Problem Description:
The performance of multiple antenna systems depends on the availability of the channel state information (CSI) at the transmitter (CSIT) and at the receiver (CSIR). Often in MIMO system design and analysis, two extreme CSIT assumptions are adopted: complete CSIT where channel state information is perfectly known at the transmitter and no CSIT. We consider MIMO systems with CSI assumptions in between these two extremes, where perfect CSI is assumed to be available at the receiver, but only partial CSI is available at the transmitter which is conveyed from the receiver through a finite-rate feedback link.
Recently, several interesting papers have appeared, proposing design algorithms as well as analytically quantifying the performance of finite rate feedback multiple antenna systems. The analysis of finite rate feedback systems has proven to be difficult and results available to date are quite limited: i.i.d. channels and mainly MISO channels. We attempts to provide a general framework for the analysis of quantized feedback multiple antenna systems. This is done by exploiting the similarities between classical fixed-rate source coding and the channel quantization. These similarities would be extremely helpful in the design and analysis of finite rate feedback MIMO systems as they would benefit from the vast body of source coding theory, particularly high resolution quantization theory and VQ-based codebook design methodology. A closer examination reveals that there are enough differences between the problems that a direct use of high resolution results from source coding is not feasible. Fortunately, however, it is possible to extend some of the results to the problem at hand and provide an interesting general framework for analyzing finite rate feedback systems.
Without narrowing the scope to a specific multi-antenna channel quantization scheme, we formulates the problem as a general finite rate vector quantization problem with attributes tailored to meet the general issues that arise in feedback based communication systems. These attributes include side information available at the encoder but unavailable at the decoder, general non-mean square distortion functions, and source vectors with constraints. Asymptotic distortion analysis of the proposed general quantization problem is provided by extending Bennett’s classic analysis as well as its corresponding vector extensions. To be specific, tight lower and upper bounds of the average asymptotic distortion are proposed.
The proposed general
methodology from the source coding perspective provides a powerful
analytical tool to study a wide range of finite-rate feedback systems and is not
limited only to i.i.d. MISO flat fading channels (as in previous literatures).
It can be used to analyze more complicated schemes such as MISO system with
correlated channel distributions, MIMO systems (i.i.d. and correlated channels),
and even MISO (or MIMO) multicarrier systems over frequency selective fading
channels. The established framework is versatile enough to provide analysis of
quantizers with mismatched statistics (i.e. assumed channel
statistics for the quantizer design are different from the actual channel
statistics) and variants such as transformed codebooks.
Related Publications:
J. Zheng, E. Duni, and B. D. Rao, "Analysis of multiple antenna systems with finite-rate feedback using high resolution quantization theory", submitted to IEEE Trans. on Signal Processing, November 2005. (preprints available upon request)
J. Zheng and B. D. Rao, "Analysis of MIMO systems with finite-rate channel state information feedback", IEEE Trans. on Signal Processing, in preparation.
J. Zheng and B. D. Rao, "Analysis of vector quantization using transformed codebooks with application to feedback-based multiple antenna systems", submitted to Special Issues of IEEE Journal on Selected Areas in Communications, June 2006.
J. Zheng and B. D. Rao, "Analysis of multiple antenna systems with finite-rate channel information feedback over spatially correlated fading channels", IEEE Trans. on Signal Processing, in preparation.
J. Zheng and B. D. Rao, "Analysis of MIMO systems with finite-rate channel state information feedback," invited paper to Asilomar 2006, Asilomar, CA, October 2006.
J. Zheng and B. D. Rao, "Analysis of vector quantizers using transformed codebooks with application to feedback-based multiple antenna systems," in Proceedings of EUSIPCO, Florence, Italy, September 2006 (to appear).
J. Zheng, E. Duni, and B. D. Rao, "Analysis of multiple antenna systems with finite-rate feedback using high resolution quantization theory," in Data Compression Conference 2006, Snowbird, UT, November 2005.
J. Zheng and B. D. Rao, "Capacity analysis of multiple antenna systems with mismatched channel quantization schemes," in ICASSP 2006, Toulouse, France, May 2006.
J. Zheng and B. D. Rao, "Capacity analysis of correlated multiple antenna systems with finite rate feedback," in ICC 2006, Istanbul, Turkey, June 2006.
C. R. Murthy, J. Zheng and B. D. Rao, "Multiple antenna systems with finite rate feedback," in Milcom 2005, Atlantic City, NJ, October 2005.