# Performance Analysis of Grouped Multilevel Space-Time Trellis Coding Technique Using Cognitive Radio in Different Deployment Models

Authors: Shakti Raj Chopra; Akhil Gupta; Rakesh Kumar Jha
Journal: Wireless Communications and Mobile Computing
 (2019)

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## Abstract

In this era, the number of users in a network is increasing tremendously at a faster rate; as a consequence, quality of service (QoS) is drastically deteriorating. To compensate such kinds of problems, we attempted to enhance the QoS of the network, which leads to an improvement in throughput, link quality, spectral efficiency, and many more. To meet the requirements mentioned above, many researchers intervene to advance and propose different techniques with an appropriate design methodology. In this work, we try to emphasize symbol error rate (SER) and frame error rate (FER) by implementing some of the existing space-time coding techniques like Space-Time Trellis Coding (STTC), multilevel space-time trellis coding (MLSTTC), and grouped multilevel space-time trellis coding (GMLSTTC). Though all these techniques are proved to be efficient enough, we explicitly included a powerful method of cooperative diversity-based spectrum sensing in cognitive radio scenario. From this analysis, we landed on to the conclusion that this technique is far better to deal with all these parameters, which can improve the QoS of the network. This paper has also analyzed the effect of the proposed model of GMLSTTC with cognitive radio on various deployment setups such as urban, suburban, and rural macrodeployment setup of the ITU-R M.2135 standard.


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## Body

## 1. Introduction

In today’s technological era, the thirst for a wireless communication system is growing worldwide. It is due to the increase in the cellular mobile system’s requirements of high data rate, wireless Internet, and demands for multimedia services. To achieve higher data rates and solve the problem of the inappropriate spectrum, the design of different efficient diversity techniques is developing. In recent years, various initiatives have been put forth in developing different space-time coding (STC) methods. Space-time block codes (STBCs) and space-time trellis coding (STTC) are types of STC techniques. Space-time block coding provides diversity gain only. For achieving the coding gain, space-time trellis codes are introduced, which provide coding gain and diversity gain of higher probability. Space-time trellis codes are codes based on several performance criteria, with several modulation techniques that utilize code distribution. Better performance is given by this code, for better data transmission without the sacrifice of power, bandwidth, and various other quantities. The parameters such as codes construction, number of antennas reception, and transmission of using cooperative diversity, and its variation with fading channel characteristics is dependent on the space-time trellis code performance.The fundamental information transmission limits and channel coding design solutions are typically analyzed, which focuses on communication scenarios utilizing long block length codes. On the other hand, hardware complexity in practical applications, constraints like delay or battery life, may require short block information transmission. For instance, there are tight latency requirements to build wireless sensor networks for real-time surveillance or control which has suggested short block length utilization. With this observation, the channel coding solutions are investigated practically in a regime of the short block length. We considered Rayleigh channels and additive white Gaussian noise (AWGN) channels and focused on convolution (trellis-based) codes. Current research on code design with short block lengths demonstrates better results with convolution codes for point-to-point channels in the context of its performance gap with Shannon’s sphere packing bound (a fundamental tool for performance evaluation) [1, 2]. In contrast, in Low-Density Parity Check (LDPC) codes, the asymptotic regime focuses on the review of the code’s performance by traditional methods. Furthermore, the optimal decoding algorithm is developing, when both the users are running with trellis-based codes [3]. An attractive alternative is provided by the convolution codes from a designing aspect from the perspective of efficient decoding in the framework of short block length for Medium Access Control (MAC) channels. Deducing the weight distribution for trellis-based convolution codes’ instances increases the feasibility of computing performance significantly. [4–8]. MAC scenario has similarities with STC making it an attractive convolution code, which leads to the trellis-based code performance [7, 8]. Using cooperative diversity in cognitive radio optimizes the scarce radio spectrum utilization. It is another paradigm that guarantees opportunistic unused spectrum utilization and effective spectrum management. The cognitive radio scheme recognizes spectrum gaps even if they are unused for a specific time. Cognitive radio is an ingenious wireless system in which internal states are made stationary corresponding to actual values in the proceedings radio frequency (RF) approach. The entire radio frequency is utilized in an optimized manner, using different methods [9, 10].


### 1.1. Background Study

In the last couple of years, the investigation of various multilevel space-time trellis coding (MLSTTC) procedures has improved the situation by achieving the advantages of spectral efficiency, coding gain, and diversity gain. In [1], an elegant transmission procedure is proposed using new multilevel pseudo-space-time trellis coding (MLPSTTC) for single antenna portable hubs. The transmitted data are decoded just by accumulating individual information of all hubs which exchange their information parallel to each other. The participating hub self-data and different centers decoded data are encoded further through a multilevel code plot and (as segment codes) pseudo-space-time trellis codes. At each supportive center, the resultant produced MLPSTTC symbols, which are transmitted through the independent fading channels to the universal destination node. Hence, various data duplicates of each portable center are achieved on a destination hub. The execution that appeared in the trial consequence of the cooperative MLSTTC strategy is better in correlation with the current MLSTTC plans. The STC method used in [2] depicts the use of OFDM (Orthogonal Frequency Division Multiplexing) framework with the STC. To achieve the best result, the bit error rate (BER) using multiple-input multiple-output (MIMO) technology in a cooperative diversity environment should be limited.The STBC on the AWGN fade channel is used to decrease the BER to acquire the quality signal at the receiving end. STBC is applied at the end of the transmitter to examine the AWGN fading channel of the OFDM frame. The prior technique uses several modulation methods like quadrature amplitude modulation (QAM) and binary phase shift key (BPSK), which are analyzed based on BER and SNR (signal-to-noise ratio). Another differential encoding and disentangling procedure is proposed in [3] for differential-distributed space timing coding (DDSTC) frameworks over the slow-fading frequency selective channels with multiple relays having imperfect synchronization. The frequency selectivity causes intersymbol interference (ISI), which can be eliminated by DDSTC techniques. It is robust if synchronization errors occur while no channel is necessary on the destination. Furthermore, the maximum possible diversity has been achieved with the complexity of decoding, which is similar to the traditional DDSTC.In [4], the first spotlight is on the short-length trellis-based code outline for two clients’ Gaussian multiple-access channel (MAC). An outline strategy is exhibited, which gives code plans and execution. It is then contrasted and planned code execution for point-to-point (P2P) channels, including ideal convolutional codes. As appeared in its exploratory outcomes, unrivaled performance can be accomplished in contrast with the choices in break even with control situations, particularly in the administration of SNR (signal-to-noise ratio). A space-time code with the new class is presented in [5], which is referred to as space-time super-orthogonal trellis codes. The apportioned set and modified space-time orthogonal codes are symmetrically combined by these codes to provide enhanced coding gain as well as full-diversity gain to increase the overall development of prior space-time trellis code. The optimality of the parceled set has been additionally examined, and the investigation of coding gain is analyzed. The ideal setting has been used to plan different quantities of states up to a remarkably high conceivable rate, the codes operating at different data rates. Space-time super-orthogonal trellis codes give a tradeoff among coding and throughput. The outcomes of recreation demonstrate a more noteworthy change of 2 dB over the exhibited systems. A space-time trellis code new family is presented in [6], which broadens the space-time super-orthogonal trellis codes attributed intensely for transmission antennas in a cooperative diversity environment. In the new trellis codes, a group of semi-orthogonal trellis codes is in use as building parts. An intense system is an outcome that gives full assorted variety, rate, and higher coding gain. It has appeared in [7] that multilevel coding (MLC) and STTCs joined for outlining MLSTTCs lead to a modification in STTCs coding and assorted diversity and coding gain.MLSTTC performance is further enhanced by the use of receiver channel feedback information for adaptive selection of the generator sequence. STTC components are encoded using specific generator sequences. The receiver compares the current channel profile along with a predetermined channel profile set and a predetermined profile index and sends it back again to the transmitter. STTC encoders use a few generator arrangements set in the chosen code for creating dynamic space-time trellis codes (DSTTCs). In multilevel coding, DSTTCs are utilized as part codes to develop new systems, which are called multilevel dynamic space-time trellis codes (MLDSTTCs). In [8], assembled grouped multilevel space-time trellis codes (GMLSTTC), beamforming, and an adaptive array of the assembled cooperative diversity antenna are united for the design of a new system using state-of-the-art information using the channel at the transmitter (CSIT). This code is known as weighted adaptively GMLSTTCs. The transmit antennas are applied at a different power level, which provides a beamforming system of about 2.6 dB over the grouped multilevel space-time trellis codes.In a cognitive radio network (CRN), primary users (PUs) are given priority to receive the allocated spectrum whenever required. On the other hand, Secondary users (SUs) have to find out the unutilized bands which have not been used by PUs to transmit the data. [9, 10].Subsequently, a few methodologies are proposed for sharing and proficiently using the accessible spectrum. Cognitive radio is a promising way to deal with and take care of this issue [11–13].The authors have proposed error correction coding (ECC) for CRNs. SU’s transmitter abandons the band in CRNs once a PU is distinguished [14]. Cognitive radio and nonorthogonal multiple access (NOMA) are considered essential solutions for fifth-generation wireless networks. The integration of NOMA techniques in CRN offers considerable potential to improve spectral efficiency and increase system capacity [15]. For an OFDM-based CRN, the SU transmitter and receiver continuously sense the frequency, exchange data, and settle on the accessible and inaccessible parts of the spectrum frequency [16].Contingent upon the frequency spectrum availability, a proper Reed-Solomon coding plan is utilized to recover the bits transmitted over the inaccessible parts of the spectrum. Ko and Kim [17] additionally investigate differential space-time block codes (D-STBCs) plan to arrange the bits in error where an exchanging model was considered for dynamic and conveyed spectrum designation and also examine the impacts of differed PU identification execution. The switch is thought to be open for each of the cognitive users (CUs) identifying a PU. At the point when the switch is free, the channel is displayed as a binary eradication channel (BEC), and the cognitive transmitter keeps on transmitting its message enabling bits. Thus, the receiver used dynamic allocation of unused spectrum sensing and applied information theory and error-correcting codes for spectrum access in cognitive radio by proposing a transmit diversity scheme [18]. Another significant utilization of the error-correcting code (ECC) plans is exhibited in [19], where the authors contemplate the execution of effective cognitive radio systems by utilizing rateless coding error control system. The utilization of rateless codes permits the SU receiver to interpret or decode information. STTC scheme is discussed in [20] to moderate the detrimental consequences of multipath fading, which improves the performance of multipath fading in different modulation schemes by enhancing the coding gain and spectral efficiency with low decoding complexity.


### 1.2. Contribution

The main contribution of the paper is represented in terms of proposing a model in which the GMLSTTC is applied to the cognitive radio scenario for improving the QoS parameters of the system in terms of error rate performance, coding gain, and throughput. Grouped multilevel space-time trellis codes (GMLSTTCs) utilize multilevel coding (MLC), antenna grouping, and space-time trellis codes (STTCs) for simultaneously providing coding gain, diversity improvement, and increased throughput. Cognitive radio also helps in improving the QoS in terms of spectrum sensing. In this paper, GMLSTTC (as it is better than all other schemes compared to STTC and MLSTTC) with MIMO transmission is applied to the cognitive radio scenario, which further enhances the cognitive radio performance. This has been analyzed in terms of throughput and error rate performance. This paper has also shown the effect of a proposed GMLSTTC with cognitive radio on different deployment setups such as urban, suburban, and rural macrodeployment setup of the ITU-R M.2135 standard in terms of error rate performance.


### 1.3. Organization

The rest of the paper is organized as follows. Section2 comprises three subsections. In Section 2.1, we provide the system model and introduce the concept of different space-time trellis coding techniques. Section 2.2 introduces the idea of cognitive radio, and its application in GMLSTTCs is discussed in Section 2.3. Section 3 describes the algorithm used for realizing and representing the objectives. Section 4 presents simulation results demonstrating the improvement in the performance in terms of SER and FER based on STTC, MLSTTC, and GMLSTTC, and finally, the performance of GMLSTTC is analyzed in cognitive radio scenario and different deployment models of ITU-R M.2135. Finally, we conclude the paper and provide some future research directions in Section 5.


