Asymptotic performance of mimo wireless channels with limited feedback

Santipach, Wiroonsak; Honig, Michael L.

doi:10.1109/milcom.2003.1290092

Cited by 114 publications

(80 citation statements)

References 11 publications

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“…Other codebook design methods have been proposed as alternatives to Grassmannian line packings. Namely, random vector quantization (RVQ) [6], fourier codebooks [7] and equiangular frame based codebooks [8], just to name a few.…”

Section: Introductionmentioning

confidence: 99%

Minimum Codebook Size to Achieve Maximal Diversity Order for RVQ-Based MIMO Systems

2014

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Abstract-Multiple antenna systems provide both capacity and diversity gains relatively to single antenna based networks. These gains rely heavily on the availability of channel state information. In this manuscript we assume that the receiver has accurate channel information, which is quantized and fed back to the transmitter. Sufficient conditions for the feedback rate are provided that guarantee no loss of diversity due to channel quantization. Considering a K × M MIMO system, we show that to achieve a diversity of D = M − K + 1 which is the maximum allowable, a feedback channel with rate of log2(1 + D) bits per channel use is enough.

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Section: Introductionmentioning

confidence: 99%

Minimum Codebook Size to Achieve Maximal Diversity Order for RVQ-Based MIMO Systems

2014

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“…Some researchers have worked on feedback of channel information in vector forms, for example, for MISO channels [1], [2], [3] and for the principal eigen-mode of MIMO channels [4]. Only recently, feedback of channel information in matrix forms for MIMO channels have begun to be addressed [5], [6], [7]. In this paper, we develop efficient transmit beamforming techniques for MIMO spatial multiplexing (SM) systems with finite-rate feedback.…”

Section: Introductionmentioning

confidence: 99%

MIMO spatial multiplexing systems with limited feedback

Roh

Rao

2005

IEEE International Conference on Communications, 2005. ICC 2005. 2005

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Abstract-This paper investigates the problem of transmit beamforming in MIMO spatial multiplexing (SM) systems with finite-rate feedback channel. Assuming a fixed number of spatial channels and equal power allocation, we propose a new design criterion for designing the codebook of beamforming matrices that is based on minimizing the capacity loss resulting from the limited rate in the feedback channel. Using the criterion, we develop an iterative design algorithm that converges to an optimum codebook. Under the i.i.d. channel and high SNR assumption, the effect on channel capacity of the finite-bit representation of beamforming matrix is analyzed. Central to this analysis is the complex multivariate beta distribution and tractable approximations to the Voronoi regions associated with the code points. Furthermore, to compensate for the degradation due to the equal power allocation assumption, we propose a multimode SM transmission strategy wherein the number of data streams is determined based on the average SNR. This approach is shown to allow for effective utilization of the feedback bits. I. INTRODUCTIONThe performance of a multiple-antenna communication system depends on the nature of channel state information (CSI) available at the transmitter and at the receiver. When the transmitter has perfect CSI, a higher capacity link can be achieved in the single user case, and there are other benefits such as lower-complexity receivers and better system throughput in a multiuser environment. However, the assumption that the transmitter has perfect knowledge of multi-dimensional channel could be unrealistic as in many practical systems the channel information is provided to the transmitter through a finite-rate feedback channel. There are several studies dealing with how to feed back the channel information. Some researchers have worked on feedback of channel information in vector forms, for example, for MISO channels [1], [2], [3] and for the principal eigen-mode of MIMO channels [4]. Only recently, feedback of channel information in matrix forms for MIMO channels have begun to be addressed [5], [6], [7]. In this paper, we develop efficient transmit beamforming techniques for MIMO spatial multiplexing (SM) systems with finite-rate feedback.The contributions of the paper are as follows. First, a tractable measure of capacity loss due to finite feedback rate is derived and used to design an optimal codebook of beamforming matrices in the context of a fixed number of spatial channels with equal power allocation. The efficacy of the approach is demonstrated by using it to design quantizers in

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“…MIMO systems with only one onbeam are studied in [3] and [4], where the beamforming codebook design criterion and performance analysis are derived by geometric arguments in the Grassmann manifold. MIMO systems with multiple on-beams are considered in [5]- [9]. Criteria to select the beamforming matrix are developed in [5] and [6].…”

Section: Introductionmentioning

confidence: 99%

“…The corresponding analysis is only valid for MIMO systems with asymptotically large number of transmit antennas. The effect of beamforming quantization on information rate is investigated in [8] and [9]. The loss in information rate is quantified for high SNR region in [8] where a metric other than the chordal distance is employed.…”

Section: Introductionmentioning

confidence: 99%

“…The loss in information rate is quantified for high SNR region in [8] where a metric other than the chordal distance is employed. In [9], a formula to calculate the information rate for all SNR regimes is proposed by letting the numbers of transmit antennas, receive antennas and feedback rate approach infinity simultaneously. But the performance approximated by this formula for several feedback bits may go beyond that of CSITR case.…”

Section: Introductionmentioning

confidence: 99%

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On the information rate of MIMO systems with finite rate channel state feedback and power on/off strategy

Dai

Liu

Rider

et al. 2005

Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.

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Abstract-This paper quantifies the information rate of multiple-input multiple-output (MIMO) systems with finite rate channel state feedback and power on/off strategy. In power on/off strategy, a beamforming vector (beam) is either turned on (denoted by on-beam) with a constant power or turned off. We prove that the ratio of the optimal number of on-beams and the number of antennas converges to a constant for a given signal-to-noise ratio (SNR) when the number of transmit and receive antennas approaches infinity simultaneously and when beamforming is perfect. Based on this result, a near optimal strategy, i.e., power on/off strategy with a constant number of on-beams, is discussed. For such a strategy, we propose the power efficiency factor to quantify the effect of imperfect beamforming. A formula is proposed to compute the maximum power efficiency factor achievable given a feedback rate. The information rate of the overall MIMO system can be approximated by combining the asymptotic results and the formula for power efficiency factor. Simulations show that this approximation is accurate for all SNR regimes.

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Asymptotic performance of mimo wireless channels with limited feedback

Cited by 114 publications

References 11 publications

Minimum Codebook Size to Achieve Maximal Diversity Order for RVQ-Based MIMO Systems

Minimum Codebook Size to Achieve Maximal Diversity Order for RVQ-Based MIMO Systems

MIMO spatial multiplexing systems with limited feedback

On the information rate of MIMO systems with finite rate channel state feedback and power on/off strategy

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