I am modelling an equaliser trained by linear RLS and LMS in a simple BPSK modulation system.
I found a problem that, the short length of equaliser, (e.g. equal to length of CIR), is not able to promise no error bit in noise-free environment. In contrast, the longer length of equaliser can reduce the propabability of error bit in the same environment.
However, the long equaliser has to cause complexity of circuit implementation.
In addition, the decision delay of equaliser also determines the performance of equaliser.
So, does anyone know that how to determine the length and decision delay of an equaliser?
Many thanks
Normally the equalizer delay is kept about half of its tap-weight length.
For lengthy packets, the steady state MSD behavior of RLS degrades while that of LMS/NLMS is stable. For highly selective channels, RLS is better as it converges faster. There is an alternative solution also, that is, to use RLS in the start (training phase) for a faster convergence and LMS in the steady state with weights initialized from RLS weights.
Theoretically, in the absence of noise, your equalizer is the inverse of the channel. Therefore, channel CIR is not a good indication of equalizer length. As far as I know, the length and delay (or equivalently the position of central tap) are usually determined by experiments because they depend on channel characteristics (not only the length of the delay spread).
In addition to complexity, you should also consider the training issue. The longer the equalizer, the slower it converges under LMS. For RLS, I suspect the same although RLS in general converges much faster than LMS.
You can get better result with less BER if you take a decision feedback equalizer(DFE) as compared to linear equalizer. DFE can be designed with shorter length and it performs well in presence of high noise and ISI.
Your question spearse for linear (LTE) or decision feedback equaliser(DFE).
For a LTE, optimum decision delay is fund the half the length of the equalizer filter, which means you are to target the symbol arrived to at the center of the filter. However for the DFE, the size of the feedback filter is close to size of the expected delay spread of the channel. Having said that the expected delay span of the feedfoward filter should be equal or greater than the 1.5 times of expected delay spread of the channel. Then the decision delay is also equal to full lengthof the feedfoward filter. That means the symbol is targeted has just arrived the last tap of the feedfoward filter.
ı do not want to make further comment to confuse you. the information is given above after 20 years of experience in equaliser filter implementation, myself and by my students.
One of the thumrule is
equalizer feed forward weights=channel order+1
Feedback weights= channel order
Decision delay = channel order
Check the following reference
Minimum-BER linear-combiner DFE
Chen, S. ; Chng, E.S. ; Mulgrew, B. ; Gibson, G.
Communications, 1996. ICC '96, Conference Record, Converging Technologies for Tomorrow's Applications. 1996 IEEE International Conference on
Volume: 2
DOI: 10.1109/ICC.1996.541394
Publication Year: 1996 , Page(s): 1173 - 1177 vol.2
Cited by: Papers (21)
IEEE Conference Publications
I doubt that the decision delay equal to the span of the channel is not enough for either LTE or DFE. The feedforward filter requires more delay to reduce the precursor ISI. So, go for 1.5 times of channel span in LTE or wait until the end of feedfoward filter of DFE for an optimum result.
Sarat thanks for the work by S. Chen, I was doing my PhD and listened the presentation in ICC 96 London.
Look at the inverse of a few typical channels to get a feel for which taps are important. Then run some monte carlo simulations to fine tune your selection.
Hi everyone,
Thank you for your precious comments.
As for the normal equaliser, the decision delay should be equal to the half of length of equaliser. The length of equaliser should be larger than the length of channel for promising the qaulity of communications. As Syed Muslim Shah said, normally the length of equaliser is three times to the length of channel. However, in reality, the length of channel may be unkown. Therefore, we should design a relatively long equaliser.
As for DFE equaliser, I think that the reference provided by Sarat Kumar Patra is very useful to DFE study. the reference provides the correct decision delay and the length of feedfoward and feedback filter. In addition, as Ismail Kaya said, the decision delay equal to the span of the channel is not enough to compensate the channel distortion. the size of feedforward filter should be larger. Indeed, in my simulation, if the length of normal equaliser is equal to the total length of feedforward and feedback filters, the performance of DFE is better than that of normal equaliser.
However, these experiences are for a simple BPSK modulation system. if the communications system is OFDM, DS-CDMA or CCK. the desgin of a good equaliser is different.
Kind regards
The length and decision delay are dependent on nature of the channel and channel impairments. You should model the fading channel properly before deciding length of adaptive equalizer.
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