## 1.1. Background Study

In the last couple of years, the investigation of various multilevel space-time trellis coding (MLSTTC) procedures has improved the situation by achieving the advantages of spectral efficiency, coding gain, and diversity gain. In [1], an elegant transmission procedure is proposed using new multilevel pseudo-space-time trellis coding (MLPSTTC) for single antenna portable hubs. The transmitted data are decoded just by accumulating individual information of all hubs which exchange their information parallel to each other. The participating hub self-data and different centers decoded data are encoded further through a multilevel code plot and (as segment codes) pseudo-space-time trellis codes. At each supportive center, the resultant produced MLPSTTC symbols, which are transmitted through the independent fading channels to the universal destination node. Hence, various data duplicates of each portable center are achieved on a destination hub. The execution that appeared in the trial consequence of the cooperative MLSTTC strategy is better in correlation with the current MLSTTC plans. The STC method used in [2] depicts the use of OFDM (Orthogonal Frequency Division Multiplexing) framework with the STC. To achieve the best result, the bit error rate (BER) using multiple-input multiple-output (MIMO) technology in a cooperative diversity environment should be limited.The STBC on the AWGN fade channel is used to decrease the BER to acquire the quality signal at the receiving end. STBC is applied at the end of the transmitter to examine the AWGN fading channel of the OFDM frame. The prior technique uses several modulation methods like quadrature amplitude modulation (QAM) and binary phase shift key (BPSK), which are analyzed based on BER and SNR (signal-to-noise ratio). Another differential encoding and disentangling procedure is proposed in [3] for differential-distributed space timing coding (DDSTC) frameworks over the slow-fading frequency selective channels with multiple relays having imperfect synchronization. The frequency selectivity causes intersymbol interference (ISI), which can be eliminated by DDSTC techniques. It is robust if synchronization errors occur while no channel is necessary on the destination. Furthermore, the maximum possible diversity has been achieved with the complexity of decoding, which is similar to the traditional DDSTC.In [4], the first spotlight is on the short-length trellis-based code outline for two clients’ Gaussian multiple-access channel (MAC). An outline strategy is exhibited, which gives code plans and execution. It is then contrasted and planned code execution for point-to-point (P2P) channels, including ideal convolutional codes. As appeared in its exploratory outcomes, unrivaled performance can be accomplished in contrast with the choices in break even with control situations, particularly in the administration of SNR (signal-to-noise ratio). A space-time code with the new class is presented in [5], which is referred to as space-time super-orthogonal trellis codes. The apportioned set and modified space-time orthogonal codes are symmetrically combined by these codes to provide enhanced coding gain as well as full-diversity gain to increase the overall development of prior space-time trellis code. The optimality of the parceled set has been additionally examined, and the investigation of coding gain is analyzed. The ideal setting has been used to plan different quantities of states up to a remarkably high conceivable rate, the codes operating at different data rates. Space-time super-orthogonal trellis codes give a tradeoff among coding and throughput. The outcomes of recreation demonstrate a more noteworthy change of 2 dB over the exhibited systems. A space-time trellis code new family is presented in [6], which broadens the space-time super-orthogonal trellis codes attributed intensely for transmission antennas in a cooperative diversity environment. In the new trellis codes, a group of semi-orthogonal trellis codes is in use as building parts. An intense system is an outcome that gives full assorted variety, rate, and higher coding gain. It has appeared in [7] that multilevel coding (MLC) and STTCs joined for outlining MLSTTCs lead to a modification in STTCs coding and assorted diversity and coding gain.MLSTTC performance is further enhanced by the use of receiver channel feedback information for adaptive selection of the generator sequence. STTC components are encoded using specific generator sequences. The receiver compares the current channel profile along with a predetermined channel profile set and a predetermined profile index and sends it back again to the transmitter. STTC encoders use a few generator arrangements set in the chosen code for creating dynamic space-time trellis codes (DSTTCs). In multilevel coding, DSTTCs are utilized as part codes to develop new systems, which are called multilevel dynamic space-time trellis codes (MLDSTTCs). In [8], assembled grouped multilevel space-time trellis codes (GMLSTTC), beamforming, and an adaptive array of the assembled cooperative diversity antenna are united for the design of a new system using state-of-the-art information using the channel at the transmitter (CSIT). This code is known as weighted adaptively GMLSTTCs. The transmit antennas are applied at a different power level, which provides a beamforming system of about 2.6 dB over the grouped multilevel space-time trellis codes.In a cognitive radio network (CRN), primary users (PUs) are given priority to receive the allocated spectrum whenever required. On the other hand, Secondary users (SUs) have to find out the unutilized bands which have not been used by PUs to transmit the data. [9, 10].Subsequently, a few methodologies are proposed for sharing and proficiently using the accessible spectrum. Cognitive radio is a promising way to deal with and take care of this issue [11–13].The authors have proposed error correction coding (ECC) for CRNs. SU’s transmitter abandons the band in CRNs once a PU is distinguished [14]. Cognitive radio and nonorthogonal multiple access (NOMA) are considered essential solutions for fifth-generation wireless networks. The integration of NOMA techniques in CRN offers considerable potential to improve spectral efficiency and increase system capacity [15]. For an OFDM-based CRN, the SU transmitter and receiver continuously sense the frequency, exchange data, and settle on the accessible and inaccessible parts of the spectrum frequency [16].Contingent upon the frequency spectrum availability, a proper Reed-Solomon coding plan is utilized to recover the bits transmitted over the inaccessible parts of the spectrum. Ko and Kim [17] additionally investigate differential space-time block codes (D-STBCs) plan to arrange the bits in error where an exchanging model was considered for dynamic and conveyed spectrum designation and also examine the impacts of differed PU identification execution. The switch is thought to be open for each of the cognitive users (CUs) identifying a PU. At the point when the switch is free, the channel is displayed as a binary eradication channel (BEC), and the cognitive transmitter keeps on transmitting its message enabling bits. Thus, the receiver used dynamic allocation of unused spectrum sensing and applied information theory and error-correcting codes for spectrum access in cognitive radio by proposing a transmit diversity scheme [18]. Another significant utilization of the error-correcting code (ECC) plans is exhibited in [19], where the authors contemplate the execution of effective cognitive radio systems by utilizing rateless coding error control system. The utilization of rateless codes permits the SU receiver to interpret or decode information. STTC scheme is discussed in [20] to moderate the detrimental consequences of multipath fading, which improves the performance of multipath fading in different modulation schemes by enhancing the coding gain and spectral efficiency with low decoding complexity.


## 1.2. Contribution

The main contribution of the paper is represented in terms of proposing a model in which the GMLSTTC is applied to the cognitive radio scenario for improving the QoS parameters of the system in terms of error rate performance, coding gain, and throughput. Grouped multilevel space-time trellis codes (GMLSTTCs) utilize multilevel coding (MLC), antenna grouping, and space-time trellis codes (STTCs) for simultaneously providing coding gain, diversity improvement, and increased throughput. Cognitive radio also helps in improving the QoS in terms of spectrum sensing. In this paper, GMLSTTC (as it is better than all other schemes compared to STTC and MLSTTC) with MIMO transmission is applied to the cognitive radio scenario, which further enhances the cognitive radio performance. This has been analyzed in terms of throughput and error rate performance. This paper has also shown the effect of a proposed GMLSTTC with cognitive radio on different deployment setups such as urban, suburban, and rural macrodeployment setup of the ITU-R M.2135 standard in terms of error rate performance.


## 1.3. Organization

The rest of the paper is organized as follows. Section2 comprises three subsections. In Section 2.1, we provide the system model and introduce the concept of different space-time trellis coding techniques. Section 2.2 introduces the idea of cognitive radio, and its application in GMLSTTCs is discussed in Section 2.3. Section 3 describes the algorithm used for realizing and representing the objectives. Section 4 presents simulation results demonstrating the improvement in the performance in terms of SER and FER based on STTC, MLSTTC, and GMLSTTC, and finally, the performance of GMLSTTC is analyzed in cognitive radio scenario and different deployment models of ITU-R M.2135. Finally, we conclude the paper and provide some future research directions in Section 5.


## 2. System Model and Problem Description

Grouped multilevel space-time trellis codes (GMLSTTCs) are capable of improving the coding gain, diversity gain, link quality, and throughput, simultaneously. If GMLSTTC is applied with cognitive radio, it will help in improving the spectral efficiency with higher throughput.


### 2.1. GMLSTTC System Overview

Multilevel coding in space-time coding will further be improved in its diversity as well as coding gain. MLSTTCs are designed as a combination of multilevel coding with STTCs.Grouping of antenna applied in multilevel trellis code called as grouped multilevel space-time trellis codes (GMLSTTCs) provides a higher throughput and much higher diversity gains.STTC is one of the STCs intended for multiple-input multiple-output (MIMO) condition where different reception apparatus design is utilized at sender and receiver sides. This different antenna design is used to transmit various information over the channel, and this information is received by numerous antennas at the recipient side, using a Viterbi decoder. STTC is superior to STBC codes because both the diversity gain and coding gain are improved in it [21]. However, STTC is considered as more complex as compared to the STBC, as it uses Viterbi translating for decoding, while STBC used the necessary decoding.Execution of linear block codes and convolution codes are conveyed in the SISO channel, while STBC, STTC, and multilevel codes are actualized in the MIMO channel using cooperative diversity with various antenna setups. The execution of these strategies is assessed by plotting BER over the SNR range in the middle of (0–30) dB.STTCs disperse a trellis code over various multiple antennas and multiple time slots [1]. Furthermore, it gives both the coding gain and also assorted diversity gain. Now, the plan requires a decent tradeoff between constellation size, estimate, information rate, assorted diversity advantage, and trellis complexion. The other sort of STCs is space-time block codes [2, 3].A general STTC in a wireless communication system uses a pulse shaper, encoder, modulator, and multiple antennas called as MIMO system, i.e., multiple inputs and multiple outputs at the transmitter and the receiver side demodulator, channel estimator, and STTC decoder as shown in Figure1(a).Figure 1
(a) STTC block diagram. (b) STTC receiver block diagram.
(a)
(b)We consider versatile mobile communication withNt transmit antennas and Nr receiving antennas, as shown in Figures 1(a) and 1(b). At time instant t, binary stream B = bt=bt1,bt2,…,btB is applied into the space-time encoder after encoding and constellation mapping set of M = 2 m points, for an M-ary signal constellation, B binary input data are converted to NT modulation symbols from the signal. The column vector may signify the encoded data xt=xt1,xt2,…,xtNtT, called the space-time symbol where matrix transpose is signified by T. This coded data are passed through a serial to parallel convertor and the Nt data streams are simultaneously transmitted by Nt transmit antennas. The particular antenna j transmits the symbol xtj,where1≤j≤NT spans for all the symbols. Let us assume the length of the frame for every antenna is L, the codeword matrix can be written as(1)x=x1,x2,…,xL.The AWGN channel distorts the signal and is received byNr receiving antenna. Nr receiving antenna received space-time symbol rt=rt1,rt2,…,rtNrT, where rti represents one of the received signals at receive antenna, 1≤i≤Nr, or in matrix form as r=r1,r2,…,rL.Assume the coefficient of the channel of thejth transmitting antenna and ith receiving antenna at time t is hj,it, where hj,it is the fading coefficient between transmit antenna i and receive antenna j at time t.The value at the receiving antennai,i=1,2,…,Nr, is then(2)rti=∑i=1Nthi,jTxtj+nti,where nti is the noise at the receiving antenna i.Multilevel coding in space-time coding will further be improved in its diversity as well as coding gain. MLSTTCs are designed as a combination of multilevel coding with STTCs [6, 7].The MLSTTCs improve the bandwidth efficiency, diversity gain, and coding gain and decreases the complexity of decoding, mainly for bigger groups [22].The multileveling of space-time trellis code, i.e., MLSTTC, is distributing the basic signal constellation into the next hierarchal order of subsets. The input data are apportioned intoL data information streams utilizing a serial to parallel converter. Each cluster may itself have subgroups. MLSTTC system is displayed in Figure 2. The naming of the signal constellation points is based on partitioning and is likewise visualized in Figure 3, in which there are 2 clusters, and both the clusters have four subclusters. The circles in the diagram denote one subcluster of each cluster.Figure 2
MLSTTC block diagram.Figure 3
Partitioning and labeling of the underlying constellation for 64-QAM.The part codes are designated asC1,C2,…,CL in Figure 2. Every component codes represent the size of the cluster. Every encoder’s output is mapped to their related cluster.We consider a system withNT transmitting and NR receiving antennas. The M-QAM symbol or wave transmitted at time t by the jth transmit antenna and is indicated as Qtj, for 1≤j≤Nt. We envisioned a quasistatic Rayleigh attenuation channel that is consistent across the frames and shifts autonomously among them.The fading of each subchannel is done individually. Furthermore, we aimed to achieve accurate channel state information (CSI) at the receivers’ end, yet zero at the sender. Theith iteration of the receiving antenna throughput at time t is given by(3)rti=∑j=1NThijQtj+nti,i=1,2,…,Nr,where nti is known as AWGN related to ith iteration receiving antenna at time t. The resulting gain of the jth transmit to ith receiving antenna subchannel is demonstrated as a complex Gaussian inconsistent variable with mean value 0 and variance value 0.5 for each dimension.


