M. S. Yee

Radial basis function-assisted turbo equalization

This paper presents a turbo equalization (TEQ) scheme, which employs a radial basis function (RBF)-based equalizer instead of the conventional trellis-based equalizer of Douillard et al. (1995). Structural, computational complexity, and performance comparisons of the RBF-based and trellis-based TEQs are provided. The decision feedback-assisted RBF TEQ is capable of attaining a similar performance to the logarithmic maximum a posteriori scheme in the context of both binary phase-shift keying (BPSK) and quaternary phase-shift keying (QPSK) modulation, while achieving a factor 2.5 and 3 lower computational complexity, respectively. However, there is a 2.5-dB performance loss in the context of 16 quadrature amplitude modulation (QAM), which suffers more dramatically from the phenomenon of erroneous decision-feedback effects. A novel element of our design, in order to further reduce the computational complexity of the RBF TEQ, is that symbol equalizations are invoked at current iterations only if the decoded symbol has a high error probability. This techniques provides 37% and 54% computational complexity reduction compared to the full-complexity RBF TEQ for the BPSK RBF TEQ and 16QAM RBF TEQ, respectively, with little performance degradation, when communicating over dispersive Rayleigh fading channels.

Multi-level radial basis function network based equalisers for Rayleigh channels

Radial basis function (RBF) network based channel equalisers have a close relationship with Bayesian schemes. Decision feedback is introduced in the design of the RBF equaliser in order to reduce its computational complexity. The RBF decision feedback equaliser (DFE) was found to give similar performance to the conventional mean square error (MSE) DFE over Gaussian channels using various quadrature amplitude modulation (QAM) schemes, while requiring a lower feedforward and feedback order. Over Rayleigh-fading channels similar findings were valid for binary modulation, while for higher order modems the RBF based DFE requires increased feedforward and feedback orders in order to outperform the conventional MSE DFE scheme.

Burst-by-burst adaptive turbo-coded radial basis function-assisted decision feedback equalization

The performance of the proposed radial basis function (RBF) assisted turbo-coded adaptive modulation scheme is characterized in a wideband channel scenario. We commence by introducing the novel concept of the Jacobian RBF equalizer, which is a reduced-complexity version of the conventional RBF equalizer. Specifically, the Jacobian logarithmic RBF equalizer generates its output in the logarithmic domain and hence it can be used to provide soft outputs for the turbo-channel decoder. We propose using the average magnitude of the log-likelihood ratio (LLR) of the bits in the received transmission burst before channel decoding as the channel quality measure for controlling the mode-switching regime of our adaptive scheme.

Block turbo coded burst-by-burst adaptive radial basis function decision feedback equaliser assisted modems

A novel adaptive modem scheme is presented for transmissions over wideband mobile channels, which employs a radial basis function (RBF) based decision feedback equaliser, in order to mitigate the effects of the dispersive wideband channel. Turbo codes are invoked for improving the bit error rate (BER) and bits per symbol (BPS) performance of the scheme, which is shown to give a significant improvement in terms of mean BPS performance compared to that of the uncoded RBF equaliser assisted adaptive modem.

Coded modulation assisted radial basis function aided turbo equalization for dispersive Rayleigh-fading channels

In this contribution a range of coded modulation (CM)-assisted radial basis function (RBF)-based turbo equalization (TEQ) schemes are investigated when communicating over dispersive Rayleigh-fading channels. Specifically, 16 quadrature amplitude modulation-based trellis coded modulation (TCM), turbo TCM (TTCM), bit-interleaved coded modulation (BICM), and iteratively decoded BICM (BICM-ID) are evaluated in the context of an RBF-based TEQ scheme and a reduced-complexity RBF based in-phase/quadrature-phase (I/Q) TEQ scheme. The least mean square (LMS) algorithm was employed for channel estimation, where the initial estimation step-size used was 0.05, which was reduced to 0.01 for the second and the subsequent TEQ iterations. The achievable coding gain of the various CM schemes was significantly increased, when employing the proposed RBF-TEQ or RBF-I/Q-TEQ rather than the conventional noniterative decision feedback equalizer (DFE). Explicitly, the reduced-complexity RBF-I/Q-TEQ-CM achieved a similar performance to the full-complexity RBF-TEQ-CM, while attaining a significant complexity reduction. The best overall performer was the RBF-I/Q-TEQ-TTCM scheme, requiring only 1.88 dB higher signal-to-noise ratio at BER=10/sup -5/, than the identical throughput 3 b/symbol uncoded 8 PSK scheme communicating over an additive white Gaussian noise channel. The coding gain of the scheme was 16.78 dB.

