Efficient feedback methods for MIMO channels based on parameterization

Abstract

In this paper, we propose two efficient lowcomplexity quantization methods for multiple-input multipleoutput (MIMO) systems with finite-rate feedback based on proper parameterization of the information to be fed back followed by quantization in the new parameter domain. For a MIMO channel which has multiple orthonormal vectors as channel spatial information, we exploit the geometrical structure of orthonormality while quantizing the spatial information matrix. The parameterization is of two types: one is in terms of a set of unit-norm vectors with different lengths, and the other is in terms of a minimal number of scalar parameters. These parameters are shown to be independent for the i.i.d. flatfading Rayleigh channel, facilitating efficient quantization. In the first scheme, each of the unit-norm vectors is independently quantized with a finite number of bits using an optimal vector quantization (VQ) technique. Bit allocation is needed between the vectors, and the optimum bit allocation depends on the operating SNR of the system. In the second scheme, the scalar parameters are quantized. In slowly time-varying channels, the scalar parameters are also found to be smoothly changing over time, leading to the development of a simple quantization and feedback method using adaptive delta modulation. The results show that the proposed feedback scheme has a channel tracking feature and achieves a capacity very close to perfect feedback with a reasonable feedback rate.

Beamforming matrix quantization with variable feedback rate

“…An effort to reduce the amount of information in V was reported in [11][12][13] where a matrix Σ was multiplied with V to form À V , such that the last row of À V consists of only real numbers. Hence, we may re-express (2) as:…”

“…Using the above bit assignment, ψ and ϕ can be quantized according to (12) (where e ψ and e ϕ represent the quantized version of ψ and ϕ , respectively).…”

“…One is codebook based such as the vector quantization (VQ) scheme proposed in [5][6][7][8][9][10], and another is by using the Givens Rotation (GR) [1,4,[11][12][13]. Compared with the GR-based scheme, the VQ approach requires a higher storage, as a set of codebooks is needed for a particular antenna setting.…”

Trade-off between Feedback Load for the Channel State Information and System Performance in MIMO Communications

“…The time correlation factor is usually expressed in the literature in terms of the normalized Doppler frequency f D τ , or f D /f F B , where f F B is the frequency of feedback messages. The values for this parameter usually considered in the literature are 0.004 < f D /f F B < 0.01 (see references [10,11,12]), which correspond to 0.999 < ρ < 1. Fig.…”

Single-bit closed-loop quasi-orthogonal space-time codes for MIMO systems

“…Parameterizations involving Givens rotors have been used in the context of closed-loop eigenbeamforming, see for example [22,23,21]. Here, we consider the mapping employed in the SCGAS algorithm [21], restricted to a single beam.…”