#### 2.1.1. Encoding

Figure4 shows the body diagram of GMLSTTC. The structure uses multilevel coding and a set of partitioning. The process of multilevel coding required the constellation of M-QAM to be partitioned for L times, for 16-QAM, L = 2, N = 4, where M=NL is shown in Figure 5(a), and if L = 3, it will become 64-QAM, so as we increase the level, the Euclidean distance further increases.Figure 4
Block diagram of GMLSTTC with cooperative diversity.Figure 5
Partitioning of 16-QAM utilizing (N = 4) way segments and L = 2. (a) Level 1 sets partition into N = 4 subsets (each sets apart with various shaded circles). (b) The weighted sum of the levels 1 (white line) and 2 (grey) 4-QAM points chooses the transmitted 16-QAM point (dark).
(a)
(b)Euclidean distance increases at each level of partitioning, and the code becomes stronger, but at the same time, the complexity of the system increases. The output brings minimum Euclidean distance dominating performance. Code designing follows the trace criterion [23]. At the receiver end, the decoding of each stage has been compiled by a modified STTC decoder. The kth component code output xtk is denoted as follows: xtk=xtk,1,…,xtk,Nt, which selects the subset of constellation points. This mapping may be done by following the approach of DSTTC [24]. Output sequences of N-QAM symbols mean xtk,m=XI+jXQXI,XQ∈1,−1 assuming N=4, m=1,…,Nt.The actual transmission point is collectively defined by the N-QAM symbols of all levelsL. We can write the point M-QAM transmitted from the jth transmission antenna at the moment t in terms of the symbols L M-QAM [5] as(4)Qtj=dx1xt1,j+dx2xt2,j+…+dxlL,j,where dx1,…,dxL are the distances of subsets corresponding to x1,j,…,XxtL,j (for all j), as shown in Figure 5(b) for M = 16, N = 4, and L = 2. To reduce the error, as per the balanced distance rule [10], dx12dfreeC1=⋯=dxL2dfreeCL was required, where the free distance of the kth component code is dfreeCk. The first stage makes use of a single full-diversity STTC spanning all NT transmit antennas. To enhance the output, a combinational setup is used at later stages. It is achieved by using antenna arrays [25, 26] on different levels. By following the mentioned procedure, GMLSTTC is designed for sending multiple symbols per time slot. At higher levels, probably k > 1, the NT antennas are distributed onto Gk groups thus each having NGk antennas. The distribution of antennas corresponding to groups can be arranged in any way and at each level. An STTC for NGk antennas and N- QAM are used for each level k group.


#### 2.1.2. Detection/Decoding

We have used a decoder withL stages to decode the L-level GMLSTTC shown in Figure 4. The decoder initiates with decoding the first stage component code. Level 1 dominates performance because of propagation in error. If the levels are combined, then diversity is lowered, mink=1:LNGk, but results in increased distance properties than the first stage because of fixed partitioning. The decision x^t1, on xt1, is transferred to the succeeding decoding stage by which the values of xt2 and further ones are decoded. The last level of the decoder incorporated values from levels 1 to L − 1, namely, x^t1,x^t2,…,x^tL−1 to have x^tL. Conclude stage k, k = 1 to L. The subset labels xtk are decoded by stage k by incorporating “Viterbi” algorithm to visualize the route with the most accumulated metric across frame’s time length. By using the max-log approximation, the likelihood function calculation of the branch metric can be done [6].For 1 <k < L, the outputs of stage 1 to k − 1 decoders (i.e., x^t1,…,x^tk−1) are available. The values of xtk+1,…,xtL are not known. These are considered to be “nuisance” variables and are not considered. If more than one code is incorporated on k level, the components of xtk related by the other codes may get averaged out, whereas the state transition defines the rest of the components.Let us consider forL = 2 level GMLSTTC applied on four transmitting antennas, considering all terminals to be cooperative to each other i.e., NT=4. On the first level, single full-diversity STTC spans all antennas Nt, C1. On level 2, there are two identical STTCs (each spanning NT/2 antennas), denoted Ca2 for the first and second antennas and Cb2 for the third and fourth antennas. So the result is(5)xt2=xta2,xtb2=xta2,1,xta2,2,xtb2,3,xtb2,4.The extension can be applied to both decoder and metric to have more than one code at any stage and to different parameters ofM, N, and L. Based on (1) and (2), the signal at the ith receiving antenna at t time is(6)rTi=∑j=1Nthi,jtdx1xt1,j+∑j=1Nthi,jtdx2xt2,j+nti.For a transition labeledx (1), we decode (1) using the branch metric:(7)maxx˜ta2∈xta2,x˜tb2∈xtb2∑i=1Nrrti−∑j=12hi,jtdx2x˜ta2,j−∑j=12hi,jtdx2x˜tb2,j−∑j=1Nthi,jtdx1xt1,j2.Then, two parallel Viterbi decoders decodeCa2 and Cb2. The branch metric for Ca2 (and transition label xta2) is(8)maxx˜tb2∈xtb2∑i=1Nrrti−∑j=12hi,jtdx2x˜ta2,j−∑j=14hi,jtdx2x˜tb2,j−∑j=1Nthi,jtdx1x^t1,j2,and for Cb2, it (and transition label xtb2) is(9)maxx˜ta2∈xtb2∑i=1Nrrti−∑j=34hi,jtdx2xtb2,j−∑j=12hi,jtdx2x˜ta2,j−∑j=1Nthi,jtdx1x^t1,j2.By the usage of STTCs over ℳ-Quadrature Amplitude Modulation, each state requires ℳ branches rather thanM=NL. STTC of single full- rank needed at least MNt−1 states [7]; on the other hand, GMLSTTC uses at least MNGk−1 states for the level k code. The metric calculations are harder than those for a single STTC, with level k (for Gk = 1) requiring NrL−k+1+2k−1k−1 multiplying accumulates instead of (1 + Nt) per branch [1].


### 2.2. Cognitive Radio Network System Overview

Sensing of the spectrum can be done by using a well-defined technique called signal detection. Hypothesis test in [27–29] is applied in the cognitive radio environment to identify the presence of a signal in a noisy environment in which the signal detection can be reduced to a simple identification problem, described as shown in Figure 6.Figure 6
Hypothesis test and corresponding outcomes with their respective probabilities.Sensing of the spectrum can be made analogous to the binary hypothesis testing problem. In this, H0 mentions the inactive users, PU and H1, and confirms that the user is active. H0 is the noise-only hypothesis, and H1 is the signal plus noise hypothesis. Hence, the activeness and inactiveness can be measured by the hypotheses H0 and H1. Thus, four conclusions can be deduced from Figure6 [30]:Conclusion1:mentioning H0when H0is trueH0H0Conclusion2:mentioning H1when H1is trueH1H1Conclusion3:mentioning H0when H1is trueH0H1Conclusion4:mentioning H1when H0is trueH1H0The efficiency of sensing the spectrum can be calculated by the false alarm probability, that isPfa=PH1H0, miss detection Pm=PH0H1, and detection that is given by Pd=PH1H1. The hypothesis is decided based on a threshold being computed using equation (13) and Figure 7. H1 is considered when the energy detected is more than the defined threshold value, which means PU is active/present. H0 is considered when the energy detected is less than the threshold value, indicating that PU is inactive/absent that is discussed in Conclusion 1.Figure 7
(a) Spectrum sensing model representing detection probability. (b) Spectrum sensing model representing false alarm probability.
(a)
(b)The term specifies the decision of activeness of the first user or the primary user by the secondPd,Pfa, and Pm. Pd is the probability when SU detected the valid case, i.e., Conclusion2, shown in Figure 7(a). In Conclusion3, the PU is active, but still, it is showing inactive. This shows the extent of the missed access opportunity for the second user. The extent of interference that occurs in the primary user due to the second user is called the probability of miss detection Pm=1–Pd. Ideally, Pm is kept to be below a threshold value to secure the primary user, Pfa is the probability in which the primary user is not active, but still, the second user decides whether it is active, i.e., in Conclusion4, shown in Figure 7(b).Out of the conclusions mentioned above, the 2nd conclusion came out to be a correct detection, whereas the 3rd and 4th fall under the category of missed detection and a false alarm, respectively.In the cognitive radio network, two types of sensing are present. Networks—preliminary coarse detecting or sensing and excellent detecting or sensing. In preliminary course detecting, cognitive radio detects its condition to distinguish the range gaps. Once the range gaps are distinguished, cognitive radio gets better detection to recognize the primary user existence. The cognitive radio has a settled period to carry out proper detection and to send the information to the recipient. The period of cognitive radio is separated into two-time duration; one of these is sensing time and the other is transmission time. LetXf be the frame duration, Xs is the detecting or sensing time, and Xt is the transmission time of the cognitive radio, after that(10)Xf=Xs+Xt.As there is a tradeoff between detecting and transmission time, ideal detecting is a need where extremely conceivable throughput and least interference to the PU is required.We consider two speculations/hypotheses of the sensed signalSn as follows:(11)H0:Nnif primary user is inactive,H1:gPn+Nnif primary user is active,where n is varied from 1 to Y; Y is the number of samples, g signifies the channel gain, and it is 0 for H0 and 1 for H1.Nn represents the noise, with zero mean and variance σn2Pn represents the PU signal, and each sample is individually distributed with zero mean and variance σp2Sn is the received signal sample received by the energy detector and gives the output D necessary for the decision:(12)D=1Y∑n=1YSn2.P
det and Pfalse are the probabilities of detection and false alarm, respectively. Pdet is the probability of detection in the actual existence of PU and Pfalse in the absence of PU. If T is the threshold for the detection of PU then,(13)Pdet=PD>TH1,Pfalse=PD>TH0,Pdet=QT−µ1σ12,Pfalse=QT−µ0σ02,where T=σ02Q−1Pfalse+µ0.UnderH0, the mean and variance of the probability density function (PDF) of D are µ0 = σn4 and σ02, respectively. Under H1, the mean and variance of PDF of D are µ1 and σ12. Q is the generalized Marcum Q-function, and Q (·) is the complementary error function.Required number of samples for the targetPdet and Pfalse is calculated as follows:(14)Y=1SNR2Q−1Pfalse−Q−1Pdet2SNR+12,where SNR is the signal-to-noise ratio; now, Xs=tY, where t is the sampling time:(15)Xs=tSNR2Q−1Pfalse−Q−1Pdet2SNR+12.The sensing time optimization problem can be mathematically expressed as(16)minPfalse,SNRXs=tSNR2Q−1Pfalse−Q−1Pdet2SNR+12.There are two scenarios for cognitive radio transmission, first being the achievable throughput of cognitive radio under the condition that PU is not present:(17)TP0Xs=Xf−XsXf1−PfalseA0,and second being when PU is present and cognitive radio not detecting it, then the achievable throughput is(18)TP1Xs=Xf−XsXf1−PdetA1,where A0 and A1 are the throughputs of cognitive radio when PU is not present and when PU is present, respectively.The average throughput of cognitive radio that can be achieved is given by:(19)TPXs=PH1TP1Xs+PH0TP0Xs.PH0 is the probability that PU is inactive and P H1=1−PH0.The objective function that needs to be optimized is as follows:(20)maxPH1TP1Xs+PH0TP0Xss.t.Pdet≥Pdet′,where Pdet′ is the target probability of detection, and according to FCC guidelines, it should be at least 90%.The notations mentioned above are described in Tables1 and 2.Table 1
Notations.
Notation
Description
X
f
Frame duration
X
s
Sensing time
X
t
Transmission time
H
0
Hypothesis (if PU is inactive)
N
n
Noise
σ
n
2
Noise variance
H
1
Hypothesis (if PU is active)
P
n
PU signal
σ
p
2
Variance for PU
S
n
Received signal
D
Energy detector output
P
det
Probability of detection
P
det
Probability of false alarm
T
The threshold for the detection of PUTable 2
Notations based on cognitive radio.
Notation
Description
T
Sampling time
K
Number of cognitive radio
S
Signal
W
Noise
t
Timestep
SNR
For linear scale
P
d
The average probability of detection
P
f
The average probability of false alarm
P
m
Average probability of missed detection (1−Pd)
Q
d
Calculation of the global probability of detection
Q
f
Calculation of the global probability of false alarm
Q
m
Calculation of the global probability of missed detection (1−Qd)
Error
Error calculation (Qf+Qm)


