In this paper, we studied the end-to-end average bit error rate (BER) performance of decode-and-forward (DF) relaying multi-hop chain systems (MCSs) over log-normal fading channels. After specifying the distribution of the signal-to-noise rate for each hop, the analytical expression of the end-to-end average BER has been derived. The derived end-to-end average BER model can be used in the case that all the single-hops in the chain have different statistical behaviors, i.e., all links suffer various types of fadings, not limited to one type of fading. The comparisons between Monte Carlo simulation results and analytical results under various conditions verify the accuracy of the proposed model.
Multi-hop relaying has been regarded as a promising technique for expanding network coverage and realizing space diversity [1] and [2]. In multi-hop relaying chain systems, a source communicates with its corresponding destination via a multi-hop chain link, which consists of several intermediate relays. Multi-hop chain link is a most common and basis communication topology in practical scenarios, especially in cell communication systems, e.g., IEEE 802.16j [3] and LTE-Advanced [4], where the base station communicates with the terminals on the edge of the cell or in the coverage hole via one/several relay stations.
The performance of amplify-and-forward (AF) cooperative systems have been widely studied over log-normal fading channels by researchers [5], [6], [7], [8], [9] and [10]. Among these works, the authors of [7] developed a comprehensive framework for performance analysis of multi-branch multi-hop wireless relay systems over log-normal fading channels based on the Gauss quadrature rule of the moment generation function for the log-normal distribution. In [8], end-to-end outage probability evaluations of multihop non-generative and regenerative relaying systems over log-normal shadowed channels have been presented. In decode-and-forward (DF) relaying multi-hop chain systems (MCSs), the relays decode the received signal and then forward the decoded information to the receiver of next hop.
In the past, the performance of DF two-way relaying systems has been well studied [11], [12], [13], [14] and [15]. In [11], the authors derived the analytical expressions for the end-to-end SNR and outage probability of cooperative diversity in correlated log-normal channels. The authors of [12] derived the analytical expressions to study the cooperative diversity performance using selection relaying over correlated log-normal channels for both selection combining and maximal ratio combining techniques at the receiver.
Recently, DF relaying multi-hop systems have gained the focus from researchers [16] and [17]. For DF relaying MCSs, the authors of [16] proposed the closed analytical expressions for the end-to-end average bit error rate (BER) over Rayleigh and Nakagami-m fading channels and with various modulation schemes. However, the main conclusion of [16] (namely, Eq. (3) in [16]) limits to the case that all the single-hops in the chain have the same statistical behavior, i.e., all the links are i.i.d with equal average received SNR. In [17], the upper bounds on the average BER in closed-form for the case of Nakagami-m fading on all hops over a DF relaying multi-hop chain link have been derived.
These existing works clearly indicate that few contribution has been made for DF relaying systems or non-relaying systems on log-normal fading scenarios [11], [12], [18], [19] and [20], especially there is no work on analyzing the average end-to-end BER of MCS. As another important channel model, log-normal fading channel model is recognized as a better model for indoor radio propagation environments to address the mixed effect of short-term fading and long-term fading indoor channels and shadowing effect in outdoor scenarios [21] and [22]. However, the literature is relatively spare in performance analysis of DF multi-hop relaying systems over log-normal fading channels.
Motivated by the observation, in this paper, the end-to-end average BER performance of DF relaying MCS over log-normal fading channels was studied. The analytical expressions for the end-to-end average BER of DF relaying MCS have been proposed by using the prosperities of log-normal distributions and mathematical induction method. Moreover, The derived closed-form expression for average BER can be applied to the cases that all the single-hops in the chain have different statistical behaviors, i.e., all the links suffer various types of fading and/or various modulations adopted at each single-hop.
The rest of this paper is organized as follows: Section 2 introduces the considered system model. In Section 3, the end-to-end average BER has been analyzed for DF relaying MCS over log-normal fading channels and the analytical expression has been derived for the end-to-end average BER. Section 4 presents simulation and numerical results to confirm our proposed model. Finally, Section 5 concludes this paper.
Motivated by a lack of study on the end-to-end performance of DF relaying MCS, the analytical expressions for the end-to-end average BER was derived by using the properties of log-normal distributions and mathematical induction method. The accuracy of the presented analytical model has been verified via Monte Carlo simulation over various scenarios.
