Optimal transmit antenna selection for LTE system using self-adaptive grey wolf optimization

Abstract

In general, MIMO upgrades the radio communication with improved capacity and reliability. As there is a presence of multiple antennas at transmitter and receiver side, the proper Transmit Antenna Selection (TAS) for attaining effective performance is still a challenging point. This paper intends to introduce a TAS algorithm in LTE system using Self-Adaptive Grey Wolf Optimization (SAGWO) for improving the system performance. It introduces self-adaptiveness in the Grey Wolf Optimization (GWO) by determining the capacity improvement accomplished by each candidate solution for the TAS problem followed by updating the candidate solution based on the improvement. The simulation model considers both Rayleigh channel and Rician channel, for four antenna configurations like 2 $\times$ 2, 3 $\times$ 2, 4 $\times$ 2 and 4 $\times$ 4. To the next of the simulation, it compares the performance of SAGWO-TAS with EDB-TAS, ECB-TAS, ABC-TAS, GA-TAS, FF-TAS, PSO-TAS and GWO-TAS, i.e., traditional TAS models using Artificial Bee Colony (ABC), Ergodic Capacity (ECB), Euclidean Distance (EDB), Firefly (FF), Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and GWO, respectively. It observes the BER (bit error ratio) and mean BER at varied SNR (signal-to-noise ratio) in the analysis section. The analysis proves that the BER is highly reduced for proposed optimal TAS model.

Keywords

LTE transmit antenna selection Rayleigh Rician bit error ratio self-adaptive grey wolf optimization

1. Introduction

In general, MIMO is a wireless technology that can aid wireless products with 802.11n. It comprises of numerous antennas (probably termed as an array of antennas) [11] at both the transmitter and receiver parts. Here, Adaptive output feedback [9, 10, 35] can control the FTC problem in the MIMO system. The effective transmission in MIMO technology is made possible by the support of STBC, and it also makes use of OSTBC. In fact, MIMO mostly depends on Antenna Diversity schemes. Moreover, the similar performance as the hardened massive MIMO channel can be achieved by the OFDM and single-carrier transmission system [10]. OFDM is used for attaining both efficient communication and channel equalization in the frequency domain. More diversity at the receiver side and high robustness can make available by the MIMO channel, where the entire details regarding the signals are given in the channel matrix. In addition, antenna spacing element is acquired based on the principles of diffraction limited optics, so that the throughput and reliability of the system can be enhanced [12].

The output system of MIMO de-multiplexes the source data stream into multiple independent channel streams. One of the fundamental benefits of MIMO channel is the achievement of high redundancy and improved channel capacity. Moreover, PPBT can estimate the singular vectors of the channel matrix [13] and Random matrix theory can analyze the performance of the precoder [14]. In some cases, OFDM with the bit-loading algorithm is adopted to attain better free space transmission [15]. On the contrary, pilot sequences can be used for downlink transmission purposes [16], and Gradient Search [17] method can be used for the recognition of signals [17]. In MIMO channel, Delayed Feedback in the Relay can improve the performance on Degree of Freedom. Similarly, Cognitive Radio Networks [19] can obtain the secrecy outage performance of TAS. However, the MIMO system suffers from the main drawbacks such as high complexity and more expensive antenna elements [36, 39]. These limitations have motivated to develop the effective antenna selection process, which has taken the fundamental role in MIMO system [37, 38].

Antenna selection, in general, is utilized for enhancing the performance of the non-selective fading channel. When all the antennas are used for spatial multiplexing, then it can be termed as “H-S/MIMO” and when the entire antennas are used for various purposes, then it can be termed as “H-S/MRC”, or “generalized selection combining”. Since the optimum selection algorithm seems to be complex, fast selection algorithms are used as it has less complexity. There is a necessity of feedback path for promoting effective TAS. In most of the TAS algorithms, sum rate analysis for all the optimal AS scheme matches the numerical results [20, 21]. Even more, Downlink Correlated channel [22] can improve the channel capacity, where the Massive MIMO systems can enhance the system performance and channel capacity [23]. The system performance can also be improved by the adoption of Joint Antenna Selection method, and two-way relay networks [24, 26] and Joint Precoding [25] method can improve the throughput of the system. The delayed channel capacity can access the beamforming strategy [27]. Basically, the effective data transmission is accomplished by selecting the antenna with higher transmit power [28]. Furthermore, physical layer security [29] is provided by the proper antenna selection process, which can be improved by Dual antenna selection methods [30].