### 2.3. Proposed Model of GMLSTTC in the Cognitive Radio Network System

In cognitive radio networks, PUs can be detected using different spectrum sensing techniques. The SU can utilize the vacant bands or spectrum holes for data transmission over the sensed ideal channel. Sensing of the primary channel is performed over a fixed interval called “Time Frame.” This Time Frame is classified further into transmission time and sensing time. If the sensing time is more, it will lead to accurate sensing but at the expense of decreased throughput. On the other hand, if the sensing time is less and the transmission time is more, then it will result in compromised PU detection and interference. The use of optimal sensing time can achieve a maximum possible throughput. So, there is a need to have a tradeoff between sensing time and transmission time. The prime factor on which the prioritization will be done is the energy of samples. The energy detector receives the signal samplesSn and gives the output D. In the following, we propose an algebraic coding approach to achieve signal space diversity for relay cognitive radios.A better signal-to-noise ratio is obtained when the interuser channel is being used. Hence, the decoding gets better by the cognitive radios due to the usage of the interuser channel shown in Figure8. After the application of space-time coding, this transmit diversity method is applied. Hence, diversity gain can be achieved at the same time; the reporting error probability is also reduced. Due to this, the gain is significantly improved, and the chances of error are also reduced. The proposed model of GMLSTTC with cognitive radio, as shown in Figure 9, represents the application of GMLSTTC in cognitive radio scenario. The cognitive module used in Figure 9 of both transmitter and receiver sides is perfectly synchronized with proper CSI, and hence, all cognitive users have perfect knowledge of the PU.Figure 8
Cognitive radio scenario for spectrum sharing.Figure 9
Proposed model representing GMLSTTC with cognitive radio scenario.The channel estimator decides the benchmark to derive the channel state information. Based on the radio spectrum scenario and the channel state information, the transmitter adapts the data rate, modulation scheme constellation size, and power. At the receiver, the signal, corrupted by interference, is received, and the data are detected using a suitable detector.Within the cognitive module, the PU is directed towards the receiver and the cognitive user is directed towards the cognitive receiver. By the analysis of the signal received at a SU, the decision is finalized using the threshold value. This threshold (T) is traditionally selected from the noise statistics so as to satisfy the false alarm rate specification of the detector based on the constant false alarm rate (CFAR) principle.


## 2.1. GMLSTTC System Overview

Multilevel coding in space-time coding will further be improved in its diversity as well as coding gain. MLSTTCs are designed as a combination of multilevel coding with STTCs.Grouping of antenna applied in multilevel trellis code called as grouped multilevel space-time trellis codes (GMLSTTCs) provides a higher throughput and much higher diversity gains.STTC is one of the STCs intended for multiple-input multiple-output (MIMO) condition where different reception apparatus design is utilized at sender and receiver sides. This different antenna design is used to transmit various information over the channel, and this information is received by numerous antennas at the recipient side, using a Viterbi decoder. STTC is superior to STBC codes because both the diversity gain and coding gain are improved in it [21]. However, STTC is considered as more complex as compared to the STBC, as it uses Viterbi translating for decoding, while STBC used the necessary decoding.Execution of linear block codes and convolution codes are conveyed in the SISO channel, while STBC, STTC, and multilevel codes are actualized in the MIMO channel using cooperative diversity with various antenna setups. The execution of these strategies is assessed by plotting BER over the SNR range in the middle of (0–30) dB.STTCs disperse a trellis code over various multiple antennas and multiple time slots [1]. Furthermore, it gives both the coding gain and also assorted diversity gain. Now, the plan requires a decent tradeoff between constellation size, estimate, information rate, assorted diversity advantage, and trellis complexion. The other sort of STCs is space-time block codes [2, 3].A general STTC in a wireless communication system uses a pulse shaper, encoder, modulator, and multiple antennas called as MIMO system, i.e., multiple inputs and multiple outputs at the transmitter and the receiver side demodulator, channel estimator, and STTC decoder as shown in Figure1(a).Figure 1
(a) STTC block diagram. (b) STTC receiver block diagram.
(a)
(b)We consider versatile mobile communication withNt transmit antennas and Nr receiving antennas, as shown in Figures 1(a) and 1(b). At time instant t, binary stream B = bt=bt1,bt2,…,btB is applied into the space-time encoder after encoding and constellation mapping set of M = 2 m points, for an M-ary signal constellation, B binary input data are converted to NT modulation symbols from the signal. The column vector may signify the encoded data xt=xt1,xt2,…,xtNtT, called the space-time symbol where matrix transpose is signified by T. This coded data are passed through a serial to parallel convertor and the Nt data streams are simultaneously transmitted by Nt transmit antennas. The particular antenna j transmits the symbol xtj,where1≤j≤NT spans for all the symbols. Let us assume the length of the frame for every antenna is L, the codeword matrix can be written as(1)x=x1,x2,…,xL.The AWGN channel distorts the signal and is received byNr receiving antenna. Nr receiving antenna received space-time symbol rt=rt1,rt2,…,rtNrT, where rti represents one of the received signals at receive antenna, 1≤i≤Nr, or in matrix form as r=r1,r2,…,rL.Assume the coefficient of the channel of thejth transmitting antenna and ith receiving antenna at time t is hj,it, where hj,it is the fading coefficient between transmit antenna i and receive antenna j at time t.The value at the receiving antennai,i=1,2,…,Nr, is then(2)rti=∑i=1Nthi,jTxtj+nti,where nti is the noise at the receiving antenna i.Multilevel coding in space-time coding will further be improved in its diversity as well as coding gain. MLSTTCs are designed as a combination of multilevel coding with STTCs [6, 7].The MLSTTCs improve the bandwidth efficiency, diversity gain, and coding gain and decreases the complexity of decoding, mainly for bigger groups [22].The multileveling of space-time trellis code, i.e., MLSTTC, is distributing the basic signal constellation into the next hierarchal order of subsets. The input data are apportioned intoL data information streams utilizing a serial to parallel converter. Each cluster may itself have subgroups. MLSTTC system is displayed in Figure 2. The naming of the signal constellation points is based on partitioning and is likewise visualized in Figure 3, in which there are 2 clusters, and both the clusters have four subclusters. The circles in the diagram denote one subcluster of each cluster.Figure 2
MLSTTC block diagram.Figure 3
Partitioning and labeling of the underlying constellation for 64-QAM.The part codes are designated asC1,C2,…,CL in Figure 2. Every component codes represent the size of the cluster. Every encoder’s output is mapped to their related cluster.We consider a system withNT transmitting and NR receiving antennas. The M-QAM symbol or wave transmitted at time t by the jth transmit antenna and is indicated as Qtj, for 1≤j≤Nt. We envisioned a quasistatic Rayleigh attenuation channel that is consistent across the frames and shifts autonomously among them.The fading of each subchannel is done individually. Furthermore, we aimed to achieve accurate channel state information (CSI) at the receivers’ end, yet zero at the sender. Theith iteration of the receiving antenna throughput at time t is given by(3)rti=∑j=1NThijQtj+nti,i=1,2,…,Nr,where nti is known as AWGN related to ith iteration receiving antenna at time t. The resulting gain of the jth transmit to ith receiving antenna subchannel is demonstrated as a complex Gaussian inconsistent variable with mean value 0 and variance value 0.5 for each dimension.


### 2.1.1. Encoding

Figure4 shows the body diagram of GMLSTTC. The structure uses multilevel coding and a set of partitioning. The process of multilevel coding required the constellation of M-QAM to be partitioned for L times, for 16-QAM, L = 2, N = 4, where M=NL is shown in Figure 5(a), and if L = 3, it will become 64-QAM, so as we increase the level, the Euclidean distance further increases.Figure 4
Block diagram of GMLSTTC with cooperative diversity.Figure 5
Partitioning of 16-QAM utilizing (N = 4) way segments and L = 2. (a) Level 1 sets partition into N = 4 subsets (each sets apart with various shaded circles). (b) The weighted sum of the levels 1 (white line) and 2 (grey) 4-QAM points chooses the transmitted 16-QAM point (dark).
(a)
(b)Euclidean distance increases at each level of partitioning, and the code becomes stronger, but at the same time, the complexity of the system increases. The output brings minimum Euclidean distance dominating performance. Code designing follows the trace criterion [23]. At the receiver end, the decoding of each stage has been compiled by a modified STTC decoder. The kth component code output xtk is denoted as follows: xtk=xtk,1,…,xtk,Nt, which selects the subset of constellation points. This mapping may be done by following the approach of DSTTC [24]. Output sequences of N-QAM symbols mean xtk,m=XI+jXQXI,XQ∈1,−1 assuming N=4, m=1,…,Nt.The actual transmission point is collectively defined by the N-QAM symbols of all levelsL. We can write the point M-QAM transmitted from the jth transmission antenna at the moment t in terms of the symbols L M-QAM [5] as(4)Qtj=dx1xt1,j+dx2xt2,j+…+dxlL,j,where dx1,…,dxL are the distances of subsets corresponding to x1,j,…,XxtL,j (for all j), as shown in Figure 5(b) for M = 16, N = 4, and L = 2. To reduce the error, as per the balanced distance rule [10], dx12dfreeC1=⋯=dxL2dfreeCL was required, where the free distance of the kth component code is dfreeCk. The first stage makes use of a single full-diversity STTC spanning all NT transmit antennas. To enhance the output, a combinational setup is used at later stages. It is achieved by using antenna arrays [25, 26] on different levels. By following the mentioned procedure, GMLSTTC is designed for sending multiple symbols per time slot. At higher levels, probably k > 1, the NT antennas are distributed onto Gk groups thus each having NGk antennas. The distribution of antennas corresponding to groups can be arranged in any way and at each level. An STTC for NGk antennas and N- QAM are used for each level k group.


### 2.1.2. Detection/Decoding

We have used a decoder withL stages to decode the L-level GMLSTTC shown in Figure 4. The decoder initiates with decoding the first stage component code. Level 1 dominates performance because of propagation in error. If the levels are combined, then diversity is lowered, mink=1:LNGk, but results in increased distance properties than the first stage because of fixed partitioning. The decision x^t1, on xt1, is transferred to the succeeding decoding stage by which the values of xt2 and further ones are decoded. The last level of the decoder incorporated values from levels 1 to L − 1, namely, x^t1,x^t2,…,x^tL−1 to have x^tL. Conclude stage k, k = 1 to L. The subset labels xtk are decoded by stage k by incorporating “Viterbi” algorithm to visualize the route with the most accumulated metric across frame’s time length. By using the max-log approximation, the likelihood function calculation of the branch metric can be done [6].For 1 <k < L, the outputs of stage 1 to k − 1 decoders (i.e., x^t1,…,x^tk−1) are available. The values of xtk+1,…,xtL are not known. These are considered to be “nuisance” variables and are not considered. If more than one code is incorporated on k level, the components of xtk related by the other codes may get averaged out, whereas the state transition defines the rest of the components.Let us consider forL = 2 level GMLSTTC applied on four transmitting antennas, considering all terminals to be cooperative to each other i.e., NT=4. On the first level, single full-diversity STTC spans all antennas Nt, C1. On level 2, there are two identical STTCs (each spanning NT/2 antennas), denoted Ca2 for the first and second antennas and Cb2 for the third and fourth antennas. So the result is(5)xt2=xta2,xtb2=xta2,1,xta2,2,xtb2,3,xtb2,4.The extension can be applied to both decoder and metric to have more than one code at any stage and to different parameters ofM, N, and L. Based on (1) and (2), the signal at the ith receiving antenna at t time is(6)rTi=∑j=1Nthi,jtdx1xt1,j+∑j=1Nthi,jtdx2xt2,j+nti.For a transition labeledx (1), we decode (1) using the branch metric:(7)maxx˜ta2∈xta2,x˜tb2∈xtb2∑i=1Nrrti−∑j=12hi,jtdx2x˜ta2,j−∑j=12hi,jtdx2x˜tb2,j−∑j=1Nthi,jtdx1xt1,j2.Then, two parallel Viterbi decoders decodeCa2 and Cb2. The branch metric for Ca2 (and transition label xta2) is(8)maxx˜tb2∈xtb2∑i=1Nrrti−∑j=12hi,jtdx2x˜ta2,j−∑j=14hi,jtdx2x˜tb2,j−∑j=1Nthi,jtdx1x^t1,j2,and for Cb2, it (and transition label xtb2) is(9)maxx˜ta2∈xtb2∑i=1Nrrti−∑j=34hi,jtdx2xtb2,j−∑j=12hi,jtdx2x˜ta2,j−∑j=1Nthi,jtdx1x^t1,j2.By the usage of STTCs over ℳ-Quadrature Amplitude Modulation, each state requires ℳ branches rather thanM=NL. STTC of single full- rank needed at least MNt−1 states [7]; on the other hand, GMLSTTC uses at least MNGk−1 states for the level k code. The metric calculations are harder than those for a single STTC, with level k (for Gk = 1) requiring NrL−k+1+2k−1k−1 multiplying accumulates instead of (1 + Nt) per branch [1].


