Performance Analysis of Hybrid Filtering Technique for Reduction OF PAPR in Alamouti Coded MIMO-OFDM Systems

Multiple-Input Multiple-Output (MIMO) technique combined with Orthogonal Frequency Division Multiplexing (OFDM) is the proficient air interface for upcoming generations of high data rate and high-speed wireless communication. Nonetheless, such a system suffers from the drawback of a high peak-to-average power ratio (PAPR) when the symbol phases in the OFDM subcarriers line up in such a fashion that constructive formation of a large signal peak in the time domain occurs. Classical amplitude clipping, one of the simplest techniques, is employed to reduce PAPR. However, in-band distortion caused by clipping affects the high-frequency components of the in-band signal because the signal is clipped directly into the discrete-time domain at the Nyquist sampling rate. This causes the aliasing phenomenon through which the high frequency component of the OFDM signal's spectrum actually inherits the low frequency identity of the sampled version of the spectrum. In this paper, we propose an additional filtering scheme that has been assigned to our clipping algorithm to remove the high frequency components within the feasible regions (i.e. the constellation areas of the modulated symbols), which can efficiently reduce the PAPR of OFDM signals. The performance of the hybrid filtering algorithm is evaluated and compared with other algorithms such as the Partial Transmit Sequence (PTS), Selective mapping, active constellation extension for PAPR reduction by computer simulation in Alamouti Coded MIMO-OFDM systems. The simulation has been carried out using Matlab R2018a. Also, the technique proposed is compared with some recent techniques. The hybrid filtering algorithm is found to offer a better PAPR reduction as compared to the other techniques. It is shown that at a clipping ratio of 1.8, a PAPR reduction of 9.818 dB, equivalent to a percentage difference of 97.97% with respect to the original signal is achieved, when employing QPSK modulation and 12.42% more when using clipping only. The proposed work can find applications in Massive MIMO systems for beyond 5G networks.


