Low complexity turbo equalization using superstructures

Abstract

In a wireless communication system the transmitted information is subjected to a number of impairments, among which inter-symbol interference (ISI), thermal noise and fading are the most prevalent. Owing to the dispersive nature of the communication channel, ISI results from the arrival of multiple delayed copies of the transmitted signal at the receiver. Thermal noise is caused by the random fluctuation on electrons in the receiver hardware, while fading is the result of constructive and destructive interference, as well as absorption during transmission. To protect the source information, error-correction coding (ECC) is performed in the transmitter, after which the coded information is interleaved in order to separate the information to be transmitted temporally. Turbo equalization (TE) is a technique whereby equalization (to correct ISI) and decoding (to correct errors) are iteratively performed by iteratively exchanging extrinsic information formed by optimal posterior probabilistic information produced by each algorithm. The extrinsic information determined from the decoder output is used as prior information by the equalizer, and vice versa, allowing for the bit-error rate (BER) performance to be improved with each iteration. Turbo equalization achieves excellent BER performance, but its computational complexity grows exponentially with an increase in channel memory as well as with encoder memory, and can therefore not be used in dispersive channels where the channel memory is large. A number of low complexity equalizers have consequently been developed to replace the maximum a posteriori probability (MAP) equalizer in order to reduce the complexity. Some of the resulting low complexity turbo equalizers achieve performance comparable to that of a conventional turbo equalizer that uses a MAP equalizer. In other cases the low complexity turbo equalizers perform much worse than the corresponding conventional turbo equalizer (CTE) because of suboptimal equalization and the inability of the low complexity equalizers to utilize the extrinsic information effectively as prior information. In this thesis the author develops two novel iterative low complexity turbo equalizers. The turbo equalization problem is modeled on superstructures, where, in the context of this thesis, a superstructure performs the task of the equalizer and the decoder. The resulting low complexity turbo equalizers process all the available information as a whole, so there is no exchange of extrinsic information between different subunits. The first is modeled on a dynamic Bayesian network (DBN) modeling the Turbo Equalization problem as a quasi-directed acyclic graph, by allowing a dominant connection between the observed variables and their corresponding hidden variables, as well as weak connections between the observed variables and past and future hidden variables. The resulting turbo equalizer is named the dynamic Bayesian network turbo equalizer (DBN-TE). The second low complexity turbo equalizer developed in this thesis is modeled on a Hopfield neural network, and is named the Hopfield neural network turbo equalizer (HNN-TE). The HNN-TE is an amalgamation of the HNN maximum likelihood sequence estimation (MLSE) equalizer, developed previously by this author, and an HNN MLSE decoder derived from a single codeword HNN decoder. Both the low complexity turbo equalizers developed in this thesis are able to jointly and iteratively equalize and decode coded, randomly interleaved information transmitted through highly dispersive multipath channels. The performance of both these low complexity turbo equalizers is comparable to that of the conventional turbo equalizer while their computational complexities are superior for channels with long memory. Their performance is also comparable to that of other low complexity turbo equalizers, but their computational complexities are worse. The computational complexity of both the DBN-TE and the HNN-TE is approximately quadratic at best (and cubic at worst) in the transmitted data block length, exponential in the encoder constraint length and approximately independent of the channel memory length. The approximate quadratic complexity of both the DBN-TE and the HNN-TE is mostly due to interleaver mitigation, requiring matrix multiplication, where the matrices have dimensions equal to the data block length, without which turbo equalization using superstructures is impossible for systems employing random interleavers.