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We consider the unsourced random access problem on a Rayleigh block-fading AWGN channel with multiple receive antennas. Specifically, we treat the slow fading scenario where the coherence blocklength is large compared to the number of active users and a message can be transmitted in a single fading coherence block. Unsourced random access refers to a form of grant-free random access where users are constrained to use the same codebook and therefore are a priori indistinguishable. The receiver must recover the list of transmitted messages up to permutations. In this paper, we propose an approach based on splitting the user messages into two parts. First, a small block of bits selects a relatively short codeword from a common “pilot” codebook. Then the remaining message bits are encoded by a standard block code for the Gaussian channel. The receiver makes use of a multiple measurement vector approximate message passing (MMV-AMP) algorithm to estimate the active user channels from the “pilot” part, and then uses the estimated channels to perform coherent maximum ratio combining (MRC) to decode the second part. We provide an accurate closed-form approximated analysis of the proposed scheme. Furthermore, we analyze the MRC decoding when successive interference cancellation is performed over groups of users, striking an attractive tradeoff between complexity and performance. Finally, we investigate the impact of power control policies, taking into account the unique nature of massive random access. As a byproduct, we also present an extension of the MMV-AMP algorithm which allows pathloss coefficients to be treated as deterministic unknowns by performing maximum likelihood estimation in each step of the MMV-AMP algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of user activity detection and large-scale fading coefficient estimation in a random access wireless uplink with a massive MIMO base station with a large number M of antennas and a large number of wireless single-antenna devices (users). We consider a block fading channel model where the M-dimensional channel vector of each user remains constant over a coherence block containing L signal dimensions in time-frequency. In the considered setting, the number of potential users Ktot is much larger than L but at each time slot only Ka << Ktot of them are active. Previous results, based on compressed sensing, require that Ka ≤ L, which is a bottleneck in massive deployment scenarios. In this work, we show that such limitation can be overcome when the number of base station antennas M is sufficiently large. More specifically, we prove that with a coherence block of dimension L and a number of antennas M such that Ka/M = o(1), one can identify Ka = O(L2/log2 (Ktot/Ka)) active users, which is much larger than the previously known bounds. We also provide two algorithms. One is based on Non-Negative Least-Squares, for which the above scaling result can be rigorously proved. The other consists of a low-complexity iterative componentwise minimization of the likelihood function of the underlying problem. While for this algorithm a rigorous proof cannot be given, we analyze a constrained version of the Maximum Likelihood (ML) problem (a combinatorial optimization with exponential complexity) and find the same fundamental scaling law for the number of identifiable users. Therefore, we conjecture that the low-complexity (approximated) ML algorithm also achieves the same scaling law and we demonstrate its performance by simulation. We also compare the discussed methods with the (Bayesian) MMV-AMP algorithm, recently proposed for the same setting, and show superior performance and better numerical stability. Finally, we use the discussed approximated ML algorithm as the inner decoder in a concatenated coding scheme for unsourced random access, a grant-free uncoordinated multiple access scheme where all users make use of the same codebook, and the receiver must produce the list of transmitted messages, irrespectively of the identity of the transmitters. We show that reliable communication is possible at any Eb/N0 provided that a sufficiently large number of base station antennas is used, and that a sum spectral efficiency in the order of O(L log (L)) is achievable. [ABSTRACT FROM AUTHOR]