## 2.1.1. Encoding

Figure4 shows the body diagram of GMLSTTC. The structure uses multilevel coding and a set of partitioning. The process of multilevel coding required the constellation of M-QAM to be partitioned for L times, for 16-QAM, L = 2, N = 4, where M=NL is shown in Figure 5(a), and if L = 3, it will become 64-QAM, so as we increase the level, the Euclidean distance further increases.Figure 4
Block diagram of GMLSTTC with cooperative diversity.Figure 5
Partitioning of 16-QAM utilizing (N = 4) way segments and L = 2. (a) Level 1 sets partition into N = 4 subsets (each sets apart with various shaded circles). (b) The weighted sum of the levels 1 (white line) and 2 (grey) 4-QAM points chooses the transmitted 16-QAM point (dark).
(a)
(b)Euclidean distance increases at each level of partitioning, and the code becomes stronger, but at the same time, the complexity of the system increases. The output brings minimum Euclidean distance dominating performance. Code designing follows the trace criterion [23]. At the receiver end, the decoding of each stage has been compiled by a modified STTC decoder. The kth component code output xtk is denoted as follows: xtk=xtk,1,…,xtk,Nt, which selects the subset of constellation points. This mapping may be done by following the approach of DSTTC [24]. Output sequences of N-QAM symbols mean xtk,m=XI+jXQXI,XQ∈1,−1 assuming N=4, m=1,…,Nt.The actual transmission point is collectively defined by the N-QAM symbols of all levelsL. We can write the point M-QAM transmitted from the jth transmission antenna at the moment t in terms of the symbols L M-QAM [5] as(4)Qtj=dx1xt1,j+dx2xt2,j+…+dxlL,j,where dx1,…,dxL are the distances of subsets corresponding to x1,j,…,XxtL,j (for all j), as shown in Figure 5(b) for M = 16, N = 4, and L = 2. To reduce the error, as per the balanced distance rule [10], dx12dfreeC1=⋯=dxL2dfreeCL was required, where the free distance of the kth component code is dfreeCk. The first stage makes use of a single full-diversity STTC spanning all NT transmit antennas. To enhance the output, a combinational setup is used at later stages. It is achieved by using antenna arrays [25, 26] on different levels. By following the mentioned procedure, GMLSTTC is designed for sending multiple symbols per time slot. At higher levels, probably k > 1, the NT antennas are distributed onto Gk groups thus each having NGk antennas. The distribution of antennas corresponding to groups can be arranged in any way and at each level. An STTC for NGk antennas and N- QAM are used for each level k group.


## 2.1.2. Detection/Decoding

We have used a decoder withL stages to decode the L-level GMLSTTC shown in Figure 4. The decoder initiates with decoding the first stage component code. Level 1 dominates performance because of propagation in error. If the levels are combined, then diversity is lowered, mink=1:LNGk, but results in increased distance properties than the first stage because of fixed partitioning. The decision x^t1, on xt1, is transferred to the succeeding decoding stage by which the values of xt2 and further ones are decoded. The last level of the decoder incorporated values from levels 1 to L − 1, namely, x^t1,x^t2,…,x^tL−1 to have x^tL. Conclude stage k, k = 1 to L. The subset labels xtk are decoded by stage k by incorporating “Viterbi” algorithm to visualize the route with the most accumulated metric across frame’s time length. By using the max-log approximation, the likelihood function calculation of the branch metric can be done [6].For 1 <k < L, the outputs of stage 1 to k − 1 decoders (i.e., x^t1,…,x^tk−1) are available. The values of xtk+1,…,xtL are not known. These are considered to be “nuisance” variables and are not considered. If more than one code is incorporated on k level, the components of xtk related by the other codes may get averaged out, whereas the state transition defines the rest of the components.Let us consider forL = 2 level GMLSTTC applied on four transmitting antennas, considering all terminals to be cooperative to each other i.e., NT=4. On the first level, single full-diversity STTC spans all antennas Nt, C1. On level 2, there are two identical STTCs (each spanning NT/2 antennas), denoted Ca2 for the first and second antennas and Cb2 for the third and fourth antennas. So the result is(5)xt2=xta2,xtb2=xta2,1,xta2,2,xtb2,3,xtb2,4.The extension can be applied to both decoder and metric to have more than one code at any stage and to different parameters ofM, N, and L. Based on (1) and (2), the signal at the ith receiving antenna at t time is(6)rTi=∑j=1Nthi,jtdx1xt1,j+∑j=1Nthi,jtdx2xt2,j+nti.For a transition labeledx (1), we decode (1) using the branch metric:(7)maxx˜ta2∈xta2,x˜tb2∈xtb2∑i=1Nrrti−∑j=12hi,jtdx2x˜ta2,j−∑j=12hi,jtdx2x˜tb2,j−∑j=1Nthi,jtdx1xt1,j2.Then, two parallel Viterbi decoders decodeCa2 and Cb2. The branch metric for Ca2 (and transition label xta2) is(8)maxx˜tb2∈xtb2∑i=1Nrrti−∑j=12hi,jtdx2x˜ta2,j−∑j=14hi,jtdx2x˜tb2,j−∑j=1Nthi,jtdx1x^t1,j2,and for Cb2, it (and transition label xtb2) is(9)maxx˜ta2∈xtb2∑i=1Nrrti−∑j=34hi,jtdx2xtb2,j−∑j=12hi,jtdx2x˜ta2,j−∑j=1Nthi,jtdx1x^t1,j2.By the usage of STTCs over ℳ-Quadrature Amplitude Modulation, each state requires ℳ branches rather thanM=NL. STTC of single full- rank needed at least MNt−1 states [7]; on the other hand, GMLSTTC uses at least MNGk−1 states for the level k code. The metric calculations are harder than those for a single STTC, with level k (for Gk = 1) requiring NrL−k+1+2k−1k−1 multiplying accumulates instead of (1 + Nt) per branch [1].


## 2.2. Cognitive Radio Network System Overview

Sensing of the spectrum can be done by using a well-defined technique called signal detection. Hypothesis test in [27–29] is applied in the cognitive radio environment to identify the presence of a signal in a noisy environment in which the signal detection can be reduced to a simple identification problem, described as shown in Figure 6.Figure 6
Hypothesis test and corresponding outcomes with their respective probabilities.Sensing of the spectrum can be made analogous to the binary hypothesis testing problem. In this, H0 mentions the inactive users, PU and H1, and confirms that the user is active. H0 is the noise-only hypothesis, and H1 is the signal plus noise hypothesis. Hence, the activeness and inactiveness can be measured by the hypotheses H0 and H1. Thus, four conclusions can be deduced from Figure6 [30]:Conclusion1:mentioning H0when H0is trueH0H0Conclusion2:mentioning H1when H1is trueH1H1Conclusion3:mentioning H0when H1is trueH0H1Conclusion4:mentioning H1when H0is trueH1H0The efficiency of sensing the spectrum can be calculated by the false alarm probability, that isPfa=PH1H0, miss detection Pm=PH0H1, and detection that is given by Pd=PH1H1. The hypothesis is decided based on a threshold being computed using equation (13) and Figure 7. H1 is considered when the energy detected is more than the defined threshold value, which means PU is active/present. H0 is considered when the energy detected is less than the threshold value, indicating that PU is inactive/absent that is discussed in Conclusion 1.Figure 7
(a) Spectrum sensing model representing detection probability. (b) Spectrum sensing model representing false alarm probability.
(a)
(b)The term specifies the decision of activeness of the first user or the primary user by the secondPd,Pfa, and Pm. Pd is the probability when SU detected the valid case, i.e., Conclusion2, shown in Figure 7(a). In Conclusion3, the PU is active, but still, it is showing inactive. This shows the extent of the missed access opportunity for the second user. The extent of interference that occurs in the primary user due to the second user is called the probability of miss detection Pm=1–Pd. Ideally, Pm is kept to be below a threshold value to secure the primary user, Pfa is the probability in which the primary user is not active, but still, the second user decides whether it is active, i.e., in Conclusion4, shown in Figure 7(b).Out of the conclusions mentioned above, the 2nd conclusion came out to be a correct detection, whereas the 3rd and 4th fall under the category of missed detection and a false alarm, respectively.In the cognitive radio network, two types of sensing are present. Networks—preliminary coarse detecting or sensing and excellent detecting or sensing. In preliminary course detecting, cognitive radio detects its condition to distinguish the range gaps. Once the range gaps are distinguished, cognitive radio gets better detection to recognize the primary user existence. The cognitive radio has a settled period to carry out proper detection and to send the information to the recipient. The period of cognitive radio is separated into two-time duration; one of these is sensing time and the other is transmission time. LetXf be the frame duration, Xs is the detecting or sensing time, and Xt is the transmission time of the cognitive radio, after that(10)Xf=Xs+Xt.As there is a tradeoff between detecting and transmission time, ideal detecting is a need where extremely conceivable throughput and least interference to the PU is required.We consider two speculations/hypotheses of the sensed signalSn as follows:(11)H0:Nnif primary user is inactive,H1:gPn+Nnif primary user is active,where n is varied from 1 to Y; Y is the number of samples, g signifies the channel gain, and it is 0 for H0 and 1 for H1.Nn represents the noise, with zero mean and variance σn2Pn represents the PU signal, and each sample is individually distributed with zero mean and variance σp2Sn is the received signal sample received by the energy detector and gives the output D necessary for the decision:(12)D=1Y∑n=1YSn2.P
det and Pfalse are the probabilities of detection and false alarm, respectively. Pdet is the probability of detection in the actual existence of PU and Pfalse in the absence of PU. If T is the threshold for the detection of PU then,(13)Pdet=PD>TH1,Pfalse=PD>TH0,Pdet=QT−µ1σ12,Pfalse=QT−µ0σ02,where T=σ02Q−1Pfalse+µ0.UnderH0, the mean and variance of the probability density function (PDF) of D are µ0 = σn4 and σ02, respectively. Under H1, the mean and variance of PDF of D are µ1 and σ12. Q is the generalized Marcum Q-function, and Q (·) is the complementary error function.Required number of samples for the targetPdet and Pfalse is calculated as follows:(14)Y=1SNR2Q−1Pfalse−Q−1Pdet2SNR+12,where SNR is the signal-to-noise ratio; now, Xs=tY, where t is the sampling time:(15)Xs=tSNR2Q−1Pfalse−Q−1Pdet2SNR+12.The sensing time optimization problem can be mathematically expressed as(16)minPfalse,SNRXs=tSNR2Q−1Pfalse−Q−1Pdet2SNR+12.There are two scenarios for cognitive radio transmission, first being the achievable throughput of cognitive radio under the condition that PU is not present:(17)TP0Xs=Xf−XsXf1−PfalseA0,and second being when PU is present and cognitive radio not detecting it, then the achievable throughput is(18)TP1Xs=Xf−XsXf1−PdetA1,where A0 and A1 are the throughputs of cognitive radio when PU is not present and when PU is present, respectively.The average throughput of cognitive radio that can be achieved is given by:(19)TPXs=PH1TP1Xs+PH0TP0Xs.PH0 is the probability that PU is inactive and P H1=1−PH0.The objective function that needs to be optimized is as follows:(20)maxPH1TP1Xs+PH0TP0Xss.t.Pdet≥Pdet′,where Pdet′ is the target probability of detection, and according to FCC guidelines, it should be at least 90%.The notations mentioned above are described in Tables1 and 2.Table 1
Notations.
Notation
Description
X
f
Frame duration
X
s
Sensing time
X
t
Transmission time
H
0
Hypothesis (if PU is inactive)
N
n
Noise
σ
n
2
Noise variance
H
1
Hypothesis (if PU is active)
P
n
PU signal
σ
p
2
Variance for PU
S
n
Received signal
D
Energy detector output
P
det
Probability of detection
P
det
Probability of false alarm
T
The threshold for the detection of PUTable 2
Notations based on cognitive radio.
Notation
Description
T
Sampling time
K
Number of cognitive radio
S
Signal
W
Noise
t
Timestep
SNR
For linear scale
P
d
The average probability of detection
P
f
The average probability of false alarm
P
m
Average probability of missed detection (1−Pd)
Q
d
Calculation of the global probability of detection
Q
f
Calculation of the global probability of false alarm
Q
m
Calculation of the global probability of missed detection (1−Qd)
Error
Error calculation (Qf+Qm)