Introduction
MIMO-OFDM has evolved into a major wireless interface for 4G and 5G broadband communications. One such technology is the fusion of MIMO, which increases channel capacity by using numerous signal transmissions over multiple antennas, and OFDM which divides the radio channel into oversized, closely spaced subchannels to ensure a more reliable transmission of information at higher speed. Communication over MIMO channels can eventually lead to multipath propagation, producing inter-symbol interference (ISI) when a radio signal is transmitted and reaches the receiving antenna through multiple paths. ISI causes signal distortion and reduces signal clarity. This is an unwanted occurrence and should be minimized as much as possible for the foreseeable future by using adaptive equalization techniques and/or error correction codes. If these issues are not addressed appropriately and quickly, MIMO-OFDM systems can suffer from high peak-toaverage power ratio (PAPR) issues [1].
Actually, the high PAPR is the most adverse aspect in the MIMO-OFDM system and is of serious concern, because it not only curbs the SQNR (Signal-to-Quantization Noise Ratio) of DAC (Digital-to-Analog Converter) and ADC (Analog to Digital Converter), but also decreases the efficiency of the power amplifier at the transmitter side as its DC power consumption will be determined by the peak power level [2]. Furthermore, this implies the oversizing of the power amplifier in terms of its average power requirement with additional complexity [3]. As such, it is of utmost importance to implement various techniques for PAPR reduction.
In terms of MIMO-OFDM systems, PAPR reduction is extensively used in literatures and researches in order to reduce signal peakiness, achieve a correct spectrum shaping and improve power amplifier efficiency [4]. Likewise, in [5], a clipping algorithm is proposed to reduce the PAPR in space time block coded (STBC) MIMO-OFDM system, while comparing the results to that of a SISO-OFDM system. However, the implications of in-band and out-band distortions that result from the clipping technique have not been considered. The PTS technique has been employed in [6,7,8] for PAPR reduction in an OFDM system by applying three different types of sub-block partitioning, and comparing their performances using complementary cumulative distribution function (CCDF) distribution curves. However, the simulations could not be precisely investigated as only 10 OFDM symbols have been used, resulting in non-accurate CCDF curves. Also, in [9], a robust PAPR reduction technique is proposed namely the active constellation extension (ACE) with implementation of Smart-Gradient Project which makes use of an iterative process to obtain an acceptable PAPR in STBC, Space Frequency Block Coding (SFBC), and Vertical-Bell Laboratories Layered Space-Time (V-BLAST) systems. Selective mapping (SLM) is also a convenient and promising method for PAPR reduction among OFDM signals [10]. Some recent improved techniques are mentioned in the next paragraph.
In [11], a modified artificial bee colony (ABC-PTS) algorithm is proposed. In the simulation, 16-QAM modulation with N = 256 sub-carriers were used. The PAPR reduction at a CCDF of 10 -3 of 4.65 dB was obtained by the ABC-PTS algorithm. An adaptive PTS method based on fuzzy neural network (FNN-APTS) is proposed in [12] and a PAPR reduction of 3.05 dB at CCDF of 10 -3 was reported with N = 128. A Continuous-Unconstrained Particle Swarm Optimization based PTS (CUPSO-PTS) technique for optimum phase rotation factors searching is presented in [13] and a PAPR reduction of 5 dB at a CCDF of 10 -3 was reported with N = 128. A novel Differential Evolution based Tone Reservation (DE-TR) scheme is proposed for the reduction of the PAPR with the use of an Optimized Iterative Clipping and Filtering (OICF) technique [14]. A PAPR reduction of 7 dB at a CCDF of 10 -3 was obtained with N = 256 and with QPSK modulation. A polarcoded orthogonal frequency-division multiplexing (OFDM) system with joint channel coding and PAPR reduction is proposed in [15]. For N = 64, and 64QAM, a PAPR reduction technique of approximately 4 dB at the CCDF of 10 −3 was obtained. A selected mapping (SLM) scheme based on a Polar coding technique for PAPR reduction in orthogonal frequency division multiplexing with index modulation (OFDM-IM) systems is proposed in [16]. A PAPR reduction of 6 dB at a CCDF of 10 -3 was reported with N = 128. In [17], a companding method using orthogonal frequency division multiplexing with offset quadrature amplitude modulation (OFDM/OQAM or OFDM/OQAM signal was used and a PAPR reduction of approximately 6.5 dB at a CCDF of 10 -3 was observed with N = 512. In [18], a novel clipping-based method established on the clipping noise compression (CNC) method and a PAPR reduction of 5.8 dB is observed with 64QAM and N = 256. The PAPR for the various techniques mentioned above is summarised in Table 1 with oversampling factor L = 4.
As mentioned earlier, the high PAPR is the most adverse aspect in the MIMO-OFDM system and is of serious concern. Although clipping is the simplest technique that can be used to alleviate problems of high PAPR, such a nonlinear process causes in-band signal distortion and out-of-band radiation. While in-band distortion directly causes a degradation in the BER at the receiver side, out-of-band radiation enforces adjacent channel interference. Moreover, spectral spreading is the key attribute of out-of-band radiation, and hence should be eliminated by the process of filtering the clipped signal [19,20,21]. However, in-band distortion affects the high-frequency components of the in-band signal because the signal is clipped directly into the discrete-time domain at the Nyquist sampling rate. This causes the aliasing phenomenon through which the high frequency component of the OFDM signal's spectrum actually inherits the low frequency identity of the sampled version of the spectrum. The motivation of this work is to propose an additional filtering scheme that has been assigned to the clipping algorithm so as to remove the high frequency components within the feasible regions (i.e. the constellation areas of the modulated symbols) and which can efficiently reduce the PAPR of OFDM signals. Principles from [22] scheme have been applied to our current system. Moreover, the algorithm developed in this work can be applied to the Massive MIMO system recently implemented in [23]. The paper investigates the CCDF for demonstration of the PAPR reduction scheme. Besides, for a better analysis of this technique, emphasis is placed on the CCDF comparisons under the same system while varying certain factors with respect to each approach. Hence, in line with the motivations of this paper, the aim of this paper is to evaluate the performance of MIMO-OFDM systems in determining the reduction of PAPR by assessing CCDF performances. Such analysis is done through adaptation of the following technique: Clipping, Hybrid Clipping and Filtering and compared with Partial Transmit Sequence (PTS), Selective mapping (SLM), active constellation extension (ACE) for PAPR reduction by computer simulation in Alamouti Coded MIMO-OFDM systems. The hybrid filtering scheme is also compared with some recent techniques.
The paper structure is as follows. The PAPR and the CCDF are defined in Sect. 2. Section 3 gives details on the methods used in the realisation of this research work. Section 4 provides a descriptive analysis of the results obtained while using various PAPR reduction techniques. Finally, Sect. 5 highlights the main findings of the study.

