Maximization of Total Throughput Using Pattern Search Algorithm in Underlay Cognitive Radio Network Ibrahim Zewail1, Waleed Saad2, Mona Shokair3 and Sami. A. El_dolil4 1
Higher Institute of Engineering and Technology, kafr El-Shiekh, Egypt
2, 3 and 4 Faculty of Electronic Engineering, El-Menoufia University, Menouf, 32952, Egypt E-mail address:
[email protected],
[email protected],
[email protected] and
[email protected] Abstract: The concept of Cognitive radio (CR) is considered as a promising solution for efficient spectrum utilization to solve the spectrum scarcity problem. This paper proposes Pattern Search (PS) algorithm for maximization of the total throughput of the communication system and increases the Quality-of-Service (QoS) of the Secondary Users (SUs) with saving QoS of the Primary Users (PUs). Moreover, a comparison between the proposed algorithm and other algorithms will be drawn. Further, the effect of the number of Primary Users (PUs), the number of Secondary Users (SUs) and the number of subcarriers are studied for increasing the total throughput for the SUs. Keywords: Cognitive Radio Network (CRN), spectrum sharing, Orthogonal Frequency Division Multiplexing (OFDM), Pattern Search Algorithm (PS). INTRODUCTION Wireless connectivity and mobility have witnessed a widespread deployment for all wireless networks. Nowadays, the wireless systems increased and took a wide portion of the spectrum band as a licensed band to work and the spectrum band became more crowded by the licensed systems. Actually, the spectrum-policy task force prepared a report published by the Federal Communication Commission (FCC) [1] to preview the radio spectrum utilization and indicated that the licensed systems had utilized their spectrum band by percentage reached about 85% [2]. I
CR technique uses the holes of the spectrum to enhance the efficiency for the utilization of the spectrum. In fact, it comes to be an extension of the Software Defined
Radio (SDR) [3] and it has the ability to adapt its reception or transmission parameters corresponding to the interaction with the radio environment to communicate efficiently [4]. There are four main functions for CR: spectrum sensing, spectrum management, spectrum mobility and spectrum sharing [5]. Moreover it has three modes of transmission: overlay, underlay and interweaved [6]. In the overlay mode, the SUs communicate over the free licensed spectrum (spectrum hole) making no interference with PUs [7]. In the underlay mode, there is no cooperation between SUs and PUs, the SUs can share all the spectrum with Pus making interference below a limited threshold. In interweaved mode, works as (Sensing-based spectrum sharing), where the SUs can access the spectrum after sensing it to detect the holes [8]. Actually, this paper assumes the case of underlay mode. The Quality of Service of the SUs is required to be maximized taking into consideration QoS of PUs, by increasing the total throughput of the system taking some constraints into account. This could be done by using some techniques such as: multicarrier modulation and power allocation using optimization algorithms [9-10]. These optimization algorithms were used for determining the optimum power level needed to maximize the total throughput of the system considering interference and power constraints in downlink underlay CRN. OFDM system was used as multicarrier modulation [11]. Ref. [12] used a subcarrier and power allocation for maximization of data rate and minimization the interference to PUs by achieving fairness among all the SUs. In [13] a binary power allocation with combining between the multi-user diversity gains and the spectral sharing techniques was investigated. In [14] Levenberg-Marquardt Algorithm is done to maximize the throughput for CRN. The authors in [15], used Pattern Search algorithm as optimization algorithm for finding the optimum values and improving the QoS of the system. Pattern Search algorithm and Genetic Algorithm optimization methods were compared in [16]. This paper uses OFDM system as a multicarrier modulation due to its advantages [11]. Strategies of power allocation for maximizing the sum data rate for all SUs using PS algorithm in the underlay CRN considering two constraints: interference threshold to PUs to preserve its Quality of service and the other is power of SUs in which it doesn't exceed maximum power of Access point (AP) which are not clarified until now. Using PS algorithm increases the total throughput of the system compared to Genetic Algorithm. The effect of some parameters such as: changing the number of SUs, the number of PUs and the number of subcarriers will be studied. The rest of this paper will be organized as follows: the System model based on OFDM modulation technique will be described in Sect. II. Throughput analysis will be presented in Sect. III. Pattern Search algorithm will be discussed in Sect. IV. Simulation
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results will be then demonstrated in Sect. V. Finally in Sect. VI, conclusions will be made. II
SYSTEM MODEL
Considering a downlink of multiuser OFDM system underlay the CR network has two groups of users, the first is L PUs that served by the Base station (BS) and uses a licensed spectrum band and the second is M SUs served by the Access Point (AP) which are randomly distributed in a circuit. The network radius is 1km and the users sharing the same licensed spectrum band W of the primary users as shown in Figure1.
