Is CMA equalization applicable for OFDM

Question

I have a question regarding the constant modulus algorithm (CMA), as you know it's one of the known algorithms used for blind equalization. The cost function of the CMA is build blindly, it means based on received signal only. The cost function of that algorithm is:

$J = \frac12\left[\left\lvert w^T*y(n)\right\rvert^2 - R_{cm}\right]^2$

where $R_{cm}$ is the constant of CMS algorithm which is usually equals 1. $w^T$ is the equalizer coefficients and $y(n)$ is the received signal.

My question, is that algorithm applicable for OFDM system?

If so, and what's the constant $R_{cm}$ will be?

Answer 1

No.

OFDM isn't constant modulus (i.e. constant envelope) in time domain, if you look at it as one system. It's quite the opposite; it's known for its high PAPR (which you probably know!). This is the case, by the way, even if you use a CM modulation for the individual subcarriers.

So, CMA's central requirement isn't fulfilled.

Also, the whole point of doing OFDM is that you don't need an overall equalizer. So don't use one. OFDM in itself is designed to transform your equalizer-necessitating wideband channel into narrowband channels that are "flat" enough. So, whenever you apply an equalizer to an OFDM system: you're either doing something wrong, or the OFDM system was designed incorrectly (i.e. not for the channel that you're having).

(That is not to say that there's absolutely no room for time-domain equalization in OFDM systems, but it's going to be extremely specific corner cases.)