Should we use Maximal ratio combining and an equalizer together?

Question

I have confusion on MRC (Maximal Ratio Combining) method, which I would like to clarify. An example is where I have 1 transmit antenna and 4 receive antennas. The concept of MRC is to combine all the signals from the 4 receive antennas such that the combined SNR is increased (given the phase is corrected). To achieve this, a weight is computed for each antenna branch, such that it weights the received signal in proportion to the signal strength.

Once the MRC process is completed, are we required to equalize the channel effect with some equalizer (for e.g. ZF or MMSE). Most of the online materials refer to MRC as a equalizer, which is causing confusion. With my understanding, we should equalize, as the MRC is only increasing the SNR but not inversing the channel effect.

If we require to use an equalizer (ZF / MMSE) after combining, which channel coefficient should we use? Because once the received symbols are combined, we just have a vector (with increased SNR). But the channel coefficients are different between 1 tx antenna and each 4 rx antenna.

Answer 1

Combining signals can improve SNR as you have said. Equalization on the other hand reduces the effect of distortion, which could be deterministic, in which case combining signals would not improve the transmission as the effect would be the same in all the received signals. So yes you are right, you could have a situation where it is beneficial to both equalize and combine signals.

For the channel coefficients, you would have to estimate the channel coefficients for a specific application, in the same way as you would estimate them if you weren't doing any combining: for instance this could either be by explicit physical modelling of the transmission medium, or experimentally by applying a test signal and fitting a model.

I have borrowed from the answer to this almost identical question: Confusion with Maximal Ratio Combining(MRC) in SIMO OFDM. There's some discussion about the order of combining/equalization too which might be of interest, as this has implications for estimating the channel coefficients.