Enhancement of Equal Gain Combiner for Detection of Spectrum Hole in a Cognitive Radio System

Cognitive Radio System (CRS) is of paramount importance in wireless communication for spectrum management. However, channel impairment affects accurate Spectrum Hole Detection (SHD) in CRS resulting in harmful interference to a licensed user. Conventional Equal Gain Combiner (EGC) which is one of the techniques being used to solve the problem suffers from hardware complexity resulting in high Sensing Time (ST). Hence, in this paper, an Enhanced EGC (EEGC) for SHD in a CRS is proposed to reduce the hardware complexity of conventional EGC. Ten thousand (10,000) bits are randomly generated, modulated using Binary Phase Shift Keying (BPSK) scheme and propagated over Rayleigh fading channel. The received signals through three antennas are scanned by three Selection Combiners (SCs) to select the branch with highest Signal to Noise Ratio (SNR). The outputs of the three SCs are then combined using conventional EGC. The output of conventional EGC is used as input to single Energy Detector (ED) to determine the energy of the combined signal. A mathematical expression for Probability of False Alarm (PFA) for the proposed technique is derived using 𝑋𝑋 2 distribution to set thresholds at 0.01 and 0.02. The proposed technique is simulated using MATLAB software and evaluated using Probability of Detection (PD), ST and Probability of Missing (PM). The results obtained show that EEGC gives better performance with lower ST, higher PD and lower PM.


Introduction
Wireless Communication (WC) is the exchange of information between two or among many points through an unbounded environment. In WC, information is transmitted through the air using electromagnetic waves. The exponential rise in the number of users accessing WC services resulting in rapid increase in the demand for high data rate services leads to spectrum scarcity. Previous researches have shown that spectrum scarcity is not only limited to insufficient spectrum but also to poor utilization of the allocated spectrum. In 1999, Mitola proposed a technique known as Cognitive Radio Networks (CRNs) that overcome spectrum scarcity [1,2]. Cognitive Radio (CR) is a WC technique in which a transceiver intelligently senses the spectral environment over a wide frequency band to detect unused spectrum and provide wireless links through the unused spectrum [3,4]. CR is made up of two users namely: licensed Users (LUs) and Unlicensed Users (ULUs). LUs are authorized users who have the precedence to use the assigned spectrum, while ULUs are unauthorized users who are allowed to make use of assigned spectrum only when LU is not present [5,6,7,8]. 290 Enhancement of Equal Gain Combiner for Detection of Spectrum Hole in a Cognitive Radio System Spectrum Sensing (SS) is the process of determining the idle spectrum (spectrum hole) in a CR network. It is one of the key operations in CR system to evaluate the performance of CR [9,10,11]. The accuracy of spectrum hole detection, which is the ability of ULU to sense LU without interference depends on the channel impairments. The channel impairment such as atmospheric factors, different type of obstacles affects signal propagation resulting in fluctuation of the received signals causing poor reception of the signal at ULU. The poor signals reception of the ULU makes the accurate spectrum detection to be difficult and results in hidden licensed user which poses to be one of challenges of CRS [12]. The problem of hidden licensed user is overcome by the use of multiple antennas at the ULU that receives multiple copies of LU signal. However, the performance of multiple antenna technique in CRS depends on diversity combiner and detector employed. Energy Detector (ED) and Eigenvalue Detector (EVD) are the two major detectors used in CRS to detect the presence of spectrum hole. The choice of these detectors is due to fact that no prior information about LU signal is required, therefore, synchronization is not necessary. ED is very simple to implement and has a better detection rate in comparison with EVD. Therefore, this leads to adoption of ED to determine the presence of spectrum hole in a CRS [13,14]. Several techniques being proposed to take care of the hidden LU problem in CRS include Equal Gain Combiner (EGC), Selection Combiner (SC) and Square Law Combiner (SLC). From the existing literature, EGC and SLC have better performances with high detection rate even at a low signal strength than SC but at the expense of Hardware Complexity (HC) [15]. SC is often used in practice, but there is a trade-off between the HC and the detection rate when compared with SLC and EGC [16]. Therefore, in this paper, an Enhanced EGC (EEGC) is proposed to improve the detection rate and at the same time reduce the hardware complexity of the conventional EGC.

