February 25th, 2008 by Robert Heath

It’s rare that you see the term MIMO these days without OFDM (orthogonal frequency division multiplexing) following close behind. I dare say that MIMO-OFDM, as it’s called, is the most prevalent embodiment of MIMO. Several systems use MIMO-OFDM including IEEE 802.11n, IEEE 802.16, as well as the forthcoming 3GPP2 UMB (ultra mobile broadband) and 3GPP LTE (long term evolution). Why is there a marriage between MIMO-OFDM?

To understand, some background in OFDM is in order. OFDM is a digital modulation technique, first proposed in the 1960’s (in an analog form) and developed in the 1980’s and early 1990’s into the form most commonly used today. The main application of OFDM is to simplify equalization of the multi-path propagation channel at the receiver. Multi-path arises from multiple different propagation paths between the transmitter and receiver, each with a different path delay, phase shift, and attenuation. This creates distortion in the received signal. Wide bandwidth signals are especially susceptible to multi-path since their large bandwidth implies smaller sample spacing. Consequently, using wider bandwidth signals (typically 1MHz or more, but this depends on the coherence bandwidth of the channel) will require some form of equalization at the receiver.

Just like in audio systems, an equalizer is used to restore attenuated frequency components. In systems that do not use OFDM, some form of inverse convolution (a type of filter) or nonlinear detector is required for equalization. OFDM, through a specially constructed transmit signal involving a cyclic prefix, is able to simplify equalization by operating directly in the frequency domain.

MIMO is unique in that it can exploit multi-path to enhance system capacity. Unfortunately, this capacity benefit comes at the expense of more challenging equalization. In a MIMO system, the receiver must deal not only with multi-path but also co-antenna interference, which is created from the transmissions from all transmit antennas. Thus equalization in MIMO systems is even more challenging than in single antenna systems. Thus MIMO benefits even more from efficient equalization techniques like OFDM. This is the core reason for the union between MIMO-OFDM in most practical systems.

There are other more technical benefits in the connection. Perhaps the most important is that efficient rate allocation is possible through the use of adaptive modulation and coding. It is also possible to share the bandwidth more efficiently through the use of OFDMA (A for access), where users are allocated different parts of the spectrum but the equalization benefits are still obtained. There are also challenges, most inherited from OFDM. These include tighter synchronization requirements and a high peak-to-average-power-ratio. Alternatives such as single carrier frequency domain equalization (SC-FDE) have been suggested to solve this problem but has yet to see commercial success. Thus it appears that MIMO-OFDM will continue its dominance, at least for the next five years.

History Behind Switching Between Multiplexing and Diversity for MIMO Systems

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.