## 2.3. Proposed Model of GMLSTTC in the Cognitive Radio Network System

In cognitive radio networks, PUs can be detected using different spectrum sensing techniques. The SU can utilize the vacant bands or spectrum holes for data transmission over the sensed ideal channel. Sensing of the primary channel is performed over a fixed interval called “Time Frame.” This Time Frame is classified further into transmission time and sensing time. If the sensing time is more, it will lead to accurate sensing but at the expense of decreased throughput. On the other hand, if the sensing time is less and the transmission time is more, then it will result in compromised PU detection and interference. The use of optimal sensing time can achieve a maximum possible throughput. So, there is a need to have a tradeoff between sensing time and transmission time. The prime factor on which the prioritization will be done is the energy of samples. The energy detector receives the signal samplesSn and gives the output D. In the following, we propose an algebraic coding approach to achieve signal space diversity for relay cognitive radios.A better signal-to-noise ratio is obtained when the interuser channel is being used. Hence, the decoding gets better by the cognitive radios due to the usage of the interuser channel shown in Figure8. After the application of space-time coding, this transmit diversity method is applied. Hence, diversity gain can be achieved at the same time; the reporting error probability is also reduced. Due to this, the gain is significantly improved, and the chances of error are also reduced. The proposed model of GMLSTTC with cognitive radio, as shown in Figure 9, represents the application of GMLSTTC in cognitive radio scenario. The cognitive module used in Figure 9 of both transmitter and receiver sides is perfectly synchronized with proper CSI, and hence, all cognitive users have perfect knowledge of the PU.Figure 8
Cognitive radio scenario for spectrum sharing.Figure 9
Proposed model representing GMLSTTC with cognitive radio scenario.The channel estimator decides the benchmark to derive the channel state information. Based on the radio spectrum scenario and the channel state information, the transmitter adapts the data rate, modulation scheme constellation size, and power. At the receiver, the signal, corrupted by interference, is received, and the data are detected using a suitable detector.Within the cognitive module, the PU is directed towards the receiver and the cognitive user is directed towards the cognitive receiver. By the analysis of the signal received at a SU, the decision is finalized using the threshold value. This threshold (T) is traditionally selected from the noise statistics so as to satisfy the false alarm rate specification of the detector based on the constant false alarm rate (CFAR) principle.


## 3. Realization and Representation of Objectives

This section comprises of the algorithms that are very useful for implementing and comparing the space-time trellis coding, multilevel space-time trellis coding, and grouped multilevel space-time trellis coding scheme applied in the cognitive radio scenario as shown in Figure9. Algorithms are divided into four parts, Algorithm 1 includes Algorithms 2–4, and it explains the initialization and scenario realization, while Algorithms 2–4 explain the generation of STTC, MLSTTC, and GMLSTTC.Algorithm 1:Application of different space-time trellis coding in cognitive radio scenario.
Step 1: input parameters
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Step 2: initialization of the probability matrices
For t=10:0.5:60
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Step 5: initialization
Initialize the matrix for storing the values of:Pdc,Pfc,error
//∗ Application of space-time coding process ∗//
Step 6: apply the space-time trellis coding
Follow the process in Algorithm 2
Step 7: apply the multilevel space-time trellis coding
Follow the process in Algorithm 3
Step 8: apply the group multilevel space-time trellis coding
Follow the process in Algorithm 4
//∗ Application of space-time coded signal on the cognitive radio scenario ∗//
For
i = 1 : 1 : rel
Step 9: initialize SNR and convert to linear phase
SNR
=
10
;
SNR
=
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SNR
/
10 //∗dB to linear phase conversion∗//
Step 10: generation of the signal and adding of noise variance
Generate the signal (s)
Add Rayleigh Fading
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Step 11: signal energy calculation
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Step 12: calculation of SNR
Eb/No calculation
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Step 13: calculation of energy when PU absent
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Step 14: calculation of energy when primary is present
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Step 15: calculate the global probability of detection (calculate Pdc and Pfc using E1 and E0)
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End
Step 16: calculate the global probability of false alarm
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End
End
Calculate Pd and Pf using Pdc and Pfc
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/
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f
=
p
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;
Step 17: detection and false alarm signal evaluation/optimization
For
l = n: 1: K
Step 18: calculate the global probability of detection
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Step 19: calculate the global probability of false alarm
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End
Step 20: calculate missed detection probability
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−
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Step 21: calculate total error probability
error
=
Q
f
+
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m
End
Calculate BER
End
EndAlgorithm 2:Trellis coding.
Step 1: input parameters
n, k, L, number of symbols, M, N, S, bits per symbol
Step 2: generation of trellis code polynomial
Calculate the number of constellation points using the number of bits per symbol
Store the value of the symbol that needs to be transmitted in N
Define the generator polynomial
Initialize the Codeword, Next state, and previous state matrices
Apply the random interleaver for removing the burst errors
Step 3: apply modulation of the Type-64 QAM
Step 4: defining the simulation parameters
Total energy of the codeword, EbN0dB EbN0dBStop
Calculate the number of information bits = number of symbols ∗n
Calculate the number of coded bits = number of symbols ∗k
While (EbN0dB≤EbN0dB_Stop)
Step 5: initialize the counters to store
Number of errors = error counts
Number of frame = frame count
Number of bits = bit count
Step 6: calculate SNR
SNR
=
E
b
N
0
d
B
−
10
log
10
n
N
0
=
10
E
b
N
0
/
10
While (error counts < 1000 and frame count ≤ 100)
Step 7: compute energy per bit
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b
=
E
c
/
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Step 8: compute noise variance
N
0
=
E
b
∗
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b
N
0
−
1
Step 9: apply the input bits
Input bits = round (rand (1, numberofInformationbits))
Step 10: convert number of bits to symbols
Symbols = bits to the symbol (n, number of symbols, input bits)
Step 11: apply convolution encoding
Generate the transmitted signal
Step 12: calculate the received signal
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Step 13: apply the demodulation
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Step 14: apply decoding
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End
Step 15: calculate bit error rate
EndAlgorithm 3:Multilevel trellis coding.
Step 1: input parameters
N, k, L, data serial, data serial to parallel, d1, d2, d3, d4.
Step 2: conversion of data from serial to parallel
Converting serial data of length “N” to parallel data having “l” blocks of length “k” each such that sum (k) for i = 0 to l-1 is N
Step 3: generation of the codeword
Inserting a convolutional encoder for each data block which converts data block of length “k” to a codeword of length, i.e., rate = 2/3
Step 4: generation of trellis code polynomial
Define the generator polynomial
Initialize the codeword, next state, and previous state matrices
Generate the code from each parallel encoder
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Store the value of the symbol that needs to be transmitted in N
Apply the random interleaver for removing the burst errors
Step 5: apply modulation of the Type-64 QAM
Step 6: defining the simulation parameters
Total energy of the codeword, EbN0dB EbN0dBStop
Calculate the number of information bits = number of symbols ∗n
Calculate the number of coded bits = number of symbols ∗k
While (EbN0dB≤EbN0dB_Stop)
Step 7: initialize the counters to store
Number of errors = error counts
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Step 8: calculate SNR
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Step 13: apply convolution encoding
Generate the transmitted Signal
Step 14: calculate the received signal
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Step 17: calculate bit error rate
EndAlgorithm 4:Grouped multilevel trellis coding.
Step 1: input parameters
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Step 2: defining the simulation parameters
Define the constellation vector
Define the receiver vector
Step 3: initialize SNR and EbN0
SNR needed
EbNo needed
Step 4: calculate SNR and EbN0 for grouped multilevel
Calculate the instantaneous channel power gain between transmit antennai and all the receive antennas
Step 5: selection of antenna grouping with the best SNR value
For iconst=1:lengthconstellation_vec
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Step 6: apply multilevel trellis
End
//∗display constellation name and rate ∗//
For snr_index=starting_snr_index:lengthsnrdbvec
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Plot the EbN0dB
EndAlgorithms2–4 involve the generation and implementation of STTC, MLSTTC, and GMLSTTC, respectively, while Algorithm 1 consists of the application of different space-time trellis coding techniques in the cognitive radio scenario. Here, in the initial stage of algorithm 1, the same inputs have been taken, which are discussed in Table 3.Table 3
Simulation parameters based on coding techniques.
Parameters
Definition
Value
n
Bits per symbol
2
K
Number of subblocks for coding
3
L
Number of levels for the constellation
3
M
Number of levels
64
N
Number of symbols
512
B
Signal bandwidth
10 MHz
Δ
f
Subcarrier spacing
15 kHz
E
c
Total energy of the codeword
1
S
N
R
r
a
n
g
e
Range of signal-to-noise ratio
0 to 60 dB
E
b
N
0
d
B
Range of bit energy and noise
6
i
n
f
o
b
i
t
s
Number of information bits
1024
c
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d
e
d
b
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t
s
Number of coded bits
1536
t
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t
b
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Target block error
10^(−5)
r
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t
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Rate vector
[1/32, 1/16, 1/8, 1/4, 2/4, 3/4, 7/8]Algorithm1 involves the initialization and scenario realization. In this algorithm, first, the values are made fixed for various parameters to be used, and then matrices are made for the next level of processing. The secondary phase of Algorithm 1 involves the application of different space-time coding schemes including trellis, multilevel trellis, and grouped multilevel trellis, as discussed in the previous sections, on the cognitive radio scenario.Algorithm2 involves the generation of trellis code used in Algorithm 1 by defining the generator polynomial and then applying 64-QAM constellation and generates the transmitted signal using the convolutional encoder, and finally, the signal is received and decoded using the Viterbi decoder.Algorithm3 requires parallel cascading of trellis code to generate multilevel trellis code. Finally, in Algorithm 4, the grouping of antenna has been done to get the best optimal value of SNR.


