Communications Laboratory
Co-author: prof. Roberto Cusani, University of Rome "La Sapienza"
Research problem
The channel impulse response (CIR) of a sparse channel typically comprises few nonzero powerful taps spaced by many zero taps of negligible amplitude. As an example, TDMA transmission at symbol rate 2.Msymb/s over the channel with maximum delays of the order of 20ms corresponds to more than 40 multipath components in the receiver. The conventional countermeasure against inter-symbol interference (ISI) channels is the channel equalisation by the viterbi algorithm or the MAP algorithm. However, the algorithms can only handle up to 7-8 first taps because their complexity increases exponentially with respect to the number of taps. Thus the problem is to find a solution that allows us to select the strongest taps for equalisation with arbitrary (not necessarily consecutive) locations.
Known solutions for the problem
First solutions for the sparse channel equalisation were based on making the channel minimum-phase by appropriate filtering; in other words, the energy from the farthermost taps was transferred to the beginning of the CIR so that the conventional equalisation techniques were applicable. Many reduced state solutions for the viterbi algorithm and the DFE equalisation have been proposed in the literature. However, the solutions are typically parameter dependent so that a new model need be derived for each channel tap configuration.
Our solution for the problem
We derived a SC-MAP algorithm for sparse channel equalisation that has a complexity
proportional to the number of nonzero taps and not to the overall CIR length. The receiver
exploits the symbol-by-symbol SBS-MAP algorithm that for time-varying channels is coupled
with a Kalman channel estimator that tracks only the nonzero taps. The locations of the
nonzero taps are identified from the training sequence via the cross-correlation method or
data-aided Kalman filter. The simulation results show that the performance of the receiver
is related to the energy of the nonzero taps so that when all energy is used in
equalisation, the performance of the conventional full-MAP is obtained. The papers [1] and
[3] summarise the results of this part.
Co-authors: prof. Roberto Cusani and Marco Di Felice, University of Rome "La Sapienza"
Research problem
This work addresses how to utilise efficiently soft and hard tentative decisions in the multistage parallel interference cancellation (MPIC). Hard decisions enable total cancellation therefore they are always preferable when the symbol estimates are sufficiently reliable. However, they may also double the estimation error in the case of wrong decisions. In the multistage cancellation especially the first stage appears to be problematic with hard symbol estimates because the presence of severe multiple-access interference (MAI) makes the symbol estimates very unreliable.
The soft estimate of a symbol is a floating point number, say, within [-1,1] for binary modulation obtained via some non-linearity (e.g., hyperbolic tangent function) that gives an ultimate estimate about the reliability of the symbol decision. For example, in the presence of severe interference the symbol estimate for binary modulation might be close to zero causing no cancellation of that particular symbol; this realises the idea that no cancellation is better than poor cancellation. The problem with soft symbol estimates is that they may make only partial cancellation when the interference level is not very high, causing a performance loss compared to hard symbol estimates. The best strategy seems to be to use both soft and hard decisions in the multistage cancellation and we have tried to find the optimum way for doing that.
Known solutions for the problem
The first solutions used the decorrelating detector at the first stage to improve the quality of initial data estimates. This enhances considerably the performance of the following PIC detector with fully hard decisions. The main problem of this hybrid solution is the high complexity that is due to the matrix inversion in the decorrelating detector.
The first pure PIC cancellation approach was partial cancellation introduced by Divsalar et al. in [Div98] for binary modulation and AWGN channel. Partial cancellation takes into account the estimate of the symbol of interest from the previous stage in the calculation of the new symbol estimate, in contrast to the conventional PIC cancellation that employs the previous stage symbol estimate only to calculate the interfering signal for the other users. This leads to an iterative structure where the contribution of the previous stage symbol estimate is determined by the stage specific weight factors. The paper gives the optimum minimum mean-square error (MMSE) estimator for obtaining soft binary decisions. However, the paper shows results only for hard decisions because the optimisation of the scale factor of the non-linearity for each stage (in addition to the weight factors) appears to be too complicated.
Our solution for the problem
We introduce a strategy how to perform multistage interference cancellation in the presence of multipath by applying coherent combining and despreading before multi-user detection. This is based on modelling the MAI and ISI by the symbol level S-CIRs that can be calculated from the estimated chip level C-CIRs and known correlation values between the user spreading codes. The approach closely follows the definition of the single user ISI channel and is also applicable for asynchronous transmission (see the papers [4],[5]).
We extend the idea of partial cancellation over multipath fading channel and complex modulation using the concept of the S-CIRs. We show the non-linearity for obtaining soft decisions with QPSK modulation and the stage specific parameters optimised via simulation trials for various channels. Secondly, we introduce Bayesian cancellation that circumvents the optimisation problems of partial cancellation. The optimum MMSE estimator for Bayesian cancellation is derived for any complex coherent modulation. The nice feature of Bayesian cancellation is that the scale factor of the non-linearity is given directly in terms of the interference power that can be estimated symbol-by-symbol via a simple procedure (see the paper [6] for details).
The simulation results obtained from the time-division TD-CDMA system show that Bayesian cancellation clearly outperforms partial cancellation in all circumstances. This is due to the difficulty in optimising the parameters of partial cancellation. The Bayesian cancellation with a simple symbol-by-symbol interference power estimator has the performance very close to the ideal cancellation with known channel and has a minor loss with estimated channel coefficients. The channel estimation schemes for the downlink and uplink of TD-CDMA are given in [6].
[1] R. Cusani, J. Mattila, "A new receiver for digital mobile radio channels with large multipath delay", Proc. URSI International Symposium on Signals, Systems, and Electronics, ISSSE'98, Pisa, Italy, pp.304-309, September 29 - October 2, 1998. / Conference presentation slides.
[6] R. Cusani, M. Di Felice, J. Mattila, "Multistage Symbol-by-Symbol Bayesian Interference Cancellation for CDMA Links Affected by Severe Multipath", Proc. GLOBECOM'99, Rio de Janeiro, Brasil, pp. 2223-2227, Dec.1999. / Conference presentation slides.