Figure 1 System model [17]. The total spectrum bandwidth (W) is consisted of smaller subchannels in which each one has bandwidth (Ws), and the stream of high data rate is divided into lower data rate substreams and modulated into N OFDM symbols which are transmitted over N orthogonal subcarriers simultaneously. It is presumed that the channel state information is perfect. The following notations were used: the index of the Secondary User (SU) i lies between 1 and M, the subchannel n lies between 1 and N, the signal power is P and channel gain is h. III
THROUGHPUT ANALYSIS
It is required to enhance QoS for the SUs without affecting QoS of the PUs by maximizing the throughput for all SUs over all subcarriers under power and interference constraints. The achievable data rate for the secondary user i over subchannels n can be expressed as [17]: Ci= Ws log2 (1 + SINR)
(1)
where
SINR=
i p p h p ,i N 0Ws
Pi ,n hi ,i
M i pM ,n hi ,M
(2)
The maximum data rate for SU i over all the subchannels N can be denoted by: CN =
Pi ,n hi ,i N max n 1 nWs log 2 1 N M i p M ,n hi , M i p p h p ,i N 0Ws
(3)
The maximum data rate for all secondary users over all subchannels is given by: CT=
max i 1
M
N n 1
nWs log2 1
M
Pi , n hi ,i M i pM , n hi , M i p p hp ,i N0Ws
,
(4)
S.T.
M
N
i 1
n 1
pi , n ps
pi ,n ≥ 0, 𝜌𝑖 ∈ {1,0}, 𝛿𝑛 ∈ {1,0},
pi , n hi , p m ,
(5) (6)
(7)
Where Pi,n is the optimum power transmitted for the SU i over the subchannel n, hi,i is the data channel power gain for the SU i, Ws is the subcarrier distance and n is the subchannel activity. hp,i is power gain of the channel for the transmitter of PU to the SU receiver i, hi,M is the channel power gain for the SU i transmitter to the SU M receiver and is a factor of QAM mapper related to the bit error rate. hi,p is the channel power gain for theSU i transmitter to the PU receiver, Pp is the power transmitted by the PU and i is the PU activity factor. Ps is the maximum power allocated by the Access Point (AP). No is the noise power of additive white Gaussian noise with zero mean and variance σ2 and m is the threshold of the interference at PU. IV
PATTERN SEARCH ALGORITHM
The proposed optimization algorithm that is considered in this paper is the Pattern Search (PS) algorithm which is one of the direct search methods that are considered as a derivative-free method. It has some properties such as: very simple in concept, less computing time and easy to implement when compared with other heuristic algorithms such as Genetic Algorithm (GA) as illustrated in Ref. [16]. PS aimed to improve the Quality of Service of SUs by searching number of mesh points and detecting the optimum power to each subcarrier for all SUs that maximize the total throughput for all SUs under two constrains: power and interference in the downlink underlay mode for CRN.
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PS algorithm has two kinds of moves: the pattern move and exploratory move that sets a current point as (initial point) then search number of points around the initial point called mesh points as shown in Figure 2.
Figure 2. Pattern Search Algorithm [18]. And then check if the objective function of the new point is smaller than the objective function of the initial point then it replace the initial point with the new point (new pattern) and double mesh size to expand the search space range. Else, the initial point doesn't change and the mesh size will be reduced by half to reduce the search space range [19]. The PS steps are depicted by the flow chart of Figure 3 and can be stated as the following: 1. Setting the PS parameters such as mesh size, mesh expansion factor, mesh contraction factor and maximum number of iterations. 2. Setting the starting point (initial point). 3. Constructing the pattern vector and mesh points according to mesh size. 4. Calculating the objective function for each mesh point. 5. Asking for the termination condition such as: o The algorithm reached the Max. Number of iterations. o The mesh size less than mesh tolerance. o The algorithm reached to the predefined maximum number of function evaluations. o The distance between two points founded at one successful poll and the next successful poll is less than a set tolerance.
