OFDM with ICI Frequncy Equalization

[David83]

OFDM with ICI Frequency Equalization

Hello,

I have an OFDM system over a time varying frequency selective channel, which means I have ICI at the receiver side. I am dealing with the ICI using linear frequency equalizer like MMSE. Without ICI equalization, there is an error floor in the ABER vs. SNR. With ICI equalization, the curve decays well until a certain SNR point, and then it gets worse (going upward). Is this expected to happen in such systems? If anyone has a related paper, I appreciate if he/she gives it to me.

Thanks

 

[rcdaniels]

Re: OFDM with ICI Frequency Equalization

Hi David,

Interesting topic. Can you provide some more details?

Are you equalizing each subcarrier independently? If so, I'm surprised that equalization mitigates ICI.

Perhaps the equalization is only removing the ISI (intersymbol interference) effects? Are you doing something separate for ISI?

The error floor performance is as expected since both ISI and ICI, unmitigated, effectively add noise that is independent of the SNR.

There are some strategies for removing ICI such as:
(1) array processing to focus on the strongest path (Doppler corrected through standard frequency offset removal)
(2) lowering the OFDM FFT size (increases subcarrier bandwidth)
(3) advanced equalization where multiple subcarriers are equalized simultaneously
(4) spreading and windowing to reduce the contribution of ICI

3 and 4 are often preferred since they don't change the structure of the OFDM modem substantially.

For 3, use scholar.google.com to find "Low-complexity ICI suppression for OFDM over time-and frequency-selective Rayleigh fading channels" by Cai and Giannakis. For 4, the reference is "General self-cancellation scheme for mitigation of ICI in OFDM systems" by Seyedi and Saulnier, but I couldn't find a PDF on scholar.

 

[David83]

Re: OFDM with ICI Frequency Equalization

Since I am using OFDM, ICI can be thought as ISI but in the frequency domain. I do MMSE equalization for the whole block together. The received signal can be written as Z=H*X+W. When I compare the noise-free received signal with H*X, I get the same results. Also, after equalization, the equalized signal is the same as X. But when I add the noise, the system breaks down. So, my guess is that the noise power in the received signal and the noise covariance matrix in the MMSE equalizer are not the same. I define the noise power as following:

N0=T/SNR;
n=sqrt(N0/(2*Ts)).*(randn()+1i.*randn());

where T is the OFDM block duration and Ts the sampling time. Is this correct?

Thanks

 

[rcdaniels]

Re: OFDM with ICI Frequency Equalization

Can you be more specific about your equalization algorithm? Are your operations in the frequency or time domain? What are your dimensions for H and X? What is your model for ICI?

Unlike ISI (which is cyclic in the time domain thanks to the cyclic prefix), ICI is not cyclic in the frequency domain. How do you handle this?

Without knowing more I'd guess that you are using a similar model to this paper my Hyrcak and Matz: https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.134.3563&rep=rep1&type=pdf

You might want to check model specifics there to make sure you conform.

 

[David83]

Re: OFDM with ICI Frequency Equalization

OK, I am transmitting CP-OFDM signal over time-varying frequency selective channel. The received signal in the time-domain and after removing the CP can be written as y=H*x+n. In case of time-invariant frequency selective channels, H is circulant matrix, because the channel taps remain constant over one OFDM block. Which means the orthogonality between sub carriers maintained in the frequency domain, and the frequency samples can be written as Yk=Hk*Xk+Nk for k=0,...,N-1, where Yk, Hk, Xk, and Nk are the kth frequency sample of the received signal, channel, transmitted signal, and AWGN, respectively.

In the case of time-varying channel, H is no longer circulant, which implies that each frequency sample is interfered by all other samples, i.e.,: the orthogonality between the subcarriers destroyed which results in ICI. The optimum solution in this system is ML receiver, whose complexity is very high for practical values of N, because the solution space is now 2^N at least!!. So, instead, I arrange the received samples as [Y0 Y1 ... YN-1]^T and do MMSE equalization to it in the frequency domain to reduce the effect of ICI before doing symbol-by-symbol detection. This solution is suboptimal, but should give good results, and eliminate the error floor.

Hope this help

If you have specific questions, I am glad to answer them.

Thanks

 

[Priya274]

Re: OFDM with ICI Frequency Equalization

Hi David

Can you please help me how you are applying mmse in OFDM ? Which error you are minimizing ? Is this alogorithm can be applied to time domain?