This paper contributes a TAS algorithm in LTE system using SAGWO for improving the system performance. The SAGWO is exploited for solving the TAS model, where the ergodic capacity of Rayleigh channel is considered. The channel model is extended to Rician channel and the simulation is observed for four antenna configurations. Further, the performance of the proposed SAGWO is compared with conventional EDB-TAS, ECB-TAS, and ABC-TAS, GA-TAS, FF-TAS, PSO-TAS and GWO-TAS models. The rest of paper is organized as follows. Section 2 describes the literature review with related works and problem definition. Section 3 illustrates the TAS model in LTE system. Section 4 portrays the optimized rank based TAS. Section 5 illustrates the simulation results and Section 6 concludes the paper.

2. Literature review

In 2016, Jang et al. [1] have accomplished the near optimal sum rate performance in MIMO system using an advanced antenna selection approach. At first, they have analyzed the average sum rate of the optimal selection method and best antenna set solution. Further, the experimental results have validated the effective performance of the proposed algorithms, as it has 15% of performance gain.

In 2015, Jung and Kim [2] have developed the correlated D-MIMO systems with less complexity using an effective near-optimal antenna selection algorithm. They have attained utmost channel gain, with reasonable antenna support. In addition, the adopted optimal selection algorithm has provided high capacity with low cost and less complexity. The performance gain was seemed to be efficient with high energy efficiency when a small count of antennas was used.

In 2013, Lari et al. [3] have studied two different cases of MIMO system. In the first case, when CSI was not available and when CSI is available whereas in the second case when CSI was not available, TAS is difficult and so RAS is done. During this process, one antenna at the receiver may have maximum instantaneous Signal to Noise Ratio. On the contrary, TAS scheme was executed for the condition of not having CSI in the transmitter part. Further, they have analyzed the optimal power adaptation and powerful capabilities of the proposed model.

In 2015, Le et al. [4] had dealt the energy efficient algorithm for promoting valuable antenna selection in MIMO system. The received bits per unit of energy consumption were evaluated to validate the energy efficient algorithm. In some cases, error was occurred as the main drawback. Thus the optimal values of the transmitted symbols were gained, which has improved the performance of energy efficient algorithm.

In 2016, Le et al. [5] have maintained the energy efficient antenna selection method. In fact, EE-SE has faced the significant loss in energy efficiency. Furthermore, the proposed method has used the exhaustive search technique in the case of small count of antennas. Here, the Greedy algorithm was developed to complete near optimal performance with complexity compared to the optimal search method.

In 2016, Tiwari et al. [6] have analyzed the performance level of MIMO system over Weibull-Gamma fading channel. They have evaluated the error rate performance by exploiting the CSIT. Here, antenna selection method was used to accomplish CSIT. Thus AS was adopted in the OSTBC to enhance the performance of MIMO system.

Furthermore, in 2013, Hu and Luo [7] have developed a competent antenna-pair selection scheme, for a non-regenerative dual-hop amplify and forward MIMO systems. They have also diminished the hardware complexity with the proposed method without affecting the symbol error rate. In 2016, Amadori and Masouros [8] have executed the antenna selection at low complexity using an advanced antenna selection scheme. With this technique, they have attained the ability to match the constructive interference among diverse users. The linkage of simple matched filter precoder in the transmitter part has enhanced the performance of the system. Thus, maximum power savings and reduced complexity were made possible through this method. Table 1 represents the state of the art of the TAS algorithm.

Table 1
State-of-the-art of TAS algorithms

Author [Citation]	Methodology	Merits	Demerits
Jang et al. [1]	Greedy search	– Computational efficiency	– Requires appropriate framework – Stops when problem arises.
Jung and Kim [2]	Probabilistic search	– Cost Effectiveness – Less time consumption	– Redundant – Monotonous
Lari et al. [3]	Water filling approach	– Ability to allocate problems	– Complex updating model
Le et al. [4]	Deterministic approach	– Precise estimation	– Highly complex – Need problem specific updating process
Le et al. [5]	Exhaustive search method	– Simple for code generation and checking	– Due to numerous solutions it become expensive
Tiwaria et al. [6]	Deterministic approach	– Accurate searching	– No proper controlling process
Hu and Luo [7]	K-best breadth- first search algorithm	– Systematic searching process	– Memory constraints – Time consuming
Amadori and Masouros [8]	Exhaustive search	– Reduced memory	– Mapping restriction

The distinctive TAS method proceeds by exhaustive search, choosing the optimal probable subset of the full set of antennas [33]. Although the performance of the exhaustive search can be optimized, its complexity still increases linearly with the total number of antennas, as well as the number of antennas to be chosen. As a result, much research on TAS schemes has been performed, in an effort to attain lesser complexity than that of exhaustive search methods [34, 35]. In [1], the greedy search method was proposed for that purpose. Moreover, the simplest approach is to choose the transmitting antenna by means of computing the norm of the thermal vector of the entire channel. Nevertheless, in place of simply minimizing the complexity, this also minimizes the user’s attainable rate of transmission.

