This article introduces the rationale and techniques involved with MIMO (Multiple-Input Multiple-Output)-based communication systems. The communication impairments due to multipath channels provide the base motivation for the application of the MIMO technique, and, in particular, the use of OFDM (Orthogonal Frequency Division Multiplexing) and spatial multiplexing for equalizing broadband wireless channels with non-selective fading.
The presence of multiple reflections and multiple communication paths between two radio terminals causes signal fading impairments to a wireless communication link. There is both selective and non-selective fading. Nonselective fading is where the frequency components over the signal bandwidth are dynamically attenuated by the same amount and do not create any signal distortion; rather, only temporal signal loss. Selective fading is where smaller frequency segments of the signal’s spectrum are attenuated relative to the other remaining frequency segments. When this occurs, the signal spectrum is distorted and this, in turn, creates a communication impairment that is independent of signal level.
For the case of narrow-band signals with non-selective fading, the communication impairment can be countered by providing more signal-level margin in the communication link or using selection diversity techniques to select the best antenna input based on the relative signal strength. However, in the case of non-selective fading, the signal must be equalized to restore the signal fidelity and expected communication performance.
This fading is produced by the arrival of multiple replicas of the transmitted signal at the receiving antenna. The signal replicas are produced by multiple random reflections within the communication medium, such as an indoor communication channel. The multipath concept is shown in Figure 1, and is based on the notion of an ellipsoidal fading model1.
If one constructs a simple, two-ray fading model and is able to generate the signal attenuation versus communication range, one finds the presence of crests and nulls due to the constructive and destructive interference caused by the arrival of the signals at different delay times and therefore, different phase angles. In some cases, the phase angle can be at or near 180 degrees and can cause partial signal cancelation, or, conversely in the case of signals that are in-phase, partial signal enhancement.
As mentioned previously, the effects of this localized and sudden attenuation can be compensated for by receiving the signal at two different receiver antenna placement locations and selecting the best antenna based on the signal strength or some other receiver performance measure. Figure 2 illustrates this by showing the signal strength at two different antenna placements over communication range and/or time. The signal strengths associated with the antennas are generally not correlated in time and/or space, and when one signal is in a null, the other can be found near a maximum and selected for communication.
The selection of one antenna over the other based on signal quality or selection diversity is a technique that works well for non-selective fading in that the antenna selection essentially is a signalstrength restoration technique. The effects of antenna diversity for a Rayleigh fading channel show a 17.5 dB gain in performance. The same performance can be achieved by introducing additional signal level margin of 27.5 dB without the additional antenna and selection scheme.
For broader-band signals more commonly used in modern wireless systems such as wireless LAN, selection diversity and other signal strength restoration techniques are not enough to equalize the impairments imposed by the multipath channel due to selective fading.
Selective fading occurs when the signal bandwidth exceeds the coherence bandwidth of the channel2. The coherence bandwidth of the channel is approximately the reciprocal of the delay spread of the channel2. The delay spread is the rms average of the delay times of the complex impulse response of the channel. The impulse response of the channel is the received complex envelope at a particular point in space, assuming that a carrier signal is modulated by a Dirac impulse. The arrival of the various signal components can be modeled by a finite impulse response filter. Ideally, the channel transfer function only adds a flat fading process (constant attenuation versus frequency) and a single fixed time delay (linear phase). However, the case shown above creates a transfer function for the signal that provides asymmetric and frequency dependent fading of amplitude as well as a nonlinear phase response, assuming that significant sidebands of the signal are distributed across the entire transfer function shown.
If the sidebands of a complex modulated signal where distributed across the transfer function shown, there would be significant signal distortion and modulation conversion (AM to PM and AM to PM). This again is the effect of a multipath channel with a coherence bandwidth that is less than the signal bandwidth.
In order to compensate for these effects, the transfer function encountered via the communication channel must be equalized at the receiver. Ideally, if the inverse of the transfer function could be applied to a signal prior to detection to flatten the amplitude response and to linearize the phase, the signal impairments would be eliminated.
There are several different types of transversal equalizers that operate on the time domain representation of the baseband signal to achieve the equalization; however, many rely on training sequences and training periods (receipt of non-information bearing training information that creates communication overhead).
OFDM and Channel Equalization
The introduction of OFDM signaling not only provided a means of spectrally efficient communications, but also provided for a means of channel equalization in the frequency domain. OFDM essentially provides a means of sampling the magnitude and phase of the channel at any or all of the subcarrier frequencies, since the carrier phase tracked at the receiver and all of the subcarrier phases are coherent to the main carrier. However, in practice, performing continuous subcarrier phase tracking on each of the subcarriers is not executed; rather, short and long training symbols with known patterns are transmitted with each packet such that the receiver can determine the channel transfer function, invert it, and then apply the inverse to the received spectrum in order to equalize the channel on a packet by packet basis.
The channel transfer function, due to selective fading, weights the received spectrum. At the receiver, the magnitude and phase of each of the subcarriers provide an estimate of the channel transfer function, Hc( ). An equalization transfer function, He( ), can be applied to the channel-weighted spectrum to re-normalize the spectrum such that the effects of the channel can be reduced or eliminated.
In general, there are different permutations of redundant transmitters and receivers to improve the robustness of a communication link and the information- carrying capacity of the link. Shown in Figure 3 are the different, general redundancy configurations SISO, SIMO, MISO, and MIMO.
SISO, or Single-Input Single-Output, systems do not provide any type of robustness or capacity improvement, and represent a basic wireless communication link. SIMO, or Single-Input Multiple-Output, systems are configurations that provide receive-side diversity and provide additional robustness, but no capacity improvement. Examples of SIMO systems are receivers with selection diversity schemes or Linear Maximal Ratio Combining (LMRC) schemes2. MISO, or Multiple-Input Single-Output, provides transmitter diversity in that it couples to the channel at a different point in space such that the links will not have the same fading characteristics, though the receive antenna and spatial sum of the signals will be dominated by the stronger of the two signals. The transmitter signal design can be such that the combining at the single receiver can made in an optimal fashion as is done in Space-Time Coding Techniques2. MIMO systems demultiplex the source data stream into multiple independent channel streams. This provides for both redundancy and channel capacity improvement3.
The MIMO technique, also referred to as Spatial Division Multiplexing, is a single-source data stream multiplexed between two spatial streams. As shown in Figure 3, there are direct links and cross links between the two transmitters and two receivers. As a result, there are now four different communication channels that connect the two terminals, and the characterization of the channel has a higher complexity. However, the signaling technique, when combined with the properties of OFDM modulation, can lead to an efficient channel estimation and equalization scheme.
The spatial multiplexing technique associated with MIMO is another method to minimize the effects of a multipath communication channel through its redundancy and channel equalization properties.
This article was written by Brian Petted, CTO of LS Research, Cedarburg, WI. For more information, Click Here
- Diagram after: “MIMO Channel Modeling and Emulation Test Challenges,” K.Bertlin, Agilent Technologies, 2008.
- C. Oestges and B. Clerckx “MIMO Wireless Communications,” Academic Press, 2007.
- B. Holter, “On the Capacity of the MIMO Channel- A Tutorial Introduction,” Norwegian University of Science and Technology, Department of Telecommunications, O.S.Bragstads plass 2B,N-7491 Trondheim, Norway.