A closed-form precoder for spatial multiplexing over correlated MIMO channels

Akhtar, Jabran; Gesbert, David

doi:10.1109/glocom.2003.1258558

Cited by 21 publications

(26 citation statements)

References 11 publications

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“…For the interested reader, results on the optimization of the input covariance under various criteria other than the capacity, a process sometimes referred to as precoding, can be found in [17]- [23].…”

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confidence: 99%

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

Tulino¹,

Lozano²,

Verdú

2006

IEEE Trans. Wireless Commun.

217

145

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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...

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confidence: 99%

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

Tulino¹,

Lozano²,

Verdú

2006

IEEE Trans. Wireless Commun.

217

145

View full text Add to dashboard Cite

show abstract

“…For instance, K = 0 gives φ2 = −ψ while µ1 = 2, µ2 = 2ρ and µ3 = 2 which coincides with the results of [11] given for 4-QAM:…”

Section: Interpretationssupporting

confidence: 66%

“…Nevertheless, for this particular MRC receiver, the exact phase rotation is also dependent upon H0, which the transmitter is unaware of, and therefore the selection of (33) will in practice only have minor effect. In contrast, the decoder of [11] eliminates H0 before further processing and the phase change thus plays a more important role. The essential information destined to differentiate the signals is though determined by the choice of power weights:…”

Section: ) Phase Optimizationmentioning

confidence: 99%

“…A high K factor with precoding makes the slope of the curve steeper as the fading is virtually non-existing. Further simulation results for transmit correlation cases may be found in [11], [12]. …”

Section: Simulationsmentioning

confidence: 99%

“…A closed-form solution for transmit correlation only, avoiding the need of any numerical optimization was presented in [11], [12]. The precoder is found in a closed-form as the solution to a linear equation parametrized as a function of the transmit correlation coefficient.…”

Section: Introductionmentioning

confidence: 99%

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Linear closed-form precoding of MIMO multiplexing systems in the presence of transmit correlation and ricean channel

Akhtar

Gesbert

Hjørungnes

IEEE Global Telecommunications Conference, 2004. GLOBECOM '04.

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Abstract-This paper presents a closed-form linear precoder for a MIMO spatial multiplexing (SM) system in the presence of transmit correlation and a Ricean component. Existing SM (V-BLAST and similar schemes), based upon channel matrix inversion, rely on the linear independence of antenna channel responses for stream separation and suffer considerably from high levels of fading correlation and/or dominating ill-conditioned line-of-sight channel components. We propose a simple algorithm that adjusts the transmitted constellation through power weighting and phase shifts that can be interpreted in some extreme case as a higher order constellation design scheme. We obtain a rate-preserving MIMO multiplexing scheme that can operate smoothly at any degree of transmit correlation and any type of LOS channel component.

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Covariance precoding schemes for MIMO OFDM over transmit‐antenna and path‐correlated channels

Fu¹,

Krzymien²,

Tellambura³

2010

Trans Emerging Tel Tech

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SUMMARYThis paper considers covariance-feedback based linear precoding (LP) and nonlinear Tomlinson-Harashima precoding (THP) for multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems. Orthogonal space-time block coded (OSTBC) ‡ OFDM and spatially-multiplexed (SM) § OFDM are analysed. The main objective is to design precoders to mitigate the impact of transmit-antenna and path correlations. The impact of path correlations on the pairwise error probability (PEP) of MIMO OFDM is also analysed. Closed-form, waterfilling-based covariance precoders are derived to minimize the worst case PEP in OSTBC OFDM. An adaptive transmission strategy is also developed for switching between precoded SM OFDM and precoded OSTBC OFDM. The switching criterion is the minimum Euclidean distance of the received codebook. The switching decision sent to the transmitter requires one feedback bit per subcarrier. The proposed precoders considerably reduce the error rate in antenna and path-correlated channels; nonlinear precoders perform better than linear precoders. We show that the adaptive strategy can achieve full diversity gain, and it outperforms either SM or OSTBC applied individually in terms of the bit error rate (BER).

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A closed-form precoder for spatial multiplexing over correlated MIMO channels

Cited by 21 publications

References 11 publications

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

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

Linear closed-form precoding of MIMO multiplexing systems in the presence of transmit correlation and ricean channel

Covariance precoding schemes for MIMO OFDM over transmit‐antenna and path‐correlated channels

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