Equal Gain Combiner with Energy Detector
One of the techniques previously used to solve the problem of hidden LU in a CRS is Equal Gain Combiner (EGC) with ED. EGC is a combining technique in which all the branches of the signals weighed with the same weight before summing and co-phased to increase signal strength. In EGC, the received signals from different branches are first multiplied with equal weights and then co-phased to avoid signal reduction before summing up. In detecting SH, output of EGC is used as input to Energy Detector (ED) in determining the energy of the received LU signals. The energy obtained is, then, compared with set threshold to find the presence of SH. EGC with ED is usually employed to find spectrum hole due to high detection rate, but characterized with hardware complexity due to multiple RF chains and Matched Filters (MFs). The received signal passes through each of the RF chains, MFs and then, sums all the signals before applying ED as shown in Fig. 1

Related Work
In [18] EGC for SS in Cognitive Radio systems was proposed to solve hidden LU problem in CR networks. The technique comprised five ULU antennas that received LU signal and multiplied with equal branch weight. The resultant signal was then made to pass through RF chain and Match Filter (MF) before applying ED to obtain the energy of the received signals. Output of ED was then compared with the set threshold to make a decision on the presence of SH. The result of the paper revealed that, the technique had high detection rate but at the expense of HC. Also, in [11] ED based SS over fading channels was proposed. LU interference in CR was addressed using SC method. In the paper, ULU selected the path with highest signal strength and received signal from that path. The received signal was applied to ED to get energy of the selected signal and make decision on presence of SH. The results of the paper showed a reduction in HC but at the expense of low detection rate. In [19], a multi-node spectrum sensing based on ED for dynamic spectrum access was proposed to combat the problem of PU interference in CR using Collaborative-Technique Hard-Decision (CTHD) with logic table. In the paper, each ED received signal from each antenna and made a decision on the redundancy of the spectrum. The decision from individual ED was then combined to make a final decision using logical table. The result of [19] showed that the probability of missing was low but with high sensing time due to several energy detectors involved in the technique.
Multiple detectors based analytical performance of SS is presented in [20] to address hidden LU problem in CRS using Maximal Ratio Combiner (MRC) technique. The received signal from different branches were multiplied with the channel gain and summed before applying single ED to get the energy of the combined signal. The obtained energy was then compared with the set threshold to determine the redundancy of spectrum. The result of [20] showed that, the technique had a higher detection rate but suffered from hardware complexity due to estimation of channel gain on each branch thereby leading to high sensing time. Also, [21] worked on ED of unknown signal over fading channel to address hidden LU problem in a CRS using SLC method. In [21], five antennas, five EDs and a combiner were used to determine the presence of LU signal. ED received signal from each of the antennas and output of each of the EDs were combined and compared with the set threshold to make a decision on the presence of spectrum hole. The result of [21] showed that, the technique had a high detection rate even at a very low signal strength. Also, it was very easy to set decision threshold as it did not require perfect channel knowledge but with HC as a result of several EDs leading to high sensing time and high implementation cost. Past researches have shown that EGC, CTHD, MRC and SLC have better performances but suffer from HC. while, SC was associated with a poor detection rate. Therefore, this work proposes an Enhanced EGC (EEGC) technique to reduce the HC of existing EGC and fluctuation of the received signal.

A. Spectrum Sensing in Cognitive Radio
Signal detection technique which is used to describe the method that reveals the presence of SH known as SS in a noisy environment is employed in this work. The technique is formalized as two hypothesis tests H1 and H0 which represent the presence and absence of LU, respectively. H1 and H0 indicate that LU communicates and LU does not communicate, respectively. The two hypotheses are given by [22,23,24] as. (2) and (3), four different possible cases that can occur in signal detection are defined: firstly, Probability of Detection (PD) which is declaring H1 when LU signal is actually present and Secondly, Probability of Missing (PM) which describes declaring idleness of spectrum when LU signal is present. Probability of False Alarm (PFA) is the third one that describes the occupancy of the spectrum when LU is not actually present and the fourth one is declaring 0 when LU is not present. PM is the biggest problem in spectrum sensing because increase in PM, increases the chances of ULU interfering with the LU. However, it is required to have PFA as low as possible in order for the system to dynamically make use of the available idle spectrum [25].

B. Energy Detector in Signal Detection
Energy Detector (ED) is used in signal detection to find the spectrum hole based on the energy of the received LU signal. It is a commonly used detector due to its low computational complexity and can be implemented in time domain as well as frequency domain. The detection is carried out by comparing the energy of the LU signal with the set threshold. The set threshold is a function of PFA [24]. This detector has a Band-Pass Filter (BPF) which allows certain frequency range called the passband to pass while attenuating the others, a squaring device and an integrator to obtain the energy of the received signal. The obtained energy at the output of the integrator is then compared with the set threshold and if the obtained energy is above the threshold, then, spectrum is occupied, that is, spectrum hole is not exist otherwise spectrum is idle [14, 292 Enhancement of Equal Gain Combiner for Detection of Spectrum Hole in a Cognitive Radio System 21,26]. ED approach is implemented without any prior knowledge of LU signal, but has some challenges which include poor performance under low SNR [26]. The output of ED, " " is given by [27] as where: is the set threshold Equation (5) represents the threshold which indicates whether PU signal exists or not. Small noise power, long detection time and high signal power resulting in better performance of ED [24].

