Fundamental Limits of Many-User MAC With Finite Payloads and Fading

Abstract

Consider a (multiple-access) wireless communication system where users are connected to a unique base station over a shared-spectrum radio links. Each user has a fixed number k of bits to send to the base station, and his signal gets attenuated by a random channel gain (quasi-static fading). In this paper we consider the many-user asymptotics of Chen-Chen-Guo'2017, where the number of users grows linearly with the blocklength. Differently, though, we adopt a per-user probability of error (PUPE) criterion (as opposed to classical joint-error probability criterion). Under PUPE the finite energyper-bit communication is possible, and we are able to derive bounds on the tradeoff between energy and spectral efficiencies. We reconfirm the curious behaviour (previously observed for non-fading MAC) of the possibility of almost perfect multi-user interference (MUI) cancellation for user densities below a critical threshold. Further, we demonstrate the suboptimality of standard solutions such as orthogonalization (i.e., TDMA/FDMA) and treating interference as noise (i.e. pseudo-random CDMA without multi-user detection). Notably, the problem treated here can be seen as a variant of support recovery in compressed sensing for the unusual definition of sparsity with one non-zero entry per each contiguous section of 2 k coordinates. This identifies our problem with that of the sparse regression codes (SPARCs) and hence our results can be equivalently understood in the context of SPARCs with sections of length 2 100 . Finally, we discuss the relation of the almost perfect MUI cancellation property and the replica-method predictions.Index Terms-Finite blocklength, many-user MAC, per-user probability of error, approximate message passing, replicamethod I. INTRODUCTIONWe clearly witness two recent trends in the wireless communication technology: the increasing deployment density and miniaturization of radio-equipped sensors. The first trend results in progressively worsening interference environment, while the second trend puts ever more stringent demands on communication energy efficiency. This suggests a bleak picture for the future networks, where a chaos of packet collisions and interference contamination prevents reliable connectivity.This paper is part of a series aimed at elucidating the fundamental tradeoffs in this new "dense-networks" regime

Binary Subspace Chirps

“…and the second equality follows by (19). Thus F D (P 1 )F U (S 1 )F Ω (r), where P 1 := P P, S 1 := P −1 S r P −T (30) represents the same coset.…”

“…Note here that Ω = F Ω (m) and ΩF Ω (r)Ω = F Ω (m − r). Then it follows by (20) (and by (19)) that every F ∈ Sp(2m; 2) can be written as…”

“…Polyanskiy [12] proposed a framework in which communication occurs in blocks of N channel uses, and the task of a receiver is to identify correctly L active users (messages) out of 2 B , with one regime of interest being N = 30, 000, L = 250, and B = 100. Ever since its introduction, there have been several follow-up works [11,[14][15][16][17], extensions to a massive MIMO scenario [18] where the base station has a very large number of antennas, and a discussion on the fundamental limits on what is possible [19].…”

Optimizing information freshness using low-power status updates via sleep-wake scheduling

“…We now show the effectiveness of the proposed scheduler when deployed in "dense networks" [21], [22]. Dense networks are characterized by a large number of sources connected to a single AP.…”

“…Examples include massive machine-type communications [21]. The dataloads in such "dense networks" [21], [22] are created by applications such as home security and automation, oilfield and pipeline monitoring, smart agriculture, animal and livestock tracking, etc. This introduces high variability in the data packet sizes so that the transmission times of data packets are random.…”