In a digital communication system, the source signal is transmitted over an intersymbol interference (ISI) channel, corrupted by noise, and then received as a distorted signal. In most cases, the additive white Gaussian noise (AWGN) can be used to model the background noise; however, the noise includes not only ISI and AWGN but the nonlinear distortion as well. If the channel response introduces both intersymbol interference and nonlinear distortions, transmitted signal will be corrupted nonlinearly, leading to worse performance. For example, the saturation of non-ideal amplifier and automatic gain control (AGC) loss in transceivers will produce nonlinear distortions that further degrade the performance of equalizers. Therefore, it is necessary to apply data equalizers to recover the original waveform from the distorted one in practical communication systems [1], [2]. A good equalization design can enhance the whole system performance with an acceptable cost.
Conventionally, the NRZ signal recovery is based on either linear equalizers (LEs)
[1], [3], or decision feedback equalizers (DFEs) [1], [2], [3]. A linear equalizer can restore the original transmitted signal in a wireline band-limited channel, where the channel distortion is linear without spectral nulls in the channel frequency response. Nevertheless, as the channel frequency response has spectral nulls, the received noise will be enhanced in the process of compensating these nulls, resulting in degraded performance. For linear equalization scheme, such channels that lead to malfunctions of equalizers have been termed “severe” ISI channels [4].
The decision feedback equalizer employing previous decisions to remove the ISI on the current symbol has been extensively exploited to serve intersymbol interference rejection. The least mean squares (LMS) algorithm is used to estimate the coefficients of the equalizer [1], [2], [3] whose accuracy determines the system performance.
For wireline high data rate applications, timing uncertainly degrades the system performance [5]. The channel response variance that is caused by manufacturing deviation makes the worse situation. It is necessary that using an equalizer to overcome clock skew and channel response variance. In addition, interconnect paths of parallel data I/O would cause the co-channel interference (CCI) [6]. The transmitted signals are tainted by the intersymbol interference that caused by the band-limited channel, the co-channel interference that caused by crosstalk between different channels, and background white noise. For recover the distorted data as well as suppress ISI, CCI and AWGN, a multi-input multi-output (MIMO) channel equalizer is essential.
Error control codes (ECC) are applied to enhance the accuracy of the transmitted data in wireless applications. The channel decoder with soft information inputs is widely employed to improve the error correction capability [7], and the bit interleaving is included [8] in wireless fading channels. With the soft output [9] and soft feedback [10]
channel equalizers, the soft decision channel decoder will receive more information from
the channel and therefore precisely decode the data sequence, leading to better BER performance.
Besides, the equalization schemes can be thought of a mapping from the received waveform to the transmitted data. The pattern recognition techniques have been used to identify the severely distorting date. Having the capability of classifying the sampling pattern and fault tolerance, artificial neural networks are very suitable for the channel equalizations. Recently, various equalizer designs based on artificial neural networks have been studied to the severely distorting signal recoveries [11]. Neural-based approaches have more flexibility and better performance than conventional equalization techniques.
The proposed approaches are based on the most popular multi-layer perceptron neural network with backpropagation algorithm (MLP/BP) [12], [13], [14], [15], [16]. As well, the MLP architecture can be regarded as a separateness-summation modus operandi in separating pattern space.
For wireline applications, we apply the MLP/BP-based channel equalization schemes to different applications. In the wireline band-limited channel that the data rate is ten times as much as the channel bandwidth, the MLP/BP-based feedforward equalizer (FFE) can recover the distorted data [17]. The MLP/BP-based DFE provide better performance, tolerate sampling clock skew, and permit channel response variance [18]. In wireline parallel I/O channels, the MIMO MLP/BP-based DFE can suppress ISI, CCI and AWGN, simultaneously [19]. However, the traditional MLP/BP-based DFEs are not good enough for the severe ISI channels with nonlinear distortions. We present a new neural network model, which is based on the MLP/BP neural network. This model utilizes a multivariate power series for the summation function of the MLP/BP neural networks [20], [21]. The corresponding training algorithm is deduced by the gradient steepest descent method;
consequently, the convergence solutions exist. Compared to the conventional approach
using a first order multivariate polynomial, the boundaries separating the pattern space change from piecewise linear into piecewise nonlinear. Therefore, this novel model is a generalized MLP/BP neural network (GMLP/BP) that is more flexible than other piecewise linear approaches because of the nonlinear separating pattern space. In such channels, the GMLP/BP-based DFE can outperform the traditional MLP/BP-based equalization schemes [22]. Also, the performance of the MIMO GMLP/BP-based DFE is better than that of the MIMO MLP/BP-based DFE in wireline parallel channels that contain ISI, CCI, and background white noise [23].
For wireless applications, a modified approach, which is also based on the most popular MLP/BP neural network, is presented. We apply the soft output and the soft decision feedback structure to the MLP/BP-based channel equalizer that concatenates with the soft decision channel decoder to improve whole performance on multi-path fading channels. Moreover, the performance of the MLP/BP-based soft DFE is also increased with the optimal scaling factor searching of the transfer function in the output layer of the MLP/BP neural networks and extra small random disturbances added to the training data [24].