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MIMO Streams, Channels and Condition Number Reveal a Defect

Blog Post created by benz on Sep 12, 2016

Originally posted Dec 26, 2014

Streams multiply complexity but they can also add insight

Multiple-input multiple-output (MIMO) techniques are powerful ways to make efficient use of scarce RF spectrum. In a bit of engineering good fortune, MIMO methods are also generally most effective where they’re most needed: crowded, reflective environments.

However, MIMO systems and signals—and the RF environments they occupy—can be difficult to troubleshoot and optimize. The number of signal paths goes up with the square of the number of transmitters, so even “simple” 2×2 MIMO provides the engineer with four paths to examine. 4×4 systems yield 16 paths, and in some systems 8×8 is very much on the table!

All these channels and streams, each with several associated measurements, can provide good hiding places for defects and impairments. One approach for tracking down problems in the thicket of results is to use a large display and view many traces at once, the subject of my Big Data post a while back. Engineers have powerful pattern recognition and this is a good way to use it.

Another way to boil down lots of measurements and produce some insight—measuring condition number—is specific to MIMO. This trace is a single value for every subcarrier, no matter how many channels are used, and it quantifies how well MIMO is working overall. Sometimes not too well, as in this measurement:

This condition number trace is flat over the channel, at a value of about 25 dB. The ideal value is 0 dB and condition number should be similar to the signal/noise ratio (SNR), so signal separation and demodulation is likely to be very poor unless SNR is very good.

This condition number trace is flat over the channel, at a value of about 25 dB. The ideal value is 0 dB and condition number should be similar to the signal/noise ratio (SNR), so signal separation and demodulation is likely to be very poor unless SNR is very good.

The signal for the measurement above was produced with four linked signal generators, so SNR should not be a problem. However, the fact that the condition number is far above 0 dB certainly indicates that there is a problem somewhere.

Analysis software such as the 89600 VSA provides several other tools to peer into the thicket from a different angle. As mentioned previously, this 4×4 MIMO system has 16 possible signal paths, and they can be overlaid on a single grid. In this instance a dozen of the paths looked good, while four showed a flat loss about 25 dB greater than the others. That is suspiciously close to the 25 dB condition number.

Of course, when engineers see two sets of related parameters they tend to think about using a matrix to get a holistic view of the situation. That’s just what’s provided by MIMO demodulation in the 89600 VSA software as the MIMO channel matrix trace, and in this case it reveals the nature of the problem.

The MIMO channel matrix shows the complex magnitude of the 16 possible channel and stream combinations in a 4×4 MIMO system with spatial expansion. Note that the value of channel 4 is low for all four streams.

The MIMO channel matrix shows the complex magnitude of the 16 possible channel and stream combinations in a 4×4 MIMO system with spatial expansion. Note that the value of channel 4 is low for all four streams.

This MIMO signal was using spatial expansion or spatial encoding, as I described recently. Four streams are combined in different ways to spread across four RF channels. The complex magnitudes are all different—to facilitate MIMO signal separation—and very much non-zero.

All except for channel 4, where the problem is revealed. The matrix shows that the spatial encoding is working for all four streams, but one channel is weak for every stream. In this case the signal generator producing channel four had a malfunctioning RF attenuator, reducing output by about 25 dB.

As is so often the case, the solution comes down to engineers using pattern recognition, deduction and intuition in combination with the right tools. For Keysight, Job 1 is bringing the tools that help you unlock the necessary insights.

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