6. The algorithm polls the mesh points by comparing the calculated objective functions. 7. If it reached to such point that has smaller objective function than the current point, then the poll successful and the algorithm sets this point equal to current point. Then expand the mesh size by a factor and return to step 2. 8. If the poll is unsuccessful, and none of the mesh points has a smaller objective function than the current point, the algorithm does not change the current point at the next iteration and the algorithm multiplies the mesh size by contraction factor and return to step 2.
Figure 3. Flow chart of Pattern search.
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SIMULATION RESULTS In this section, we demonstrate the results of using the Pattern search algorithm for a power allocation strategy and the values of the simulation parameters for PS algorithm are set as follows: mesh size = 1, expansion factor = 2, contraction factor = 0.5 and Max. Number of iteration = 100. For OFDM multicarrier system, the parameters will be selected as shown in the Table I, [17]. V
Table I. Parameters of the simulation. Parameter
Variable
OFDM
PUs Number
L
2, 4, 6... 12
SUs Number
M
8, 16... 32
Mapping
16 QAM
subcarriers Number
N
32
subsymbols Number
V
1…9
cyclic prefix
CP
V*8
Cyclicsuffix Number
NCS
0
Subcarrier distance
Ws
0.3 MHz
Total band width
WT
10 MHz
Figure 4 shows variation of the total throughput for all SUs in the downlink CR network versus the maximum transmitted power at the AP using two different optimization algorithms; the PS algorithm and the Genetic Alogrithm (GA) using OFDM system [17]. It is observed that increasing the maximum transmitted power level at the AP improves the total throughput for all SUs until it reached to a constant level (saturation ). Moreover, It can be concluded that the PS algorithm improves the total throughput for all SUs over the GA by a percentage reached about 5 % at maximum transmitted power by the AP equal 15 dB.
Figure 4 Sum rate for all SU in CRN with maximum transmitted power for PS and GA.
Figure 5. Total throughput for all SUs in CRN versus maximum transmitted power at AP with different number of PU Using PS algorithm.
Figure 5 investigates the effect of varying the number of PUs on the total throughput for all SUs. As shown in this Figure, when doubled the number of PUs, the total throughput deceased by small value reached about 2% at 15 dB, until the system reached to the fully utilized by the PUs, The total throughput is decreased by about 13.6% at maximum transmitted power by the AP at 15 dB.
Figure 6 Total throughput for SUs in CRN versus maximum transmitted power at AP with different number of SUs Using PS algorithm.
Figure 7 Total throughput for SUs in CRN versus maximum transmitted power at AP with different number of subcarriers Using PS algorithm.
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Figure 6 investigates the effect of varying the number of SUs on the total throughput for all SUs. As shown in this Figure, through the low transmitted power level of the Access Point from -20 dB to -5dB, that there is approximately no effect of increasing the number of SUs on the total throughput for all SUs. But, when increasing the maximum transmitted power of the AP until it reached 15 dB, the total throughput is increased by about 5.5% at this point. Figure 7 offers the effect of varying the number of subcarriers on the total throughput for all SUs. From this figure, it is concluded that increasing the number of subcarriers leads to increase the total throughput for all SUs until reaching the high transmitted power level. In fact, when doubled the number of subcarriers, the total throughput is increased by about 40.3% at maximum transmitted power by the AP equal 15 dB. VI
CONCLUSIONS
CR has been considered as a promising paradigm to solve the spectrum scarcity problem based on OFDM system as a multicarrier technique. This paper investigated a power allocation strategy by using the Pattern Search algorithm that helped to find the optimal power needed for maximizing the total throughput for all SUs, without affecting the QoS of the PUs under power and interference constraints which is not clarified until now. The simulation results showed that PS algorithm exhibits a better performance than Genetic Algorithm in the downlink underlay mode of CRN. Moreover, the system performance under varying the SUs number, the PUs number and the subcarriers number had been studied for increasing the total data rate for SUs. References [1]
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