilot-assisted scheme, which is suboptimal especially when K_a is large. Building on non-asymptotic results, when all users are active and J=Θ(1), we obtain scaling laws as follows: when L=Θ(n^2) and P=Θ(1/n^2), one can reliably serve K=𝒪(n^2) users with no-CSI; under mild conditions with CSIR, the PUPE requirement is satisfied if and only if nLln KP/K=Ω(1).
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