Efficient feedback methods for MIMO channels based on parameterization

• Published in: IEEE transactions on wireless communications Vol. 6; no. 1; pp. 282 - 292
• Main Authors: Roh, J.C., Rao, B.D.
• Format: Journal Article
• Language: English
• Published: Piscataway, NJ IEEE 01.01.2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Allocations; Antennas; Applied sciences; Array signal processing; Bit rate; Channel capacity; Channel state information; Channels; Codes; Exact sciences and technology; Feedback; Mathematical analysis; MIMO; Mutual information; Parametrization; Quantization; Radio transmitters; Radiocommunications; Rayleigh channels; Scalars; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Vectors (mathematics); Fading channels; MIMO system; Time variable channel; Parameter estimation; Vector quantization; Data compression; Rayleigh channels; channel state information; Parameterization; Adaptive method; Beam forming; Bit allocation; MIMO systems; Signal quantization; Channel information feedback; transmit beamforming; Channel estimation; Delta modulation; multiple antennas; Antenna array; Multiple channel; Adaptive modulation; Signal to noise ratio; quantization
• ISSN: 1536-1276; 1558-2248
• DOI: 10.1109/TWC.2007.05195

In this paper, we propose two efficient low-complexity quantization methods for multiple-input multiple-output (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. flat-fading 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