February 16th, 2008 by Robert Heath

I thought I would kick off this blog with some history about one of my early research topics: switching between diversity and multiplexing. I did this work while working at Iospan Wireless and later it became part of my Ph.D. dissertation at Stanford under Prof. Paulraj’s supervision. The essential concept is vary the choice of spatial formatting, e.g. spatial multiplexing, space-time block coding, etc, based on channel state information. At this point the need for switching is obvious, it has been incorporated into every MIMO standard, but let me explain the origins of [1][2] in more detail.

The stage for this story is set in late 1999. In the 1990’s, interest grew in a topic that was called transmit diversity. The idea was to devise some kind of transmit strategy that would achieve the same diversity gain with receive diversity but to do it with multiple transmit antennas. This line of research resulted in several interesting concepts including delay diversity, phase sweep transmit diversity, and then the revolutionary concepts of space-time trellis coding and space-time block coding. The objective of the work on transmit diversity was to extract all the diversity from the fading channel and to support mobile users with a single receive antenna.

In parallel, in the late 1990’s, work started on the high capacity MIMO communication using concepts like V-BLAST and spatial multiplexing, inspired by information theoretic results. The idea at its core was to send independent data streams on different transmit antennas. The transmit power was split among all transmit antennas. Using multiple receive antennas, it was possible to recover all the transmit data streams, obtaining the well known capacity scaling corresponding to the minimum number of transmit and receive antennas. The key difference between this early work on MIMO and transmit diversity is that MIMO was designed especially considering multiple receive antennas while transmit diversity was initially intended for single antenna systems.

Initially there was a lot of confusion between the topics of space-time coding, MIMO, transmit diversity, and other multiple antenna concepts. Some of my confusion came from the following observation. The diversity performance of spatial multiplexing was inferior to that of transmit diversity with the same number of transit and receive antennas. Spatial multiplexing, though, potentially had higher data rates. To understand these distinctions, I decided to fix the constellation size so that the total spectral efficiency for each approach was the same and tried to understand for a given channel how each technique performed from a bit error rate (versus a capacity) perspective. I found that it was possible to quantify which channels were suitable for multiplexing and which for diversity. In particular I found a concrete relationship was found for the case of two transmit and two receive antennas between the Demmel condition number of the matrix channel, confirming intuition that high rank channels are good for multiplexing and low rank channels more suitable for diversity. This provided a key insight into how link adaptation algorithms should work for MIMO systems - specifically MIMO technique should be varied as well as the modulation and coding rate.

The concept of switching between diversity and multiplexing should not be confused with the diversity-multiplexing tradeoff (DMT). The reason is that the DMT is an analysis tool. It is good for understanding performance of families of space-time formatting techniques over all channel realizations but does not provide insight into choosing the best technique for a given channel realization.

Since early work on switching between multiplexing and diversity there have been many extensions. My research group at UT Austin, the Wireless Systems Innovations Lab, developed several of these methods. For example, we have pursued a generalization of the switching concept called multi-mode transmission, where the number of streams are varied. We have studied multi-mode antenna selection, multi-mode precoding, and extensions to MIMO-OFDM. We have also investigated the case where switching between modes is determined by the spatial correlation in the channel. Of course, many other researchers are also investigating the topic and doing exceptional work — there are too many contributions to mention.

[1] R. W. Heath, Jr.and A. J. Paulraj, “Switching between multiplexing and diversity based on constellation distance,” Proc. of the Allerton Conf. on Comm. Control and Comp., pp. 212-221, Sept. 30 - Oct. 2, 2000.

[2] R. W. Heath, Jr. and A. J. Paulraj, “Switching Between Diversity and Multiplexing in MIMO Systems,” IEEE Trans. on Communications, vol. 53, no. 6, pp. 962-968, June 2005.