Definition of PAPR and Cumulative Distribution (CCDF)
The PAPR is generally defined as the ratio of the instantaneous maximum power in a given OFDM signal x(t) to the average signal power of that OFDM symbol in the MIMO-OFDM channel as represented below [24]: The PAPR characteristic can also be described in terms of its crest factor (CF) which defines its magnitude as: In the MIMO-OFDM system with N subcarriers, when all the N− subcarrier components are added with identical phases, maximum power occurs [25]. Assuming.
The resulting PAPR will be: whereby, the maximum power will be equivalent to N times the mean power. As such, the amplitude of the OFDM signal x(t) follows a Rayleigh distribution. From Eq. 3, it can be deduced that the PAPR n value will be independent and identically distributed (i.i.d) Rayleigh random variables z normalised with its own average power, and its probability density function (PDF) can be expressed as: whereby denotes the average (RMS) power and Let a maximum threshold value of PAPR be denoted by PAPR 0 (which is an analogy to the CF ), (i.e. PAPR 0 = maxPAPR n , n = 0, 1, … , N − 1).
Accordingly, the complementary cumulative distributive function (CCDF) of PAPR 0 is defined as: whereby, To find the probability that PAPR 0 exceeds z , the following CCDF is defined: Equations 7 and 8 are derived under the assumption that N is amply large and that the N samples are independent. Furthermore, the probability that PAPR n is above the threshold PAPR 0 is determined as follows:

Methods
The performance of the hybrid filtering algorithm is evaluated and compared with other algorithms such as the Partial Transmit Sequence (PTS), Selective mapping (SLM), active constellation extension (ACE) for PAPR reduction by computer simulation in Alamouti Coded MIMO-OFDM systems. MATLAB R2018a software was used to implement the systems.

Hybrid Clipping Filtering
Although clipping is the most basic technique for dealing with high PAPR issues, such a nonlinear process causes in-band signal distortion and out-of-band radiation. While in-band distortion directly affects the receiver's BER, out-of-band radiation causes adjacent channel interference. Furthermore, because spectral spreading is a key characteristic of out-of-band radiation, it should be eliminated during the clipped signal filtering process [19]. However, because the signal is clipped directly into the discrete-time domain at the Nyquist sampling rate, in-band distortion affects the high-frequency components of the in-band signal. This results in the aliasing phenomenon, in which the high frequency component of the spectrum of the OFDM signal actually inherits the low frequency identity of the sampled version of the spectrum.
The following steps are required to combat the effects of aliasing, prior to clipping, (i) The original signal is oversampled (sampled at a rate slightly exceeding the Nyquist rate), (ii) The signal is then processed using a longer IFFT length to reshape portion of the noise outside the signal band. After clipping, the oversampled signal is lastly filtered to eliminate the reshaped noise and out-of-band radiation, thus preserving the spectral efficiency as depicted in Fig. 1.
These techniques comprise of two methods. One possibility is to generate several permutations of the OFDM signal and send one with the least PAPR. Another method is to introduce a phase shift to alter the OFDM signal. MATLAB codes are implemented The transfer function coefficients of the 3rd-order lowpass digital Butterworth filter are computed with normalised cut-off frequency W n .
The clipped data x is filtered through a rational transfer function defined by the numerator coefficient c and denominator coefficient d . The flowchart shown in Fig. 2 summarises the overall process adopted by the hybrid clipping-filtering scheme in order to improve the clipping.

Multiple Signalling and Probabilistic Schemes
These techniques comprise of two methods. One possibility is to generate several permutations of the OFDM signal and send one with the least PAPR. Another method is to introduce a phase shift to alter the OFDM signal.