This paper intends to introduce a TAS algorithm for enhancing the system performance. The proposed TAS is on the basis of the advanced meta-heuristic search approach termed as GWO, which is inspired based on the hunting behaviour grey wolves. Firstly, the channel capacity is estimated through the channel model and it is defined as the objective model for the TAS problem. The selected objective model defines the Ergodic capacity of the system in Rayleigh fading channel, for that accurate channel estimate will be adopted. Secondly, a self-adaptive GWO proposes to solve the TAS model. The self-adaptiveness in the GWO is introduced by determining the capacity improvement accomplished by each candidate solution for the TAS problem followed by updating the candidate solution based on the improvement.

3. TAS model in LTE

3.1 TAS model

The architecture of MIMO-OSTBC model shown in Fig. 1 is related to the feedback for the TAS case. Further, it is applied to the M-ary PSK modulator, and the OSTBC encoder encodes the modulated output. In fact, the current experiment is carried out for an individual TAS and hence, a single transmission link is considered. Here, $N_{(T)}$ is assigned as the number of transmit antennas linked at the output side of a switch. In general, an individual antenna is selected by the switch on the basis of feedback move up from the receiver. Similarly, $N_{(R)}$ is assigned as the number of antennas linked at the receiver side. Moreover, the channels of the model undergo flat Rayleigh fading environment. The system with no appropriate antenna selection is denoted as $({N_{(T)};N_{(R)}})$ .

Figure 1.

Architecture of TAS model.

Let $M$ be the channel matrix, which has a dimension $({N_{(T)}\times N_{(R)}})$ and $m_{i,j}$ be the channel fading coefficients, where $i=1,2,\ldots,N_{(T)}$ and $j=1,2,\ldots,N_{(R)}$ . The fading coefficients mentioned above are the patterns of Rayleigh fading operation. Moreover, the column vector of form $({N_{(T)}\times 1})$ represents the channel between individual transmit antenna and $N_{(R)}$ receive antennas. For a transmission section, the channel is assumed to be constant, and this particular constant value within the section may alter independently. In fact, the constant value can be the consolidation of constant phase and constant gain of the channel.

Equation (1) represents the model of received signal vector $Z$ for the transmitted signal $a$ over the antenna that is selected as single for a particular time instant $t$ . Here, $E_{a}$ indicates the energy of symbol, $L$ represents the number of selected antenna subsets, $M_{pk}$ specifies the matrix of channel gain, $p k$ indicates the index of $k^{\rm th}$ chosen column matrix, $a$ indicates the signal vector of OSTBC encoder and $n^{({\textit{vector}})}$ specifies the noise vector.

$\displaystyle Z=\sqrt{\frac{E_{a}}{L}}M_{pk}a+n^{({\textit{vector}})}$ (1)

3.2 TAS constraints

To measure the channel capacity, it is essential to transmit the pilot signal from every transmit antennas $N_{(T)}$ towards the entire receive antennas $N_{(R)}$ . Thus Eq. (2) formulates the channel capacity for every path. In Eq. (2), $C_{M}$ indicates the covariance matrix with size $\left({N\times N}\right)$ , $I_{d}$ specifies the identity matrix and $C_{M}$ denotes the Hermitian matrix.

$\displaystyle C^{\textit{channel}}=\max\limits_{C_{M}\left\{{p_{1},p_{2},% \ldots,p_{l}}\right\}}\log_{2}\det\left({\begin{array}[]{l}I_{d}\\ +{\displaystyle\frac{E_{a}}{LL_{0}}}M_{\left\{{p_{1},p_{2},\ldots,p_{l}}\right% \}}C_{M}M_{\left\{{p_{1},p_{2},\ldots,p_{l}}\right\}}^{H}\\ \end{array}}\right)$ (2)

Consider an equal power is allotted for every channel in the model (based on Rayleigh fading channel) so that the covariance matrix is equal to the identity matrix as $C_{M}=I_{L}$ . Since the number of antenna selected here is single, the value of $I_{L}=1$ . Hence, Eq. (3) portrays the modified format of Eq. (2), where $i$ represents the chosen subset of antenna for the transmission purpose.

$\displaystyle C^{\textit{channel}}=\max\limits_{C_{M}\left\{{p_{1},p_{2},% \ldots,p_{l}}\right\}}\log_{2}\det\left({\begin{array}[]{l}I_{d}\\ +{\displaystyle\frac{E_{a}}{L_{0}}}M_{\left\{{p_{1},p_{2},\ldots,p_{l}}\right% \}}M_{\left\{{p_{1},p_{2},\ldots,p_{l}}\right\}}^{H}\\ \end{array}}\right)$ (3)

As shown in Eq. (3), it is essential to focus only the single subset for the computation of channel capacity for every transmit antennas. The channel capacity is generally a random variable $1\leqslant i\leqslant N_{(R)}$ and it should be organized in ascending format of magnitude, where $C_{(1)}^{\textit{channel}}\leqslant C_{(2)}^{\textit{channel}}\leqslant\ldots C% _{N_{(R)}}^{\textit{channel}}$ . The chosen transmit antenna for transmission corresponds to $C_{N_{(R)}}$ , which is based on Eq. (3).

