In this paper, non-orthogonal multiple access (NOMA) in amplify-and-forward relay systems with partial relay selection (PRS) is investigated. More specifically, new exact closed-form expressions for the outage probabilities at two users are derived, based on which an asymptotic analysis at high signalto-noise ratio (SNR) is carried out. Additionally, in order to investigate the performance gap between the NOMA and orthogonal multiple access (OMA) schemes, a closed-form approximate expression at high SNR for the sum rate is derived. Furthermore, relying on our results, the impact of the PRS on the sum rate and outage probability of the proposed NOMA scheme is examined. In particular, the derived asymptotic expressions show that the proposed scheme can improve over the traditional OMA not only the sum rate but also the user fairness. Finally, simulation results are presented to corroborate the analytical results. Index TermsNon-orthogonal multiple access (NOMA), spectrum efficiency, amplify-and-forward (AF) relay, partial relay selection, outage probability, sum rate.

Multi-dimensional model order selection (MOS) techniques achieve an improved accuracy, reliability, and robustness, since they consider all dimensions jointly during the estimation of parameters. Additionally, from fundamental identifiability results of multi-dimensional decompositions, it is known that the number of main components can be larger when compared to matrix-based decompositions. In this article, we show how to use tensor calculus to extend matrix-based MOS schemes and we also present our proposed multi-dimensional model order selection scheme based on the closed-form PARAFAC algorithm, which is only applicable to multidimensional data. In general, as shown by means of simulations, the Probability of correct Detection (PoD) of our proposed multi-dimensional MOS schemes is much better than the PoD of matrix-based schemes.

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Channel estimation is a crucial problem for massive multiple input multiple output (MIMO) systems to achieve the expected benefits in terms of spectrum and energy efficiencies. However, a considerable number of pilots are usually distributed over a large number of time-frequency resources using orthogonal frequency division multiplexing (OFDM) to effectively estimate a large number of channel coefficients in space and frequency domains, sacrificing spectral efficiency. In this paper, by assuming MIMO-OFDM transmission, we start by proposing a tensor-based minimum mean square error (MMSE) channel estimator that exploits the multidimensional nature of the frequency-selective massive MIMO channel in the frequency-domain, being a low-complexity alternative to the well-known vector-MMSE channel estimation. Then, by incorporating a 3D sparse representation into the tensor-based channel model, a tensor compressive sensing (tensor-CS) model is formulated by assuming that the channel is compressively sampled in space (radio-frequency chains), time (symbol periods), and frequency (pilot subcarriers). This tensor-CS model is used as the basis for the formulation of a tensor-orthogonal matching-pursuit (T-OMP) estimator that solves a greedy problem per dimension of the measured tensor data. The proposed channel estimator has two variants which may either resort to a joint search per tensor dimension or to a sequential search that progressively reduces the search space across the tensor dimensions. The complexities of the different tensor-based algorithms are studied and compared to those of the traditional vector-MMSE and vector-CS estimators. Our results also corroborate the performance-complexity tradeoffs between T-MMSE and T-OMP estimators, both being competing alternatives to their vector-based MMSE and OMP counterparts.