C. Selection Combiner
The choice of Selection Combiner (SC) is made due to its low HC and ability to choose the signal on the branch with the highest SNR. In this combiner, the sum of the individual signal from different branches is not required since output of SC is equal to the signal on only one branch [28,29,30,31]. It is one of the simplest detection techniques in which ULU is assumed to have the knowledge of channel status at a particular time and thus, selects the branch with highest gain and receives signal from that branch. The SNR output of the SC ′ ′ is given by [20,32,33,34] is the received SNR per bit of the ℎ branch at any instant

D. Rayleigh Distribution
Rayleigh fading distribution is adopted due to its appropriate distribution that matches a cluster environment in a CR. It is a statistical distribution used for modeling the effect of signals propagating in a cluster environment where the effect of heavily built up environments is of paramount importance. It is mostly useful when there is no dominant line of sight along the propagation channel. In this environment, the received signal characterized by obstructions is the summation of all the diffused signal components. The amplitude of the received signal is described by Rayleigh Probability Density Function (PDF).
The PDF of this distribution denoted by ( ) is given by [28,32] as where: is the magnitude of the signal received is the peak value of the signal received 2 is the average power of the signal received

E. Development of an enhanced EGC using SC
The multiple copies of LU signals propagated through the Rayleigh fading channel considered are received by ULU multiple antennas and first scanned by SC. Scanning through the received multiple antenna signals is carried out to select the path with the highest value of SNR and ignore the weaker branches through SC. There are nine branches at the inputs of three SCs which result into three branches at the SCs output, through branch selection based on highest SNR. The three branches at the output of SCs are used as inputs to EGC. The three branches of signal are then co-phased, weighted, and summed up. Output of EGC is then used as input to ED to determine the energy of the received LU signal. The obtained energy is compared with the set threshold to decide on the presence of SH. The assumption is that if the values of energy obtained are above the set threshold, SH is not present due to ongoing transmission of LU, otherwise, spectrum hole is present, that is, the spectrum is idle. The threshold is set using PFAs of 0.01 and 0.02. Block diagrams of the proposed technique are shown in Figs. 1 and 2, where ℎ represents Rayleigh fading channel. MF and RF chain are the major components that determine the complexity of EGC. However, the number of branches to combine are proportional to number of RF chains and MFs in conventional EGC. In this paper, nine branches were considered using conventional EGC as a combiner requires nine MFs and nine RF chains leading to hardware complexity. The number of RF chains and MFs are reduced in this paper from nine (9) to three (3) using SC to select only the best three paths and ignore weaker ones, thereby reducing the HC.   (5) and (6), with ED and SC output SNR as the input of EGC, output signal of an enhanced EGC ' ' is given as where: is the number of SC ( ) is the output of each SC

F. False Alarm Probability of EEGC
Using Equation (8), output of ED ' ' under 0 hypothesis is given as Since / 0 is the sum of square the distribution of test statistics becomes X 2 distribution. Using X 2 distribution, the output of ED ′ƒ / 0 ( )′ is given by [10] as Equation (10) is integrated to obtain PFA of the proposed EEGC technique.

G. Probability of Detection and Probability of Missing (PM) for the Proposed EEGC
Probability of Detection (PD) for the proposed EEGC ( ( ) ) is given as where: is the energy obtained Probability of Missing (PM) is the probability that ULU detects the idleness of spectrum when spectrum is actually busy. PM for the EEGC ( ( ) ) is given as The results obtained reveal that, the proposed EEGC has a better performance with lower PM value than the conventional EGC due to SC that is first applied to select signal with highest SNR before applying EGC. Results obtained also reveal that, PM values reduce as SNRs increase for the two techniques and this is due to performance of ED that reduces as SNR increases. The PD and PM values obtained at different SNRs are given in Tables 1 and 2 for the two values of PFA considered.  The results obtained reveal that, ST increases as PFA increases and this is due to the fact that, the detection of ED is faster at higher threshold value than at lower threshold value. The ST values obtained for both EEGC and conventional EGC for the two PFA considered are given in Table 3.

Conclusions
In this paper, an enhanced Equal Gain Combiner for detection of spectrum in CRS is proposed. The proposed EEGC technique is incorporated with the system model and simulated using appropriate simulation parameters in line with Long Term Evolution (LTE) standard. The system is developed using three Selection Combiners (SCs), EGC and only one ED. Mathematical expression of PFA for the enhanced technique is derived using 2 distribution which is used to set decision thresholds at 0.01 and 0.02. The performance of the enhanced and conventional EGC has been evaluated at PFA of 0.01 and 0.02 using PD, PM and ST as performance metrics. The results show that EEGC perform relatively better than conventional EGC with lower ST, lower PM and higher PD values.
The better performance of the Enhanced EGC (EEGC) is due to selection of signal with highest SNR before applying EGC. EEGC gives lower ST values due to reduction in RF chains and matched filters of EGC compared to conventional EGC. The results of this paper show that, the proposed technique performs better as SNR increases. Therefore, the EEGC has shown a better performance than the conventional EGC.