Since the system model is based on Rayleigh fading channel, Eq. (4) represents the PDF of the Rayleigh distribution. In the respective equation, $\Omega$ indicates the product of quadrature and inphase component of the electric field and $b$ specifies the envelope of electric field sample.

$\displaystyle P_{R}(b)=\frac{2b}{\Omega}e^{\frac{-b^{2}}{\Omega}},b\geqslant 0$ (4)

Likewise, Eq. (5) expresses the (CDF) for Rayleigh distribution, where $\Omega=2\sigma^{2}=E[b^{2}]$ .

$\displaystyle D(b)=1-e^{\frac{-b^{2}}{\Omega}}$ (5)

The current paper considers only the selection of transmit antennas. The system can be termed as $({N_{(T)}:1;N_{(R)}})$ arrangement if a single antenna is selected from the $N_{(T)}$ number of transmit antennas at a time instant $t$ . There are two cases adaptable of $({N_{(T)}:1;N_{(R)}})$ combo, such as $({3:1;2})$ and $({4:1;2})$ respectively. In this experiment, the $({N_{(T)}:1;N_{(R)}})$ combination is considered for Rayleigh fading channel with Ergodic capacity principle, which is performed for with and without TAS case. Moreover, it evaluates the BER analysis for image data for several MIMO configurations.

4. Optimized rank based TAS

4.1 Objective model

The proposed TAS model uses an implicit procedure of selecting optimal transmit antenna configuration. According to the procedure, two objective models are used. The primary objective model is an implicit model but selects the antenna configuration that holds minimal average as given in Eq. (6). Here, $R_{t}^{\mu}$ represents the average rank of $t^{\rm th}$ antenna configuration, which is given in Eq. (6), where $R_{t}^{I}$ indicates the rank of $t^{\rm th}$ antenna configuration in each iteration.

$\displaystyle T^{\ast}=\mathop{\arg\,\,\min}\limits_{\left[T\right]}R_{t}^{\mu}$ (6) $\displaystyle R_{t}^{M}=\frac{1}{I^{\max}}\sum\limits_{i=1}^{I^{\max}}{R_{t}^{% I}}$ (7)

Rank definition: $R_{t}^{I}$ is determined as the position of probability $P_{r}({B_{t}})$ as given in Eq. (8) among the BER of all the antenna configurations, where $B_{t}$ indicates the BER of $t^{\rm th}$ antenna configuration and $N_{c}$ specifies the number of antenna configurations.

$\displaystyle P_{r}\left({B_{t}}\right)=\frac{B_{t}}{\sum\limits_{t=1}^{N_{c}}% {B_{t}}}$ (8)

The secondary objective model is the explicit objective model that plays a key role in allocating ranks for antenna configuration based on the error rate of the transmitted and received data. The secondary objective model is given in Eq. (9) where $D=[{d_{1},d_{2},\ldots,d_{N}}]$ specifies the number of subcarrier symbols.

$\displaystyle D^{\ast}=\mathop{\arg\,\,\min}\limits_{\left[D\right]}\left({% \frac{1}{\max\left({B_{t}}\right)}}\right)$ (9)

4.2 Rank optimization

In this section, the optimal allocation of rank is done by the GWO algorithm [31]. GWO is a newly introduced meta-heuristic algorithm that operates based on the hunting behavior of wolves. There are mostly three wolves responsible for hunting, those are $\alpha$ , $\beta$ and $\delta$ wolves. Moreover, the fundamental phases of grey wolf hunting are depicted as follows. (1) Chasing, tracking and striking the prey, (2) encircling, pursuing and harassing the prey till the completion of prey’s movement and (3) attack towards the prey. Among the three set of wolves, $\alpha$ is allotted as the leader, which is responsible for taking decisions associated with the waking time, hunting, sleeping time, etc. On the contrary, $\beta$ and $\delta$ are the second and third best wolves that support $\alpha$ . Apart from these wolves, $\omega$ is another wolf, allowed only for eating, hence it takes no much importance during hunting actions. The mathematical model of encircling prey is given in Eqs (10) and (11), where $D_{p}(t)$ specifies the position vector of prey, $D(t)$ specifies the position vector of wolves, $t$ indicates the current iteration and $S$ and $Q$ represent the coefficient vectors, which are given in Eqs (12) and (13), respectively. In Eq. (12), $a$ denotes the component that is linearly reduced from 2 to 0 and $r_{1}$ and $r_{2}$ are the random number between [0, 1].

