Performance of M-MRC over Generalized-K Fading Channel based on Energy Harvesting Technique

The customary uses of the multi-antenna systems are to reduce the effect of fading in a wireless environment. The maximal ratio combining (MRC) scheme is one of such techniques which provide the optimal performance. This paper analyse the performance measures of an arbitrary branch MRC receiver with energy harvesting techniques over KG fading channel. We have presented the closed-form expressions for average SNR, outage probability, and average bit error rate (ABER) along with the numerical analysis. Our observations are summarized in the numerical results and discussion section for well understanding of the system. At last, we validate our proposed formulations through the Monte-Carlo simulation.


Introduction
In wireless communication systems, radio-wave propagation through wireless channels happen to be a complicated phenomenon due to the various effects, such as multipath fading due to reflection, diffraction, and scattering. Several models are presented to depict the statistical behaviour of wireless channels for different situation [1].In reality the multipath fading and shadowing occur concurrently leads to the composite fading channels. These composite fading channels are superimposed by lognormal shadowing such as Rayleigh-lognormal or Nakagami-lognormal fading channels [2]. However, such lognormal based fading models are complicated and difficult to evaluate the various performance measures of communication systems through mathematical analysis [3]. Consequently, an alternative approach a Gamma distribution is utilized, which is mathematically more versatile and also accurately describes fading and shadowing phenomena such as Generalized-K (KG) distribution [4] or K-distribution [5].
The Generalized-K fading model describes the composite multipath/shadowing fading channels and the results obtained using this model is closely matched with the experimentally obtained results. KG fading model is the composite Nakagami-Gamma distribution which closely approximates Nakagami-Lognormal distribution [6]. It also includes the K-distribution as a special case, and incorporates most of the fading and shadowing effects in wireless communication channels. The main advantage of employing the Generalized K-distribution is that it makes the mathematical analysis much simpler compared to Lognormal-based models. Diversity is a technique which improves the quality of the received signal and exploits the low probability of deep fades simultaneously in different fading paths. Depending upon the combining technique, the performance and the complexity of the diversity receiver varies. Maximal ratio combining (MRC) is the optimal combining technique which gives the best performance compared to other combining receiver [7]. wireless information and power transfer systems over KG fading channels using fixed power splitter is not available in the literature. In this paper, we have presented the closed form expression for average SNR, outage probability and ABER employing M-MRC receiver in KG fading channels and using power splitter at the receiver side.
Further, the effect of the system and fading parameters on the system performance has been verified through simulation results. In addition to this, we study the effect of average energy harvested at the receiver end with fixed power splitter.
This work is structured as follows: Section 2 presents the system model considered for analysis. Performance analysis of the system is carried out in Section 3.
In Section 4, shows the numerical results and discussion. We conclude our work in Section 5.

System Model
The channel behavior is considered as a slow and frequency non-selective with the KG fading model. Figure 1 shows the proposed model that have been considered for evaluation of the system performance. having PDF given by [12].
where k and m are the two distribution shaping parameters, Using Eq. (2) with some rearrangement and by performing RV transformation, the PDF of γ for MRC receiver over KG fading channel is evaluated as [4]   The received signal from the output of MRC is then fed into a power splitter, where the signals are split to the information receiver and energy receiver separately. For each fading state, the signal power split to information decoding (ID) is denoted by (1-β) with 0 ≤ β ≤ 1, and that to energy harvesting (EH) as β where β can be adjusted over different fading states.
Applying random variable transformation,  

Outage Probability
Outage probability is given as [ where, g (·, ·) is the incomplete gamma function.

Average Bit Error Rate
The average bit error rate (ABER) can be expressed in terms of the PDF of the output

Binary Non-Coherent Modulations
In binary non-coherent modulations, the expression for the conditional BER can be obtained as   where, Wλ,μ(·) is the Whittaker function [13, (9.220)].

Numerical Results and Discussion
In  From the power vs SNR curve as shown in Figure 5, we have plotted for M=5, m=2 and β=0.8. It can be observed from the figure that a significant amount of power can be harvested at the receiver above 40 dB SNR, beyond which the harvested power is increased exponentially. Practically, this is not possible to maintain such a high SNR in this link as the transmitter is always supposed to connect to a conventional power source.

Fig.5 Power vs SNR in dB
From the above plots, we have also observed that the order of diversity has a significant impact on the performance measures such as outage and ABER, which can be easily observed from Figure 2, Figure 3, and Figure 4. However, from the energy harvesting point of view, the improvement is not significant. In this case, the receiver has no fixed power supplies and thus we get the expected power as shown in Figure 5.

Conclusion
In this paper, the closed-form mathematical expression including the PDF of output

Declarations
Funding: The authors did not receive support from any organization for the submitted work.
Conflicts of interest: The authors have no conflicts of interest to declare that are relevant to the content of this article.