Noncoherent Communication in Multiple-Antenna Systems: Receiver Design and Codebook Construction

Abstract

We address the problem of space-time codebook design for non-coherent communications in multiple-antenna wireless systems. In contrast with other approaches, the channel matrix is modeled as an unknown deterministic parameter at both the receiver and the transmitter, and the Gaussian observation noise is allowed to have an arbitrary correlation structure, known by the transmitter and the receiver. In order to handle the unknown deterministic spacetime channel, a generalized likelihood ratio test (GLRT) receiver is considered. A new methodology for space-time codebook design under this non-coherent setup is proposed. This optimizes the probability of error of the GLRT receiver's detector in the high signal-to-noise ratio (SNR) regime, thus solving a high-dimensional nonlinear nonsmooth optimization problem in a two-step approach: (i) firstly, a convex SDP relaxation of the codebook design problem yields a rough estimate of the optimal codebook; (ii) this is then refined through a geodesic descent optimization algorithm that exploits the Riemannian geometry imposed by the power constraints on the spacetime codewords. The results obtained through computer simulations illustrate the advantages of our method. For the specific case of spatio-temporal white observation noise, our codebook constructions replicate the performance of state-of-art known solutions. The main point here is that our methodology permits to extend the codebook construction to any given correlated noise environment. The simulation results show the good performance of these new designed codes. Index TermsMultiple-input multiple output (MIMO) systems, non-coherent communications, space-time constellations, generalized likelihood ratio test (GLRT) receiver, semidefinite programming (SDP), geodesic descent algorithm (GDA).

Further Results on the Capacity and Error Probability Analysis of Noncoherent MIMO Systems in the Low SNR Regime

“…A low SNR analysis of the PEP for the generalized likelihood ratio test (GLRT) receiver is introduced, and a codebook design criterion that takes into account the information about noise correlation is obtained. For the special case of single transmit antenna and spatio-temporal white Gaussian noise, it is shown that the problem of finding good codes corresponds to the very wellknown packing problem in the complex projective space [22], [25]. New space-time constellations for some particular wireless scenarios are constructed.…”

“…The generalization to arbitrary noise covariance matrices encompasses many scenarios of interest as special cases: spatially colored or not jointly with temporally colored or not observation noise, multiuser environment, etc. A methodology for designing space-time codebooks for noncoherent communications in multiple-antenna wireless systems and an arbitrarily given noise covariance matrix in the high SNR regime has recently been proposed; see [22] for more details.…”

“…The proof is given in Appendix V. For the case of spatio-temporal white observation noise, i.e., and , from (15), we have (16) where we assume (remark that for there are maximum different principal angles where each of them is of multiplicity ). In our work [22], we derive the expression for the PEP in the high SNR regime and . For and , it is given by (17) where .…”

Low SNR analysis of the non-coherent MIMO channel under arbitrary channel and noise correlation structures

“…100 in [11]. In [12], a methodology for designing spacetime codebooks for non-coherent communications in multipleantenna wireless systems and an arbitrary given noise covariance matrix Υ in the high SNR regime has been proposed.…”

Multi-User Non-Coherent Detection for Downlink MIMO Communication

“…The main advantage of DUSTM is its efficient decoding, which can be carried out through multiple-symbol differential detection (MSSD) at the receiver side [7]. Other meaningful schemes for non-coherent MIMO communication are based on Grassmannian Constellations (GC), which can be designed in either a systematic [8], [9] or a non-systematic way [10]. Regarding the decoding of GC, these designs cannot exploit MSSD due to their non-differential construction.…”