$\displaystyle V_{\alpha}=|{Q.D_{p}(t)-D(t)}|$ (10) $\displaystyle D({t+1})=D_{p}(t)-S.V$ (11) $\displaystyle S=2a.r_{1}-a$ (12) $\displaystyle Q=2.r_{2}$ (13)

As mentioned earlier, the component $a$ is linearly reduced from 2 to 0 in the conventional GWO algorithm, instead, $a$ in the proposed SAGWO is altered based on Eq. (14) from $t=1$ . In the respective equation, $G_{B}^{f}$ indicates the global fitness, $C_{B}^{f}$ indicates the best fitness of current iteration and $t_{\max}$ specifies the maximum number of iteration. Here, the value of $a$ is altered based on the local best and global best solution. As $a$ is adaptively changed based on the fitness value, i.e., until best fitness is obtained, the proposed algorithm can be termed as Self-adaptive algorithm.

$\displaystyle a=2[{abs({G_{B}^{f}-C_{B}^{f}})\times t}]-\frac{2}{t_{\max}}$ (14)

The mathematical model of hunting action is expressed in Eqs (15) to (20).

$\displaystyle V_{\alpha}=|{Q_{1}.D_{\alpha}-D}|$ (15) $\displaystyle V_{\beta}=|{Q_{2}.D_{\beta}-D}|$ (16) $\displaystyle V_{\delta}=|{Q_{\delta}.D_{\delta}-D}|$ (17) $\displaystyle D_{1}=D_{\alpha}-S_{1}.({V_{\alpha}})$ (18) $\displaystyle D_{2}=D_{\beta}-S_{2}.({V_{\beta}})$ (19) $\displaystyle D_{3}=D_{\delta}-S_{3}.({V_{\delta}})$ (20) $\displaystyle D^{\ast}({t+1})=\frac{D_{1}+D_{2}+D_{3}}{3}$ (21)

The final update formula of GWO (attained objective) is given in Eq. (21) that is subjective to Eq. (9). The pseudo code of GWO-based Rank optimization is depicted in Algorithm 1.

Algorithm 1: Pseudo code of GWO-based rank optimization

1.	Initialize the population of grey wolf $D=1,2,\ldots n$
2.	Initialize $a$ , $S$ and $Q$
3.	Compute the fitness of each search agent
4.	Assign $D_{\alpha}$ as the best search agent
5.	Assign $D_{\beta}$ as the second best search agent
6.	Assign $D_{\delta}$ as the third best search agent
7.	While $\left({t<t_{\max}}\right)$
8.		For each search agent
9.			Update the position of current search agent using Eq. (21)
10.		End for
11.		Update $a$ using Eq. (14)
12.		Update $S$ and $Q$
13.		Compute the fitness for all search agents
14.		Update $D_{\alpha}$ , $D_{\beta}$ and $D_{\delta}$
15.		$t=t+1$
16.	End while
17.	Return $D^{\ast}$

The description of Algorithm 1 is depicted as follows.

The population of grey wolf is initialized as $D=1,2,\ldots,n$ .

Then the components, $a$ , $S$ and $Q$ are initialized and further, the fitness function of current search agent is calculated.

The search agents $D_{\alpha}$ , $D_{\beta}$ and $D_{\delta}$ are assigned as the best, second best and third best search agents.

For a particular iteration, the position of the current search agent is updated using Eq. (21).

Further, the component $a$ is updated using Eq. (14) and $S$ and $Q$ are updated.

Then the fitness function of the entire search agents is computed.

The search agents $D_{\alpha}$ , $D_{\beta}$ and $D_{\delta}$ is updated to find out $D^{\ast}$ .

The process is repeated until the completion of maximum iteration.

Figure 2.

Flowchart of SAPSO.

Figure 2 shows the flowchart of the proposed SAGWO.

Table 2

Selected antenna configurations of optimal TAS model for Rayleigh channel

Methods	Antenna configuration
	2 $\times$ 2	3 $\times$ 2	4 $\times$ 2	4 $\times$ 4
ABC-TAS	1 1	1 0 1	1 1 1 0	1 0 0 1
GA-TAS	1 1	1 0 1	1 0 0 0	1 0 1 1
FF-TAS	1 1	1 1 1	1 0 1 1	1 0 1 0
PSO-TAS	1 1	1 1 1	1 0 0 0	1 0 0 1
GWO-TAS	1 1	1 0 1	1 0 0 0	1 1 1 0
SAGWO-TAS	1 1	1 0 0	1 1 1 0	1 0 1 0

Table 3

Mean BER of proposed and conventional TAS model for Rayleigh channel

Methods	Antenna configuration
	2 $\times$ 2	3 $\times$ 2	4 $\times$ 2	4 $\times$ 4
EDB-TAS	0.007909	0.020273	0.160636	0.118455
ECB-TAS	0.125091	0.014	0.014182	0.026364
ABC-TAS	0.004182	0.006455	0.008545	0.018182
GA-TAS	0.004364	0.006273	0.008545	0.017364
FF-TAS	0.005909	0.007455	0.011182	0.022273
PSO-TAS	0.004282	0.006009	0.007282	0.0211
GWO-TAS	0.005909	0.006909	0.010182	0.022
SAGWO-TAS	0.004545	0.005727	0.006818	0.019818

Figure 3.

