Capacity-achieving input covariance for single-user multi-antenna channels

Abstract

We characterize the capacity-achieving input covariance for multi-antenna channels known instantaneously at the receiver and in distribution at the transmitter. Our characterization, valid for arbitrary numbers of antennas, encompasses both the eigenvectors and the eigenvalues. The eigenvectors are found for zero-mean channels with arbitrary fading profiles and a wide range of correlation and keyhole structures. For the eigenvalues, in turn, we present necessary and sufficient conditions as well as an iterative algorithm that exhibits remarkable properties: universal applicability, robustness and rapid convergence. In addition, we identify channel structures for which an isotropic input achieves capacity. Keywords:Channel capacity; Multi-antenna arrays; Input optimization; Fading channels; Antenna correlation; Ricean channels; Keyhole channels; Channel-state Information; * Antonia M. Tulino is with Universita Degli Studi di Napoli, Federico II, 80125 Napoli, Italy † Angel Lozano is with Bell Laboratories (Lucent Technologies), Holmdel, NJ07733, USA. ‡ Sergio Verdú is with Princeton University, Princeton, NJ08540, USA. 1 I IntroductionWhile, in most instances of wireless communication, the receiver can accurately track the instantaneous state of the fading channel, the transmitter is often unable to perform such tracking. This is prominently true in wide-area mobile systems, where the dominant form of duplexing relies on frequency separation of uplink and downlink that renders their fading nonreciprocal. On account of this lack of reciprocity, the provision of CSI (channel state information) to the transmitter hinges on the use of feedback, which consumes resources and, more fundamentally, may incur round-trip delays nonnegligible with respect to the coherence time of the CSI being reported.Statistical information about the channel, on the other hand, is virtually always accessible to the transmitter since the periods over which the fading process is basically stationary are several orders of magnitude larger than the duration of the fades. Moreover, the uplink and downlink statistics are usually reciprocal and thus statistical feedback is not only affordable, but possibly dispensable.Altogether, the most typical operating regime in mobile systems is that in which (i) the receiver has instantaneous CSI, 1 and (ii) the transmitter has only access to its distribution.In such regime, which constitutes the focus of this paper, the input cannot be tailored to the state of the channel, but only to its distribution.In multi-antenna channels impaired by additive Gaussian noise and with perfect CSI at the receiver, the unique capacity-achieving input is zero-mean Gaussian and thus its characterization boils down to the determination of its spatial covariance.Unlike in the case that the CSI can be instantaneously accessed also by the transmitter, for which the capacity-achieving input covariance is well known [5,6], for our regime of interest the structure of the capacity-achieving input covariance is only known fo...

Performance Analysis of Precoded MIMO MMSE Receivers in Transmit-Correlated Rayleigh Channels

“…를 이용하여 최적화될 수 있다 [3][4][5][6][7] . 기존 연구결과에 서는 송신 및 수신단에서 완벽한 채널 정보 (channel state information, CSI) 를 가정하였다 [3,4] .…”

“…상관 행렬 (correlation matrices) 이 송신단에만 이 용 가능하다고 가정하였고, 최적의 프리코더의 좌측 고유벡터 (eigenvector)는 Tx 상관 행렬의 고유벡터 와 일치한다고 연구되었다 [5][6][7] .…”

Bit Loading for MIMO with Statistical Channel Information at the Transmitter and ZF Receivers

“…For a rather general class of channel models [1], the capacity-achieving precoder V under CDIT contains the eigenvectors of E H H H . This precoder is also shown to be optimal from an SINR standpoint with a linear MMSE receiver [7].…”

“…Figure 3 shows the CDIT capacity according to [1] for the channel model we are considering. Interestingly, correlation has the same effect on the bit rate achieved by the proposed bit loading with ZF receiver, with the particularity that the critical SNR is higher in this case.…”

“…Under CDIT, the input cannot be adapted to the instantaneous state of the channel and thus SVD (singular value decomposition) cannot be used to diagonalize the channel. Achieving capacity requires a complex Gaussian input vector with a covariance that depends on the channel distribution [1].…”