Forums

MMSE and ZF equalization in OFDM systems

Started by Dan25 February 10, 2015
Hi,

What is the performance difference of MMSE equalizer and ZF equalizer in a
OFDM system. I have simulation 3 tap Rayleigh channel for QPSK ODFM system
and found out that both the equalizers give the same performance. 

But in Single carrier Frequency Domain Equalization, MMSE performs
significantly better than ZF. 

Can anyone please advice me in this regard.

Thanks in advance.	 

_____________________________		
Posted through www.DSPRelated.com
I thought the point of OFDM is that it does not need 
Eq.  Can you clarify?

Mark
On Tue, 10 Feb 2015 04:12:47 -0800 (PST), makolber@yahoo.com wrote:

>I thought the point of OFDM is that it does not need >Eq. Can you clarify? > >Mark
OFDM just has a less complex EQ compared to single carrier as the channel delay spread lengthens. The benefit of OFDM is that the fading becomes flat per subcarrier, so each subcarrier has a single-tap EQ with the channel estimation being done using scattered (in time and/or frequency) pilots or training sequences. That being said, I'm not sure what the OP is asking, either. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
>On Tue, 10 Feb 2015 04:12:47 -0800 (PST), makolber@yahoo.com wrote: > >>I thought the point of OFDM is that it does not need >>Eq. Can you clarify? >> >>Mark > >OFDM just has a less complex EQ compared to single carrier as the >channel delay spread lengthens. The benefit of OFDM is that the >fading becomes flat per subcarrier, so each subcarrier has a >single-tap EQ with the channel estimation being done using scattered >(in time and/or frequency) pilots or training sequences. > >That being said, I'm not sure what the OP is asking, either. > > >Eric Jacobsen >Anchor Hill Communications >http://www.anchorhill.com >
Hi Mark and Eric, Thanks for your responses. My questions is when inverting the channel effect should I consider the noise variance, specially at low SNR ? e.g. Sub carrier = i Y[i] = H[i] . X[i] + V[i] (in frequency domain) H is the flat fading channel for the ith sub carrier, X is the transmitted symbol and V is the noise sample. N0 is the noise variance. When I equalize this signal in frequency domain, My ZF equalizer: Q[i] = 1/H[i] MMSE equalizer: Q[i] = H*[i]/ (H[i].H*[i] + N0) What are you opinion about the performance of these equalizers ? _____________________________ Posted through www.DSPRelated.com
I believe you will see some difference if you implement channel estimation
from sparse pilots. 
What I expect to happen is that a "bad" subcarrier will destroy adjacent
SCs when interpolation leaks the error across frequency.
But I'm not sure, this was a long time ago... 

Generally, the channel _estimator_ will probably be the "bottleneck" in
real life. 

	 

_____________________________		
Posted through www.DSPRelated.com
On Tue, 10 Feb 2015 21:29:47 -0600, "Dan25" <98432@dsprelated> wrote:

>>On Tue, 10 Feb 2015 04:12:47 -0800 (PST), makolber@yahoo.com wrote: >> >>>I thought the point of OFDM is that it does not need >>>Eq. Can you clarify? >>> >>>Mark >> >>OFDM just has a less complex EQ compared to single carrier as the >>channel delay spread lengthens. The benefit of OFDM is that the >>fading becomes flat per subcarrier, so each subcarrier has a >>single-tap EQ with the channel estimation being done using scattered >>(in time and/or frequency) pilots or training sequences. >> >>That being said, I'm not sure what the OP is asking, either. >> >> >>Eric Jacobsen >>Anchor Hill Communications >>http://www.anchorhill.com >> > >Hi Mark and Eric, > >Thanks for your responses. My questions is when inverting the channel >effect should I consider the noise variance, specially at low SNR ? > >e.g. Sub carrier = i > >Y[i] = H[i] . X[i] + V[i] (in frequency domain) > >H is the flat fading channel for the ith sub carrier, X is the transmitted >symbol and V is the noise sample. N0 is the noise variance. > >When I equalize this signal in frequency domain, > >My ZF equalizer: Q[i] = 1/H[i] >MMSE equalizer: Q[i] = H*[i]/ (H[i].H*[i] + N0) > >What are you opinion about the performance of these equalizers ? > > >_____________________________ >Posted through www.DSPRelated.com
Meant to reply earlier but apparently neglected to do so. To add a little to what mnentwig said, I think it'll depend on a number of things. The channel estimation method will certainly have an effect, as will the type of channel and the dynamics of the channel. The relative performance of the two methods may differ based on the channels as well as the channel estimation methods. FWIW, that's not too surprising because there are similar tradeoffs between ZF and MMSE for single carrier systems as well. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com