BER analysis of TAS on four antenna configurations like (a) x, (b) 3 $\times$ 2, (c) 4 $\times$ 2 and (d) 4 $\times$ 4 for Rayleigh channel.

5. Simulation results

5.1 Procedure

The TAS scheme in LTE system using proposed SAGWO is simulated in MATLAB, and the results are observed. The particular process is carried out in both Rayleigh and Rician channels, and it concerns four antenna configurations like 2 $\times$ 2, 3 $\times$ 2, 4 $\times$ 2 and 4 $\times$ 4. The results observe the BER and mean BER with varied SNR value for each antenna configuration. The simulation results of the proposed SAGWO-TAS is compared with the conventional models like EDB-TAS, ECB-TAS, ABC-TAS, GA-TAS, FF-TAS, PSO-TAS and GWO-TAS models. The population size of the proposed SAGWO method is 10 and the chromosome length is 500.

5.2 Rayleigh channel

Figure 3 shows the BER analysis of TAS on four antenna configurations for Rayleigh channel. As shown in Fig. 3a, the BER of the proposed SAGWO model for antenna configuration 2 $\times$ 2 at SNR value of 2.5 is 80.7% better than EDB-TAS, 98.41% better than ECB-TAS, 96% better than GA and GWO-TAS, respectively, 96.83% better than PSO-TAS and same as FF-TAS algorithm. In the case of configuration 2 $\times$ 2 as shown in Fig. 3b, the proposed SAGWO-TAS produce less BER, which is 94%, 9.5%, 50%, 96.20% superior to EDB-TAS, ECB-TAS, ABC-TAS and GA-TAS, respectively and 70% superior to FF-TAS and GWO-TAS, respectively at SNR value of 4. On considering the configuration 4 $\times$ 2, the BER performance of SAGWO at SNR value of 4 is 98.76% better than EDB-TAS, 84.46% better than ECB-TAS, 65.17% better than GA-TAS, same as PSO-TAS and 2.2% better than FF-TAS and GWO-TAS, respectively. Furthermore, BER obtained from proposed SAGWO-TAS model at SNR value of 8 is 80% superior to EDB-TAS model, same as GA-TAS and 18.97% superior to ECB-TAS and FF-TAS model, respectively as shown in Fig. 3d.

The selected antenna configuration of the proposed and conventional TAS model for Rayleigh channel is shown in Table 2. Here, the antenna is selected for four configurations. For ABC-TAS model, antenna 1 and 2 is selected for configuration 2 $\times$ 2 and antenna 1 and 4 is selected for the configuration 4 $\times$ 4. Similarly, antenna 1 and 2 is selected for the configuration 2 $\times$ 2, only antenna 1 is selected for configuration 3 $\times$ 2, antenna 1, 2 and 3 is selected for configuration 4 $\times$ 2, and antenna 1 and 3 is selected for configuration 4 $\times$ 4. Furthermore, the mean BER of the proposed and conventional TAS model for Rayleigh channel is shown in Table 3. Here, BER of proposed SAGWO is 42.53%, 96.36%, 8.68%, 4.14%, 23.8%, 6.14% and 23.8% superior to EDB-TAS, ECB-TAS, ABC-TAS, GA-TAS, FF-TAS, PSO-TAS, and GWO-TAS, respectively for configuration 2 $\times$ 2. Hence, the performance of the proposed method is better than the conventional methods. In addition, BER attained by SAGWO is 71.75% better than EDB-TAS, 59.9% better than ECB-TAS, 11.07% better than ABC-TAS, 8.70% better than GA-TAS, 23.17% better than FF-TAS, 4.69% better than PSO-TAS and 17.1% better than GWO-TAS models for configuration 3 $\times$ 2. In the case of configuration 4 $\times$ 2, BER performance of SAGWO is 95.75% superior to EDB-TAS, 51.92% superior to ECB-TAS, 39.2% superior to FF-TAS, 6.07% superior to PSO-TAS, 33.3% superior to GWO-TAS and 2.21% superior to ABC-TAS and GA-TAS model, respectively. Moreover, BER obtained from SAGWO is 83.26%, 24.82%, 80.99%, 14.13%, 11.02%, 6.07% and 9.91% better than ECB-TAS, ABC-TAS, GA-TAS, FF-TAS, PSO-TAS, and GWO-TAS, respectively.