A wide-band radial basis function decision feedback equalizer-assisted burst-by-burst adaptive modem

The performance of radial basis function-based decision feedback equalized (RBF DFE) burst-by-burst adaptive quadrature amplitude modulation (AQAM) is presented for transmissions over dispersive wide-band mobile channels. This scheme is shown to give a significant improvement in terms of the mean bit error rate (BER) and bits per symbol (BPS) performance compared to that of the individual fixed modulation modes. The structural equivalence of the RBF DFE to the optimal Bayesian equalizer enables it to potentially outperform the conventional Kalman-filtered AQAM DFE scheme.

Turbo equalization of convolutional coded and concatenated space time trellis coded systems using radial basis function aided equalizers

A reduced-complexity radial basis function (RBF) aided neural-network based turbo equalization (TEQ) scheme is proposed for employment in a serially concatenated convolutional coded and systematic space time trellis coded (CC-SSTTC) arrangement. A two-path Rayleigh fading channel having a normalised Doppler frequency of 3.3615/spl times/10/sup -5/ was used. The BER performance of the RBF-CC-SSTTC(4,4) scheme employing a transmission burst consisting of 100 symbols using a space-time-trellis (STT) interleaver of at least 400 symbols and eight turbo equalization iterations was found to be similar to that of the CC-SSTTC system using a trellis-based TEQ, which attains the optimum performance. However, the Jacobian RBF based TEQ provided a complexity reduction factor of 14.

Iterative radial basis function assisted turbo equalisation of various coded modulation schemes

A radial basis function (RBF) assisted turbo equaliser (TEQ) scheme, applied to various coded modulation schemes, is investigated. Specifically, trellis coded modulation (TCM), turbo trellis coded modulation (TTCM), bit-interleaved coded modulation (BICM) and BICM with iterative decoding (BICM-ID) are studied, when communicating over frequency selective fading channels. At a given complexity, the TTCM RBF-TEQ provides the best bit error ratio (BER) and frame error ratio (FER) performance. The RBF-TEQ structure is shown to provide an SNR performance improvement of about 5.5 dB at a BER of 10/sup -4/ in comparison to the conventional non-iterative DFE scheme.

Reduced complexity in-phase/quadrature-phase turbo equalisation using radial basis functions

A novel reduced complexity radial basis function (RBF) neural network based equaliser, referred to as the in-phase/quadrature-phase RBF equaliser (I/Q-RBF-EQ), is proposed. The I/Q-RBF-EQ is employed in the context of turbo equalisation (TEQ) assisted by iterative channel estimation. The performance of the I/Q-RBF-TEQ is characterized in a noise limited environment over an equally weighted, symbol-spaced three-path Rayleigh fading channel. The I/Q-RBF-TEQ achieved the same performance as the conventional turbo equaliser, while achieving a complexity reduction by a factor of 1.5 and 109.6 for 4-QAM and 16-QAM, respectively.

Radial basis function assisted reduced complexity in-phase/quadrature-phase turbo equalisation of coded modulation schemes

A radial basis function (RBF) assisted reduced complexity in-phase/quadrature-phase (I/Q) turbo equalisation (TEQ) scheme is investigated in the context of trellis coded modulation (TCM), turbo TCM (TTCM), bit-interleaved coded modulation (BICM) and iteratively decoded BICM (BICM-ID). The proposed schemes are characterised in performance terms, when communicating over frequency selective Rayleigh fading channels. The RBF-I/Q-TEQ-TTCM achieved a similar performance to the full-complexity RBF-TEQ-TTCM, while attaining a complexity reduction factor of 36 in terms of the required additions/subtractions and a factor 9 in terms of the multiplications/divisions necessitated.