# Improving the Performance of Turbo-Coded Systems under Suzuki Fading Channels
## 1 Introduction  
Rayleigh distribution has been widely used in wireless communication as an amplitude distribution for small-scale faded channels [1; 2; 3; 4]. On the other hand, distribution for large-scale faded channels due to shadowing is represented by log-normal distribution [5; 6]. However, it is more convenient to combine both distributions in land mobile communication to express both fading effects [7; 8]. Suzuki probability density function (PDF) was introduced in Reference [9] to undertake such a task. Many articles considered the Suzuki channel model in their analysis. In Reference [10], outage probability was addressed for device-to-device (D2D) communications in the environment of Suzuki distribution. Due to the complexity in calculating integrals resulting from this distribution, two nonanalytic approximating approaches were used to derive closed forms for outage probability in the presence of additive white Gaussian noise (AWGN).  
The statistical properties of ultrareliable low-latency communication (URLLC) were analyzed in Reference [11] for several channel fading models, including Suzuki distribution. Outage probability and performance were also analyzed utilizing power-law approximation for the maximum ratio-combiner (MRC) detector. In Reference [12], a new approach was introduced to develop a nonstationary complex-channel model that has an envelope similar to Suzuki distribution to address both small- and large-scale fading. In addition, it derived and analyzed Doppler power spectral density (PSD) and local power delay profile (PDP).  
In Reference [13], separating slow and fast fading was considered, utilizing a moving average filter in which Rayleigh and log-normal distributions were individually used to analyze the effects of multipath fading and shadowing, respectively. An efficient and novel method was proposed in Reference [14] to implement Weibull, log-normal, and Suzuki fading channels that utilize CORDIC technology that does not require a multiplier.  
The work in the literature shows that the LLRs used in calculating the soft bits for the decoder are approximated using Gaussian distribution without taking into consideration the effect of channel equalization.  
Linear detectors such as zero-forcing equalizers (ZFE) and minimum-mean-square error (MMSE) reduced complexity compared to more sophisticated detectors. In addition, the tendency of wireless-communication systems is to reduce detection complexity and to improve bit error rate (BER) performance.  
According to that, we considered the ZFE detector to equalize the channel effect at the receiver. The noise PDF after the ZFE is derived for Suzuki fading channels analytically and theoretically with proposed approximations. In addition, the derived PDFs are utilized in the calculation of the log-likelihood ratios (LLRs) to be used in the soft decoding of the turbo decoder. The results showed improvement in the performance of the coded system with the proposed LLRs compared to Gaussian-based LLRs.  
The rest of this paper is organized as follows. Section 2 demonstrates the system model, and Section 3 shows the derivation of the noise PDF, including the proposed approximations. Section 4 is used to discuss the results obtained in this paper. Finally, Section 5 concludes the study.