Table 4
Selected antenna configurations of optimal TAS model for Rician channel

Methods	Selected antenna configuration
	2 $\times$ 2	3 $\times$ 2	4 $\times$ 2	4 $\times$ 4
ABC-TAS	1 1	1 0 0	1 0 1 1	1 1 1 0
GA-TAS	1 1	1 0 0	1 0 1 1	1 1 1 0
FF-TAS	1 1	1 1 1	1 1 1 0	1 0 1 0
PSO-TAS	1 1	1 1 0	1 1 0 0	1 0 1 0
GWO-TAS	1 1	1 1 1	1 1 0 0	1 1 1 0
SAGWO-TAS	1 1	1 0 1	1 0 0 1	1 0 0 1

Figure 4.

BER analysis of TAS on four antenna configurations like (a) 2 $\times$ 2, (b) 3 $\times$ 2, (c) 4 $\times$ 2 and (d) 4 $\times$ 4 for Rician channel.

5.3 Rician channel

BER analysis of TAS on four antenna configurations for Rician channel is shown in Fig. 4. Here, BER of the proposed SAGWO at SNR value of 3.5 is 99.20% better than EDB-TAS, 99.36% better than ECB-TAS, 74.35% better than ABC-TAS, 80% better than PSO-TAS and same as FF-TAS model for antenna configuration 2 $\times$ 2 as shown in Fig. 4a. Similarly, for configuration 3 $\times$ 2, the BER performance of SAGWO-TAS is 98.56%, 98.19% and 49.84% superior to EDB-TAS, ECB-TAS and FF-TAS model, respectively, 18.97% superior to ABC-TAS and GWO-TAS and 36.8% superior to GA-TAS and PSO-TAS model, respectively as shown in Fig. 4b. Moreover, BER attained by proposed SAGWO-TAS for configuration 4 $\times$ 2 (shown in Fig. 4c) is 25.37%, 36.70% and 96.01% better than ABC-TAS, PSO-TAS and GWO-TAS, respectively, 93.98% better than EDB-TAS and ECB-TAS model, respectively and 47.36% better than GA-TAS and FF-TAS model, respectively. Furthermore, SAGWO performance in reducing BER is 80%, 99%, 68.35% superior to EDB-TAS, ECB-TAS and GWO-TAS model, respectively, same as ABC-TAS and 67.74% superior to GA-TAS and FF-TAS, respectively as shown in Fig. 4d. The overall analysis states that the proposed method is better than the conventional methods.

Table 4 depicts selected antenna configuration of optimal TAS model for the Rician channel. Here for the proposed SAGWO-TAS model, antenna 1 and 2 is selected for configuration 2 $\times$ 2, antenna 1 and 3 is selected for configuration 3 $\times$ 2, antenna 1 and 4 is selected for configuration 4 $\times$ 2 and antenna 1 and 4 is selected for configuration 4 $\times$ 4. Moreover, the mean of BER of proposed and conventional models for Rician channel is shown in Table 5. For the antenna configuration 2 $\times$ 2, BER of proposed SAGWO-TAS is 99%, 99.52%, 27.3%, 65.23%, 77.78%, 43.29% and 77.42% better than EDB-TAS, E. CB-TAS, ABC-TAS, GA-TAS, FF-TAS, PSO-TAS, and GWO-TAS, respectively. Similarly, BER performance for configuration 3 $\times$ 2 is 79.20%, 66.29%, 1.23%, 2.43%, 4.46%, 0.01% and 1.38% superior to EDB-TAS, ECB-TAS, ABC-TAS, GA-TAS, FF-TAS, PSO-TAS and GWO-TAS, respectively. In addition, Similarly, BER performance for configuration 4 $\times$ 2 is 83.86% better than EDB-TAS, 85.66% better than ECB-TAS, 11.05% better than ABC-TAS, 22.68% better than GA-TAS, 18.62% better than FF-TAS, 14.50% better than PSO-TAS and 28.47% better than GWO-TAS. Likewise, SAGWO attains reduced BER for configuration 4 $\times$ 4, which is 7.56%, 53.07%, 4.95%, 1.06%, 0.10%, 1.26% and 3.13% superior to EDB-TAS, ECB-TAS, ABC-TAS, GA-TAS, FF-TAS, PSO-TAS, and GWO-TAS, respectively. Thus it is clear that the proposed SAGWO model is highly suitable to attain the best performance in TAS.

