Originally posted Aug 27, 2013
Gaining comfort from an intuitive explanation
Multiple-input/multiple-output (MIMO) is one of the most powerful techniques used in RF communications. In real-world environments, it provides a substantial increase in channel capacity, and the added capacity can be traded for other system benefits such as greater range or improved link quality. Increases in processing power coupled with MIMO’s effectiveness have led to its use in 802.11n WLAN solutions, 3GPP Long Term Evolution, WiMAX, and other standards.
Alongside diversity and space-time coding, MIMO is one of many multiple-antenna techniques. However, it’s the only one to promise the magic of a substantial increase in channel throughput—and that’s what makes it so desirable.
MIMO uses matrix math on the signals from multiple receive antennas to separate incoming signals from multiple transmit antennas and thereby establish multiple virtual RF channels over the same frequency range. And there’s the magic: more capacity by sending different signals over the same frequencies at the same time by removing co-channel interference.
Simply knowing that the matrix math works, and the technology is proven, offers cold comfort to many RF engineers. It’s natural for many of us to want an intuitive understanding, both for personal satisfaction and as a guide to better RF testing and interpretation of test results. To help create a more visceral understanding of MIMO, here’s a diagram of a demonstration that vividly illustrates the 2×2 case:
Two signal generators and two receivers produce four possible RF signal paths through “the channel.” The frequencies of the multi-tone signals are interleaved, allowing each receiver channel to determine the transmitter for each tone.
In this example, the signal sources generate multi-tone signals with a spacing of 1 MHz. The tones from one generator are offset by 500 kHz so that those from each generator can be easily separated at the receiver. Of course, frequency spacing is not the only way to separate the tones. As one alternative, wideband modulated signals could be multiplied with orthogonal codes, allowing correlation to be used at the receiver to identify the energy from each signal source.
As shown in the lower diagram, there are four possible signal paths. Each receiver measures signals from both sources as they are added together in the transmission channel. The result is four sets of tones, as shown in the two-channel measurements at the top, from which the frequency response of each path can be interpolated. The scalar spectrum is shown here, but the measurement is actually a vector (mag/phase) one.
Our system knows what signal was transmitted (amplitude/phase or I/Q) and there are four signal paths to measure. We thus have four measurements, one for each path, so we can look at this as four equations and four unknowns and use matrix math to solve.
Here is the critical step in the explanation: Now that we have full vector knowledge of the four paths, we know exactly how signals will combine. After sending known signals to measure the channel, we can send independent data streams from each transmitter. The receiver can apply the channel knowledge to the received signals to reverse the combining (i.e., remove the interference) in the channel and recover the separate transmitted signals and therefore the two independent data streams. More apparent magic: Removing the co-interference creates two virtual channels in place of one.
In practical systems, the transmitters send modulated data most of the time and intermittently send known training sequences to allow the channel measurements to be updated as frequently as the channel is likely to change.
A favorite quote from science/science-fiction author and visionary Sir Arthur C. Clarke, often known as his third law, is “Any sufficiently advanced technology is indistinguishable from magic.” However, as engineers we deal in deeper understanding, and hopefully with this explanation even this very advanced and useful technology is fully distinguishable from magic.