## 4. Simulation Parameters and Results

This section provides the simulation parameters that are used for implementing the model used in this paper. The proposed model given in Figure9 depicts the scenario and the model that has been used in this paper for the performance analysis of space-time trellis coding techniques. Table 3 shows the parameters that are used for realizing the model used in this paper.The channel used for analyzing different space-time trellis coding techniques in various deployment models is modeled similarly to multipath propagation Rayleigh fading channel model, urban, suburban, and rural macrodeployment model of the ITU-R M.2135 standard [31].In this section, the performance analysis of different space-time trellis coding techniques like space-time trellis coding, multilevel space-time trellis coding, and group multilevel space-time trellis coding is applied on multipath propagation Rayleigh fading channel environment, and after that, the same has been used for cognitive radio environment in different deployment models.Path loss models for various transmission models have been standardized in [31–39]. The bandwidth chosen is 2–6 GHz, where the models/schemes can work, and that too with the various lengths of the antenna. This proposed scheme for rural areas can work in the bandwidth from 450 MHz to 6 GHz. In the path loss model, non-line-of-sight (NLOS) channel condition is assumed, UT is user terminal, BS is the base station, hBS and hUT are the antenna heights at the BS and the UT, “W” is the street width, “d” denotes the distance between the BS and the UT, and fc indicates the carrier frequency in (MHz). These schemes are mentioned in Table 4 [40]. Further review of rateless space-time block code (RSTBC) for massive multiple-input multiple-output (MIMO) over lossy wireless environment is given in [41].Table 4
Macropath loss models for various propagation models.
Models
P
a
t
h
l
o
s
s
dB fcinGHz anddin m
Range and antenna height values
U
r
b
a
n Macro
N
L
o
S
161.04
−
7.1
log
10
W
+
7.5
log
10
h
−
24.37
−
3.7
h
/
h
BS
2
log
10
h
BS
+
43.42
−
3.1
log
10
h
BS
log
10
d
−
3
+
20
log
10
f
c
−
3.2
log
10
11.75
h
UT
2
−
4.97
10
m
<
d
<
5000
m hBS=25m,hUT=1.5m, W = 20 m, h = 20 m
S
u
b Urban Macro
N
L
o
S
161.04
−
7.1
log
10
W
+
7.5
log
10
h
−
24.37
−
3.7
h
/
h
BS
2
log
10
h
BS
+
43.42
−
3.1
log
10
h
BS
log
10
d
−
3
+
20
log
10
f
c
−
3.2
log
10
11.75
h
UT
2
−
4.97
10 m <d < 5000 m hBS=35m,hUT=1.5m, W = 20 m, h = 10 m
R
u
r
a
l Macro
N
L
o
S
161.04
−
7.1
log
10
W
+
7.5
log
10
h
−
24.37
−
3.7
h
/
h
BS
2
log
10
h
BS
+
43.42
−
3.1
log
10
h
BS
log
10
d
−
3
+
20
log
10
f
c
−
3.2
log
10
11.75
h
UT
2
−
4.97
10 m <d < 5000 m hBS=35m,hUT=1.5m, W = 20 m, h = 5 m


### 4.1. Performance Evaluation of Different Space-Time Trellis Coding Schemes for Rayleigh Fading Channel Model

Space-time block coding (STBC) is a potential scheme that provides spatial diversity gain. STBC with MIMO provided an improvement in performance as full diversity is achieved. The disadvantage of STBC is that it has high diversity gain but very less coding gain. The coding gain is improved in the STTC. Space-time trellis codes (STTCs) distribute a trellis code over multiple antennas and multiple time slots; therefore, it provides both the coding gain as well as diversity gain and has better SER and FER performance.Further, multiple antennas can be used to enhance the capacity of wireless links. But, to further improve the diversity as well as coding gain, multilevel coding in space-time coding will be used. MLSTTCs are designed as a combination of multilevel coding with STTCs. Multileveling of space-time trellis code, i.e., MLSTTC, further divides the fundamental signal constellation into a hierarchical order of subsets. The MLSTTCs improves bandwidth efficiency, throughput, diversity gain, and coding gain and decreases the complexity of decoding, mainly for bigger groups of constellation points. But, now, along with the coding gain and diversity gain, spectral efficiency also needs to be maintained. GMLSTTC will achieve this. GMLSTTCs can increase the coding gain and diversity improvement with enhanced spectral efficiency at the same time. Multidata symbol per time slot can be obtained by cascading antennas at various positions and by going for a different STTC per group. To increase throughput and to acquire better gain in diversity, one STTC coded level, which spans all antennas in a cooperative network, should be retained. The benefit of GMLSTTC structure is achieved by multistage decoding with desirous receive antennas. GMLSTTC uses multilevel coding and a set of partitioning.There is a need for improvement in the link quality of a wireless scenario, which has become degraded due to multipath propagation. For improving the link quality, different space-time coding techniques are applied on the transmitter side. The simulation results given in Figure10 depict the performance evaluation of varying space-time coding techniques in terms of SER and FER in multipath propagation Rayleigh fading scenario.Figure 10
Comparison of different coding schemes in terms of SER/FER for Rayleigh fading channel model.It is clear from the figure that GMLSTTC with cooperative diversity is performing better as compared to the other techniques as it can give a better gain in coding, increased diversity performance, and ultimately the spectral efficiency. MLSTTCs is designed for better achievement than conventional STTC, as it combines the simultaneous benefits of multilevel coding (MLC), space-time trellis coding (STTC), antenna grouping, and CSI at the transmitter. Due to the combined effects of all the schemes concatenated in a single scheme, there occurs an improvement in coding gain, diversity gain, and spectral efficiency. Further increase in performance is achieved when CSI is known to the transmitter, which is used for grouping of antennas adaptively at the transmitter side. The grouping of the antenna in the multilevel space-time trellis to form GMLSTTC is combined with the advantages of multilevel coding (MLC), trellis space-time coding (STTC), and antenna grouping. As a result, GMLSTTC retrieves more than one data symbol per time slot by creating antenna groups at certain levels using a separate STTC for each group.Table5 shows the results for coding gain/spectral efficiency at a target FER of 10-3 in the Rayleigh fading channel model for comparing the analytical results for SNR of STTC and GMLSTTC. The average coding gain of 1.8–3 dB relative to the STTC scheme has been obtained, as extracted from Figure 10. The asymptotic coding gain of 1.8 dB for a10-6 FER in Rayleigh fading is achieved. The coding gain/spectral efficiency at this lower FER is smaller. For any target FER, higher coding gains can be achieved by increasing the number of trellis states. The effective coding gain affects the power adaptation which in turn impacts spectral efficiency.Table 5
Coding gain for different values of FER.
FER
SNR (STTC)
SNR (MLSTTC)
SNR (GMLSTTC)
Coding gain (dB) (difference in SNR)
10−2
15.8
13.8
12.8
3.0
10−3
17.8
16.8
15
2.8
10−4
19.4
18.6
17
2.4
10−5
20.2
19.6
18.4
1.8
10−6
21.4
20.8
19.6
1.8Figure10 shows the performance evaluation of different space-time coding techniques in terms of SER and FER in multipath propagation Rayleigh fading scenario. But the extracted coding gain also explains the effect of GMLSTTC on the spectral efficiency in the Rayleigh fading channel model.In a wireless medium signal, power drops with time/space/frequency. When the power goes down significantly, the channel is said to be fading. To reduce the effect of fading, diversity is used in the wireless systems. To implement the diverse selection of antenna, grouping is used at the receiver at a different level. The signal is transmitted independently by fading links (or branches of diversity). The higher the number of branches of diversity, the higher the likelihood that no one or more branches at any point in time will fade. Diversity thus helps to establish a link. The simulation results show for GMLSTTCs with four transmit antennas and up to four receiving antennas.For full diversity, STTC was used, which covers all antennas that isN at level 1. At level 2, identical STTCs are used, each covering a group of N/2 antennas. The transmission antennas of each group are adaptively selected according to the CSI declaration of the receiver. Both STTCs are based on a tracking criterion and are used as component codes for multilevel coding. For the L = 2 level, GMLSTTC was applied on four transmitting antennas. On the first level, single full-diversity STTC spans all antennas, C1. On level 2, two identical STTCs (each spanning Nt/2 antennas) were denoted as Ca2 for the first and second antennas and Cb2 for the third and fourth antennas.The frame error rate (FER) performance of the GMLSTTCs shown in Figure11 is plotted against the signal-to-noise ratio (SNR) for four and two transmit antennas, with a various number of receiving antennas. Table 6 exhibits the FER performance comparison, as extracted from Figure 11 in terms of diversity gain. It is clear from the results that GMLSTTC performance with four transmission antennas is improved by adaptively grouping the CSI-based transmission antennas in the transmitter. The comparison results show that the GMLSTTC with four transmitting antennas is superior to the GMLSTTCs with two transmitting antennas with a diversity gain of 7.72 dB at the FER of 10−2 and will further increase up to 11.12 dB at FER of 10–4.Figure 11
GMLSTTCs error performance for two and four transmit antennas and various number of receiving antennas.Table 6
Diversity gain for different values of FER.
FER
SNR (dB) 2 transmitter antenna
SNR (dB) 4 transmitter antenna
Diversity gain (difference in SNR)
10−1
13.39
7.94
5.45
10−2
20.65
11.80
8.85
10−3
23.60
12.93
10.67
10−4
25.19
14.07
11.12


### 4.2. Performance Evaluation of Different Space-Time Trellis Coding Schemes for Cognitive Radio Scenario in Different Deployment Models

In this section, different deployment models of IMT advanced operating environments are used. These models help to find the effect of channel coding and signal strength. The accuracy of channel models is critical, as RF transmission is a mandate for broadband systems to be used in the coming times. This is required for multiinput multioutput systems, where radio channels could be used in any way to make it cheap and efficient and having an increased bit rate.There are chances of diffraction in the urban macrocell scene; therefore, the BTS (base transceiver station) height is kept a bit more than the surrounding workplace heights. Generally, in the urban areas, the BTSs are situated in outer areas where the blocks are making a grid type structure or may have different positions as high as at least five floors. Mostly in these models, homogenous arrangements are made, keeping in mind how dense the area is and the height of the buildings.In the urban model, propagation conditions for non-line-of-sight and base station are a little higher than the close-by building heights due to diffraction effects. While the mobile station is present at street level, building blocks are at inconsistent positions, where the height crosses 4th floors. In such a case, the height and density of the building are almost homogenous.In suburban areas, MS is stationed at the outer areas at the street level while BTS is kept at a higher level at the top of the buildings to obtain better coverage. Here, the numbers of floors are low as compared to those of urban areas. The homes and offices are also away from each other. A more significant amount of grounds are available, making it more spacious. Streets patterns are also random since they do not follow grid patterns, and foliage loss is even less.A macrocell would not be able to support an extensive speed system, as it would lead to transmission impairments. In this system, large-speed automobiles are recommended due to a larger coverage area, and therefore the particular model concentrates on bigger cells. LOS is achievable in rural areas because of a lower number of buildings and a higher length of BTS.In a cognitive radio scenario, ideal detecting is a need where extremely conceivable throughput and least interference to the PU are required. The sensing channels and the reporting channels both experience Rayleigh fading with an average SNR = 10 dB. By modeling the system, we compare the results, as the diversity becomes better, thus the signal-to-noise ratio increases, and consequently, SER is reduced, while using the cognitive radio. We further simulate the results given in Figure10, which is depicting the performance evaluation of GMLSTTC in terms of SER and FER in multipath propagation, Rayleigh fading scenarios, to be applied in cognitive radio scenario.Simulation results are given in Figure12 depict the performance evaluation of FER and SER for ITU-R M.2135 standard in urban, suburban, and rural models with cognitive radio. The rural model with cognitive gives better results as compare to suburban, and thus, suburban is better than urban.Figure 12
Comparison of urban, suburban, and rural deployment for GMLSTTC in terms of SER and FER in cognitive radio scenario.As in the rural model system, large-speed automobiles are supported due to a larger coverage area, and therefore, it concentrates on bigger cells. Also, the numbers of buildings are less, and the length of BTS is high; therefore, LOS is achievable in rural areas. In suburban areas, MS is stationed at outer areas at street level while BTS is kept at a higher level, i.e., at the top of the buildings, to obtain better coverage. Here, the numbers of floors are low as compared to the urban areas; secondly, homes and offices are away from each other. More grounds are available; hence, it is spacious. Street pattern is also random, as they do not follow a grid pattern and foliage loss is also less as compared to urban. In this model, the height and density of the building are much more as compared to suburban and rural; hence, losses are more.Cognitive radio enables opportunistic secondary spectrum access and allows SUs to utilize the licensed frequency bands as long as the interference to the PUs is limited to an acceptable level.Cognitive radio can improve spectral efficiency/throughput. Meanwhile, it will lead to lower energy efficiency due to external time overhead and energy consumption for spectrum sensing. It is concluded that there exists optimal sensing duration and an optimal SNR to achieve maximum energy efficiency.Figure13 illustrates that there exists at optimal sensing time to make the spectral efficiency/throughput of cognitive relay networks maximized under different SNR, with and without GMLSTTC. At optimal sensing time, the received SNR of PU signal is measured at the cognitive receiver of interest under the hypothesis H1. The optimal sensing time is calculated from equation (16).Figure 13
Throughput for optimal sensing time of cognitive radio with and without GMLSTTC.Finally, the GMLSTTC scheme is applied for the urban model in cognitive mode and noncognitive mode, and the results are compared. It is clear from the results shown in Figure14 that cognitive mode gives better result in the low SNR range, but when the SNR is increased, the symbol error rate of the GMLSTTC without cognitive radio scenario has decreased steeply as compared to the GMLSTTC with cognitive radio scenario. It is because of the reason that at high SNR, the energy of the SUs increases in the cognitive radio scenario, which increases the interference level, thus giving rise to high SER as compared to the scenario that is not having cognitive radio.Figure 14
Comparison of different coding schemes in terms of SER and FER for the urban deployment model.


