A Survey: Non-Orthogonal Multiple Access with Compressed Sensing Multiuser Detection for mMTC <s> Sparsity aware MAP based algorithms <s> The number of active users in code-division multiple access (CDMA) systems is often much lower than the spreading gain. The present paper exploits fruitfully this a priori information to improve performance of multiuser detectors. A low-activity factor manifests itself in a sparse symbol vector with entries drawn from a finite alphabet that is augmented by the zero symbol to capture user inactivity. The non-equiprobable symbols of the augmented alphabet motivate a sparsity-exploiting maximum a posteriori probability (S-MAP) criterion, which is shown to yield a cost comprising the l2 least-squares error penalized by the p-th norm of the wanted symbol vector (p = 0, 1, 2). Related optimization problems appear in variable selection (shrinkage) schemes developed for linear regression, as well as in the emerging field of compressive sampling (CS). The contribution of this work to such sparse CDMA systems is a gamut of sparsity-exploiting multiuser detectors trading off performance for complexity requirements. From the vantage point of CS and the least-absolute shrinkage selection operator (Lasso) spectrum of applications, the contribution amounts to sparsity-exploiting algorithms when the entries of the wanted signal vector adhere to finite-alphabet constraints. <s> BIB001 </s> A Survey: Non-Orthogonal Multiple Access with Compressed Sensing Multiuser Detection for mMTC <s> Sparsity aware MAP based algorithms <s> Compressed sensing based multiuser detection is a novel research field in massive machine to machine communication. Mainly focusing at decreasing signaling overhead, this approach implements sophisticated detection algorithms at the physical layer that jointly estimate activity and data. As a consequence, the reliability of the activity detection is crucial for the system performance as data is lost if users are erroneously classified as inactive. This paper introduces a novel approach to estimate node activity on a per frame basis by Multiple Measurement Vector Compressed Sensing approaches. This approach allows for reliable activity detection with complexity invariant of the length of the transmitted frame. Moreover, we are able to show that this approach works with only a few measurements available to the detector. In particular we demonstrate that reliable activity detection is possible if the number of observations is larger than the square root of the number of nodes in the system. <s> BIB002
In BIB001 , for the first time the possibility of exploiting the sporadic nature of user activity for multiuser detection was introduced. For the model where n ∈ C Ns×1 is the AWGN noise vector, a sparsity-aware maximum a posteriori (S-MAP) criterion is used and the detection process is formulated as BIB001 d where and A is the modulation alphabet. Two approaches were followed to solve the detection process in Equation (4): relaxed S-MAP and S-MAP with lattice search. In relaxed S-MAP, it is assumed that A = {±1, 0}, which makes Equation (4) equivalent to BIB001 d MAP = arg min Algorithms were designed for p = 1 and p = 2. Ignoring the finite-alphabet constraint, the optimal solution for p = 1 is a quadratic programming problem while for p = 2 it takes a linear form. The relaxed S-MAP multiuser detection is sub-optimal but has advantage of low complexity. In the second approach, i.e, S-MAP detectors with lattice search, the alphabet A is defined as A = {±1, ±3, . . . , ±(M −1)}, with M even. Using the QR decomposition the S-MAP problem is reformulated and the elements of vector d are obtained by searching over a subset of the alphabet. The performance of the detector improves at the cost of higher complexity. The algorithms presented aim at fully loaded (N s = K) CDMA system, however, the lattice search based algorithms can have fair performance for moderate overloaded (N < K) case. In BIB002 , MMV-CS model was considered to reduce the complexity of the receiver and increase the computation speed. The activity is detected based on the covariance matrix of the received signal Y ∈ C Ns×N d which is given as BIB002  where Φ W W is the sample noise covariance matrix, S is the spreading matrix and V = E(DD H ) is the covariance matrix of the transmitted multiuser frame. The k-th user is active if the k-th diagonal element of V is 1. A MAP detection is used to obtain the positions of non-zero elements in V. The complexity of the proposed algorithms is invariant to the length of the frame, N d , however, the performance of the algorithms is dependent on N d and improves with increasing N d . It is derived that for reliable activity detection the length of the sequence should be greater than the square root of the number of nodes BIB002 . Furthermore, the simulation results show that the algorithms can handle asynchronous frames where the time shifts are up to 60% of the frame duration.