A Turbo Equalizer with Kalman Filter Based Channel Estimator

Turbo equalization (TEQ) is a base band signal processing technique that attempts reliable detection of data in a coded data transmission system subject to intersymbol interference (ISI) and additive white Gaussian noise (AWGN). The application of the turbo principle to equalization and decoding is called TEQ. The basic transmission system is a typical serial concatenated system (SCS). An SCS consists of two forward error correcting (FEC) encoders connected by means of a suitable interleaver. The outer FEC produces coded bits in response to the input data bits. The coded bits are interleaved so as to make them statistically independent. The interleaver is an essential component in a generic turbo receiver. The interleaved data feed a second stage called the inner encoder. The ISI channel serves as the inner encoder in the present work. It is viewed as applying redundancy on the interleaved data bits in the form of a linear convolution. The corresponding receiver consists of an equalizer and decoder connected by the deinterleaver. Both the equalizer and the decoder are configured as soft-in soft-out (SISO) signal processors. The equalizer takes as input the matched filter outputs and another information called extrinsic information provided by the decoder. The output of the equalizer is soft in nature as it is a ratio of two probabilities when binary phase shift keying is applied as the modulation technique. The equalizer is a trellis matched to that of the ISI channel. This is possible when we consider an ISI channel a finite state machine (FSM). The soft outputs are generated by the equalizer in terms of the loglikelihood ratio (LLR) on all the coded bits. These soft outputs serve as a priori to the FEC decoder, after suitable deinterleaving. The soft data estimates are computed by performing an ensemble average on the decoder soft outputs. The flow of extrinsic information between the equalizer and the decoder through interleaver and deinterleaver constitutes one iteration. These iterations are carried out for a predetermined number or convergence. The trellis based equalizer needs knowledge of the channel taps in order to compute the branch metrics and the transition probability. The literature on TEQ report the performance of the turbo equalizers for perfect channel estimates. However, in a practical scenario, the receiver needs to estimate the channel taps using some algorithm. We use a Kalman filter (KF) in a decision directed (DD) mode to estimate the channel and use these estimates subsequently to feed the trellis based equalizer. This receiver operates in a DD configuration due to the fact that, the data estimates formed at the decoder output serve as the training bits for the KF. When the TEQ is converging, the decoder produces more reliable data estimates that tend to approach their true values. The improvement in the data estimates improves the channel estimates by reducing the variance and the Kalman loop gain. The training data is treated as a stochastic signal that consists of a deterministic component and the random component. As the TEQ progresses with higher iterations, the random component is also reduced and this results in improved bit error rate (BER) at the decoder output.