Table 5
Mean BER of proposed and conventional TAS model for Rician channel

Methods	Selected antenna configuration
	2 $\times$ 2	3 $\times$ 2	4 $\times$ 2	4 $\times$ 4
EDB-TAS	0.073182	0.280727	0.113273	0.093727
ECB-TAS	0.153455	0.173182	0.127455	0.184636
ABC-TAS	0.001	0.059091	0.020545	0.082545
GA-TAS	0.002091	0.059818	0.023636	0.085727
FF-TAS	0.003273	0.061091	0.022455	0.086545
PSO-TAS	0.001282	0.058373	0.021373	0.085555
GWO-TAS	0.002818	0.059182	0.025727	0.084
SAGWO-TAS	0.000727	0.058364	0.018273	0.086636

6. Conclusion

This paper has presented an optimal TAS algorithm for improving the LTE system performance using SAGWO algorithm. In fact, the self-adaptiveness in the GWO algorithm has introduced by determining the capacity improvement accomplished by each candidate solution for the TAS problem followed by updating the candidate solution based on the improvement. The simulation model has considered both Rayleigh channel and Rician channel, for four antenna configurations like 2 $\times$ 2, 3 $\times$ 2, 4 $\times$ 2 and 4 $\times$ 4. After forming the simulation model, the performance of SAGWO-TAS was compared with conventional EDB-TAS, ECB-TAS, ABC-TAS, GA-TAS, FF-TAS, PSO-TAS and GWO-TAS models. The analysis has measured the BER and mean BER of the proposed and conventional models and have validated the effective performance of proposed SAGWO-based TAS model. From the analysis of the proposed approach, it is clearly describes that the Greedy search algorithm used in [1, 2] does not work for some problems. In addition, the water filling approach in [3] cannot be directly used for power allocation in a cognitive radio system. The main drawbacks of the exhaustive search in [5, 8] is the cost of generating candidate solutions. Moreover, the Breadth first search affects from its memory requirement. For instance, BER attained by SAGWO for Rayleigh channel is 71.75% better than EDB-TAS, 59.9% better than ECB-TAS, 11.07% better than ABC-TAS, 8.70% better than GA-TAS, 23.17% better than FF-TAS, 4.69% better than PSO-TAS and 17.1% better than GWO-TAS models for configuration 3 $\times$ 2 and BER of proposed SAGWO-TAS is 99%, 99.52%, 27.3%, 65.23%, 77.78%, 43.29% and 77.42% better than EDB-TAS, ECB-TAS, ABC-TAS, GA-TAS, FF-TAS, PSO-TAS and GWO-TAS, respectively for Rician channel for configuration 2 $\times$ 2. Thus the performance of SAGWO is effective for TAS modeling.

Footnotes

Abbreviations and acronyms

Authors’ Bios

	Nitin T. Deotale received his M. Tech. from Dr. Babasaheb Ambedkar Technological University, Lonere in 2006. He is a registered Ph.D Research Scholar in Priyadarshini College of Engineering of RTM Nagpur University, Nagpur, Maharashtra, India. He is currently serving as Assistant Professor in Department of Electronics & Telecommunication Engineering, Lokmanya Tilak College of Engineering, Navi Mumbai-400709, Maharashtra, India. Having 10 years of academic experience, his fields of interest is Wireless Digital Communications.
	Uttam Kolelkar received Ph.D. degree from Bharathi Vidyapeeth University, Pune in Electronics Engineering in 2008. He has been working as Principal at A. P. Shah Institute of Technology, Thane. He has total 23 years teaching experience at various posts such as Lecturer, Assistant professor, Professor, Head of dept, Dean and Director at various Institutes of Mumbai University. He is research guide at various universities in India and more than 5 candidates are working under him as research scholars from different institutes and Industries like TCS. He has more than 15 papers in national and international Journals and conferences against his name. He is also reviewer for international journals like IEEE transactions. He is fellow member of (IETE), Life member of ISTE & ISNT also he is senior member of international association of Computer science & information technology. He conducts seminars on mobile Ad -hock network, Mobile computing, GSM, GPRS, and UMTS. He is actively involved as a reviewer for many international conferences. He has addressed many workshops on wireless networks, Sensors networks, and Cyber security.
	Anuradha R. Kondelwar received Ph.D degree from VNIT, Nagpur in 2006 under the guidance of Dr. K.D. Kulat. She has published around 30 papers in International Journals. Currently working in deparment of electronics and telecommunication in Priyadarshini college of Engineering, RTM Nagpur University, Nagpur. Her area of expertise is in Wi-max.

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Optimal transmit antenna selection for LTE system using self-adaptive grey wolf optimization

Abstract

Keywords

1. Introduction

2. Literature review

Table 1 State-of-the-art of TAS algorithms

3.1 TAS model

4.1 Objective model

5.1 Procedure

5.2 Rayleigh channel

Table 4 Selected antenna configurations of optimal TAS model for Rician channel

Table 5 Mean BER of proposed and conventional TAS model for Rician channel

Footnotes

Abbreviations and acronyms

Authors’ Bios

References

Table 1
State-of-the-art of TAS algorithms

Table 4
Selected antenna configurations of optimal TAS model for Rician channel

Table 5
Mean BER of proposed and conventional TAS model for Rician channel