## 4.1. Performance Evaluation of Different Space-Time Trellis Coding Schemes for Rayleigh Fading Channel Model

Space-time block coding (STBC) is a potential scheme that provides spatial diversity gain. STBC with MIMO provided an improvement in performance as full diversity is achieved. The disadvantage of STBC is that it has high diversity gain but very less coding gain. The coding gain is improved in the STTC. Space-time trellis codes (STTCs) distribute a trellis code over multiple antennas and multiple time slots; therefore, it provides both the coding gain as well as diversity gain and has better SER and FER performance.Further, multiple antennas can be used to enhance the capacity of wireless links. But, to further improve the diversity as well as coding gain, multilevel coding in space-time coding will be used. MLSTTCs are designed as a combination of multilevel coding with STTCs. Multileveling of space-time trellis code, i.e., MLSTTC, further divides the fundamental signal constellation into a hierarchical order of subsets. The MLSTTCs improves bandwidth efficiency, throughput, diversity gain, and coding gain and decreases the complexity of decoding, mainly for bigger groups of constellation points. But, now, along with the coding gain and diversity gain, spectral efficiency also needs to be maintained. GMLSTTC will achieve this. GMLSTTCs can increase the coding gain and diversity improvement with enhanced spectral efficiency at the same time. Multidata symbol per time slot can be obtained by cascading antennas at various positions and by going for a different STTC per group. To increase throughput and to acquire better gain in diversity, one STTC coded level, which spans all antennas in a cooperative network, should be retained. The benefit of GMLSTTC structure is achieved by multistage decoding with desirous receive antennas. GMLSTTC uses multilevel coding and a set of partitioning.There is a need for improvement in the link quality of a wireless scenario, which has become degraded due to multipath propagation. For improving the link quality, different space-time coding techniques are applied on the transmitter side. The simulation results given in Figure10 depict the performance evaluation of varying space-time coding techniques in terms of SER and FER in multipath propagation Rayleigh fading scenario.Figure 10
Comparison of different coding schemes in terms of SER/FER for Rayleigh fading channel model.It is clear from the figure that GMLSTTC with cooperative diversity is performing better as compared to the other techniques as it can give a better gain in coding, increased diversity performance, and ultimately the spectral efficiency. MLSTTCs is designed for better achievement than conventional STTC, as it combines the simultaneous benefits of multilevel coding (MLC), space-time trellis coding (STTC), antenna grouping, and CSI at the transmitter. Due to the combined effects of all the schemes concatenated in a single scheme, there occurs an improvement in coding gain, diversity gain, and spectral efficiency. Further increase in performance is achieved when CSI is known to the transmitter, which is used for grouping of antennas adaptively at the transmitter side. The grouping of the antenna in the multilevel space-time trellis to form GMLSTTC is combined with the advantages of multilevel coding (MLC), trellis space-time coding (STTC), and antenna grouping. As a result, GMLSTTC retrieves more than one data symbol per time slot by creating antenna groups at certain levels using a separate STTC for each group.Table5 shows the results for coding gain/spectral efficiency at a target FER of 10-3 in the Rayleigh fading channel model for comparing the analytical results for SNR of STTC and GMLSTTC. The average coding gain of 1.8–3 dB relative to the STTC scheme has been obtained, as extracted from Figure 10. The asymptotic coding gain of 1.8 dB for a10-6 FER in Rayleigh fading is achieved. The coding gain/spectral efficiency at this lower FER is smaller. For any target FER, higher coding gains can be achieved by increasing the number of trellis states. The effective coding gain affects the power adaptation which in turn impacts spectral efficiency.Table 5
Coding gain for different values of FER.
FER
SNR (STTC)
SNR (MLSTTC)
SNR (GMLSTTC)
Coding gain (dB) (difference in SNR)
10−2
15.8
13.8
12.8
3.0
10−3
17.8
16.8
15
2.8
10−4
19.4
18.6
17
2.4
10−5
20.2
19.6
18.4
1.8
10−6
21.4
20.8
19.6
1.8Figure10 shows the performance evaluation of different space-time coding techniques in terms of SER and FER in multipath propagation Rayleigh fading scenario. But the extracted coding gain also explains the effect of GMLSTTC on the spectral efficiency in the Rayleigh fading channel model.In a wireless medium signal, power drops with time/space/frequency. When the power goes down significantly, the channel is said to be fading. To reduce the effect of fading, diversity is used in the wireless systems. To implement the diverse selection of antenna, grouping is used at the receiver at a different level. The signal is transmitted independently by fading links (or branches of diversity). The higher the number of branches of diversity, the higher the likelihood that no one or more branches at any point in time will fade. Diversity thus helps to establish a link. The simulation results show for GMLSTTCs with four transmit antennas and up to four receiving antennas.For full diversity, STTC was used, which covers all antennas that isN at level 1. At level 2, identical STTCs are used, each covering a group of N/2 antennas. The transmission antennas of each group are adaptively selected according to the CSI declaration of the receiver. Both STTCs are based on a tracking criterion and are used as component codes for multilevel coding. For the L = 2 level, GMLSTTC was applied on four transmitting antennas. On the first level, single full-diversity STTC spans all antennas, C1. On level 2, two identical STTCs (each spanning Nt/2 antennas) were denoted as Ca2 for the first and second antennas and Cb2 for the third and fourth antennas.The frame error rate (FER) performance of the GMLSTTCs shown in Figure11 is plotted against the signal-to-noise ratio (SNR) for four and two transmit antennas, with a various number of receiving antennas. Table 6 exhibits the FER performance comparison, as extracted from Figure 11 in terms of diversity gain. It is clear from the results that GMLSTTC performance with four transmission antennas is improved by adaptively grouping the CSI-based transmission antennas in the transmitter. The comparison results show that the GMLSTTC with four transmitting antennas is superior to the GMLSTTCs with two transmitting antennas with a diversity gain of 7.72 dB at the FER of 10−2 and will further increase up to 11.12 dB at FER of 10–4.Figure 11
GMLSTTCs error performance for two and four transmit antennas and various number of receiving antennas.Table 6
Diversity gain for different values of FER.
FER
SNR (dB) 2 transmitter antenna
SNR (dB) 4 transmitter antenna
Diversity gain (difference in SNR)
10−1
13.39
7.94
5.45
10−2
20.65
11.80
8.85
10−3
23.60
12.93
10.67
10−4
25.19
14.07
11.12


## 4.2. Performance Evaluation of Different Space-Time Trellis Coding Schemes for Cognitive Radio Scenario in Different Deployment Models

In this section, different deployment models of IMT advanced operating environments are used. These models help to find the effect of channel coding and signal strength. The accuracy of channel models is critical, as RF transmission is a mandate for broadband systems to be used in the coming times. This is required for multiinput multioutput systems, where radio channels could be used in any way to make it cheap and efficient and having an increased bit rate.There are chances of diffraction in the urban macrocell scene; therefore, the BTS (base transceiver station) height is kept a bit more than the surrounding workplace heights. Generally, in the urban areas, the BTSs are situated in outer areas where the blocks are making a grid type structure or may have different positions as high as at least five floors. Mostly in these models, homogenous arrangements are made, keeping in mind how dense the area is and the height of the buildings.In the urban model, propagation conditions for non-line-of-sight and base station are a little higher than the close-by building heights due to diffraction effects. While the mobile station is present at street level, building blocks are at inconsistent positions, where the height crosses 4th floors. In such a case, the height and density of the building are almost homogenous.In suburban areas, MS is stationed at the outer areas at the street level while BTS is kept at a higher level at the top of the buildings to obtain better coverage. Here, the numbers of floors are low as compared to those of urban areas. The homes and offices are also away from each other. A more significant amount of grounds are available, making it more spacious. Streets patterns are also random since they do not follow grid patterns, and foliage loss is even less.A macrocell would not be able to support an extensive speed system, as it would lead to transmission impairments. In this system, large-speed automobiles are recommended due to a larger coverage area, and therefore the particular model concentrates on bigger cells. LOS is achievable in rural areas because of a lower number of buildings and a higher length of BTS.In a cognitive radio scenario, ideal detecting is a need where extremely conceivable throughput and least interference to the PU are required. The sensing channels and the reporting channels both experience Rayleigh fading with an average SNR = 10 dB. By modeling the system, we compare the results, as the diversity becomes better, thus the signal-to-noise ratio increases, and consequently, SER is reduced, while using the cognitive radio. We further simulate the results given in Figure10, which is depicting the performance evaluation of GMLSTTC in terms of SER and FER in multipath propagation, Rayleigh fading scenarios, to be applied in cognitive radio scenario.Simulation results are given in Figure12 depict the performance evaluation of FER and SER for ITU-R M.2135 standard in urban, suburban, and rural models with cognitive radio. The rural model with cognitive gives better results as compare to suburban, and thus, suburban is better than urban.Figure 12
Comparison of urban, suburban, and rural deployment for GMLSTTC in terms of SER and FER in cognitive radio scenario.As in the rural model system, large-speed automobiles are supported due to a larger coverage area, and therefore, it concentrates on bigger cells. Also, the numbers of buildings are less, and the length of BTS is high; therefore, LOS is achievable in rural areas. In suburban areas, MS is stationed at outer areas at street level while BTS is kept at a higher level, i.e., at the top of the buildings, to obtain better coverage. Here, the numbers of floors are low as compared to the urban areas; secondly, homes and offices are away from each other. More grounds are available; hence, it is spacious. Street pattern is also random, as they do not follow a grid pattern and foliage loss is also less as compared to urban. In this model, the height and density of the building are much more as compared to suburban and rural; hence, losses are more.Cognitive radio enables opportunistic secondary spectrum access and allows SUs to utilize the licensed frequency bands as long as the interference to the PUs is limited to an acceptable level.Cognitive radio can improve spectral efficiency/throughput. Meanwhile, it will lead to lower energy efficiency due to external time overhead and energy consumption for spectrum sensing. It is concluded that there exists optimal sensing duration and an optimal SNR to achieve maximum energy efficiency.Figure13 illustrates that there exists at optimal sensing time to make the spectral efficiency/throughput of cognitive relay networks maximized under different SNR, with and without GMLSTTC. At optimal sensing time, the received SNR of PU signal is measured at the cognitive receiver of interest under the hypothesis H1. The optimal sensing time is calculated from equation (16).Figure 13
Throughput for optimal sensing time of cognitive radio with and without GMLSTTC.Finally, the GMLSTTC scheme is applied for the urban model in cognitive mode and noncognitive mode, and the results are compared. It is clear from the results shown in Figure14 that cognitive mode gives better result in the low SNR range, but when the SNR is increased, the symbol error rate of the GMLSTTC without cognitive radio scenario has decreased steeply as compared to the GMLSTTC with cognitive radio scenario. It is because of the reason that at high SNR, the energy of the SUs increases in the cognitive radio scenario, which increases the interference level, thus giving rise to high SER as compared to the scenario that is not having cognitive radio.Figure 14
Comparison of different coding schemes in terms of SER and FER for the urban deployment model.


## 5. Conclusion

The present wireless generation is suffering from increased demand of users. But, increased demand also demands a better quality of service. This paper has contributed to maintaining the QoS of the system by incorporating different space-time coding techniques in the next-generation cognitive radio scenario. This paper has highlighted different QoS parameters, such as coding gain, diversity gain, link quality, and throughput. These QoS parameters are achieved by using GMLSTTC with a diversity technique. This paper has also proposed a model in which GMLSTTC with cooperative diversity is incorporated in the cognitive radio scenario for improving the spectral efficiency. The simulation results given in Section4 depict that the GMLSTTC is performing better in all the deployment models like urban, suburban, and rural macrodeployment model of the ITU-R M.2135 standard. In our study, performance evaluation has been done in terms of SER in the multipath propagation scenario and different deployment models of the ITU-R M.2135 standard. It is also conclusive from the simulation that the GMLSTTC using cooperative diversity is also performing well with its proposed incorporation in the cognitive radio scenario. The main contribution gained from the paper is in the terms of achieving better QoS by the integration of GMLSTTC in the cognitive radio scenario, which is evaluated in terms of SER metrics.Future Research Direction: The performance of the system can also be further improved by applying the GMLSTTC to the massive MIMO scenario.



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*Source: 5280615-2019-12-06.xml*