# Is my concept of receive diversity right? EGC,MRC and SC

Is my concept of receive diversity right?There are three combining technology belong to receive diversity.

1.Equal gain combining(EGC)

$$\sum e^{-j\theta_k}(\sqrt{P}|h_k| e^{j\theta_k}x[n]+w[n])$$

so the EGC coefficient is $$e^{-j\theta_k}$$ just because we assume the channel phase is $$e^{j\theta_k}$$,so it seems that this method is hope the signal can have same phase direction and sum it.

2.Selection combining(SC)

we have a receiver with multiple antenna,so theoretically we have multiple SNR in the receiver,now we select the highest SNR as real SNR. It seems that this method like Ostrich Syndrome,that is ,we don't do any other process to the signal,we just choose the highest SNR and ignore the other weaker SNR.

3.Maximal ration combining(MRC)

we use the Cauchy–Schwarz inequality to realize the MRC coefficient is the conjugate of the channel,that is

$$\sum |h_k|e^{-j\theta_k}(\sqrt{P}|h_k| e^{j\theta_k}x[n]+w[n])$$

So theoretically,the SNR performance order is

MRC>EGC>SC,because MRC not only do some process in the phase,but also amplitude,however,EGC just do some process in the phase.we all know that the signal power has a high relation with amplitude,so the performance of MRC will be the highest in these three method.

Is my concept and thinking right?

• Sounds pretty solid to me. It's not necessarily MRC>EGC>SC, you'd need to write $\geq$ technically, since for the special case where all $|h_k|$ are equal you have MRC=EGC and for the special case of a single branch (antenna), they are all equal. – Florian Nov 19 '19 at 11:58
• @Florian Consider turning your comment into an answer. – MBaz Nov 19 '19 at 16:05
• Thanks for the suggestion. I followed it. – Florian Nov 19 '19 at 16:40

It's not necessarily MRC>EGC>SC, you'd need to write $$\geq$$ technically, since for the special case where all $$|h_k|$$ are equal you have MRC=EGC and for the special case of a single branch (antenna), they are all equal.