Abstract
In this paper, four tensor-based receivers for a multiuser multirelay cooperative uplink are proposed, with the relays employ the amplify-and-forward (AF) protocol and a time-spread coding. Two different scenarios are considered regarding the multiuser interference at the relays. When multiuser interference at the relays is ignored, a quadrilinear PARAFAC model is adopted for the received signals. Otherwise, a new tensor model called Nested PARAFAC-Tucker decomposition (NPT1D) is used to represent the received signals. The proposed receivers jointly estimate the transmitted symbols, channel gains and spatial signatures, two of them being based on the Alternating Least Squares (ALS) algorithm and two of them using the non-iterative Least Squares Khatri-Rao Factorization (LS-KRF) method. Uniqueness is discussed and simulation results are provided to illustrate the performance of the proposed techniques.
Highlights
T HE use of multilinear algebra concepts, such as tensor decompositions, has found applications in several areas [1], [2] and allowed the development of new receivers for telecommunications systems
We present a new nested decomposition called Nested Parallel Factor Analysis (PARAFAC)-Tucker decomposition (NPTD), which can be viewed as a special case of the nested Tucker decomposition (NTD) and a generalization of the nested PARAFAC decomposition (NPD)
For the scenario presented in subsection III.A, where no multiuser interference at the relays is considered, the baseband signal received on the RD link can be viewed as a four-way array with its dimensions related to space, cooperative slot, symbol and time spreading
Summary
T HE use of multilinear algebra concepts, such as tensor decompositions, has found applications in several areas [1], [2] and allowed the development of new receivers for telecommunications systems. One of the main features of the receivers proposed in these works is the fact that they do not require the use of training sequences, nor the channel knowledge, with weak identifiability conditions These tensor decompositions do not rely on statistical independence between the transmitted signals. Tensor decompositions have been successfully employed in wireless cooperative communications, as in [15], where a receiver was proposed for a two-way relaying system. More recent works include [19], where a semi-blind receiver was proposed for a two-hop MIMO relaying system, adopting two tensor decompositions (PARAFAC and PARATUCK). The works [22] and [23] present tensor-based approaches for channel estimation and multiuser detection in cooperative MIMO systems, respectively. ∈ CI1,··· ,Ip−1,J1,··· ,Jq−1,Jq+1,··· ,JM ,Ip+1,··· ,IN defined by:
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