Selective Mapping (SLM)
SLM essentially generates multiple instances of the same OFDM symbol, followed by selecting the one with minimum PAPR [10].
Basically, the OFDM data-source block X consists of N subcarriers sequences: Furthermore, a set of U independent phase sequences P is generated, which has the same length N: The data source is multiplied with the phase vectors to produce U independent phaserotated candidate vectors XP (U) , denoted by X (U) , whereby After the multiplication process, each sequence undergoes an IFFT process, producing a block of several time-domain signals x (U) : Finally, the PAPR of the independent signals from the data block is compared and the candidate exhibiting the lowest PAPR, denoted by x ũ , is selected for transmission, as represented below: Figure 3 illustrates the block schematic of the SLM technique applied in Alamouti MIMO-OFDM system to reduce the PAPR.

Partial Transmit Sequence (PTS)
Unlike SLM where all the N subcarriers in the OFDM block are phase-rotated, the input data stream is split into M sub-blocks which are eventually phase-rotated in the PTS technique [7]. The input OFDM data block X consists of N subcarriers. Pseudo-random partitioning is applied to partition X into M disjoint sub-blocks X m for 0 ≤ m ≤ M − 1 such that The time-domain signal x is defined as follows: From Eq. (19) , x m is now cited as a partial transmit sequence. Furthermore, the key objective is finding the phase vector b m which provides best PAPR minimisation of the combined signal x.
Subsequently, the corresponding weighted transmitted signal with the minimum PAPR vector is expressed as:  Figure 4 shows the block diagram of PTS based Alamouti coded MIMO-OFDM system for PAPR reduction.

Scrambling Techniques (ACE)
This section provides a comprehensive description of all the procedures required for establishing Active Constellation Extension (ACE) technique, belonging to the category of scrambling techniques which work by changing the constellation points.
With ACE technology, the modulation constellation is pre-distorted or modified through the subcarriers of the OFDM block so that BER performance is not compromised. During the modification process, some modulation points are extended outside the constellation area. Traditionally, this is done in an iterative manner until the target PAPR is achieved, or the procedure is halted after a fixed number of iterations [9]. Nonetheless, the iterative approach is time-consuming and requires intensive FFT/IFFT computation, and hence a novel ACE scheme is proposed in this paper whereby subcarrier grouping along with convex optimisation techniques are applied using arguments from [22].
As shown in Fig. 5, the modulated time-domain signal x is obtained after the IFFT and the clipped-off portion signal c clip is removed from the clipped signal x such that (20) x == The clipped-off portion signal is defined as follows: The signal c clip is now subject to an FFT operation to yield the frequency domain clipped-off portion signal C clip defined as: Eventually, C clip is adjusted according to the ACE constraints which is given as Which gives rise to the vector C as follows: For n = 0, 1, … , N − 1 and with respect to the signal constellation, an outer point indicates a point lying on an unbounded detection region and the feasible region denotes the ( is an outer point 0; Otherwise

Fig. 5
Alamouti MIMO-OFDM system with ACE scheme region for a specific outer point contributing to a larger distance between the outer point itself to its nearest neighbouring outer points.
Furthermore, C is then extended into U non-overlapping sub-vectors to yield C u and masked by a partitioned set of subcarrier indices denoted by Γ u such that And, Subsequently, C u undergoes an IFFT operation to obtain the time-domain signal block c u given as: The transmitted signal is obtained as where the parameters a 0 , a 1 , ⋯ , a U−1 are real positive integers, put in such a way so as to achieve the minimum possible PAPR. Table 2 tabulates the main parameters used for simulation.

Clipping and Filtering
The CCDF performance curves for the clipped OFDM signals is simulated and plotted as shown in Fig. 6 in order to demonstrate and evaluate the impacts on PAPR and its reduction. It can be examined that the PAPR of the OFDM signals decreases significantly after clipping, and greater CR yields to greater PAPR reduction effect. As the CR increases, numerous parts of the OFDM signal are clipped directly, which gives rise to the shapes of the curves at various CRs.
Nonetheless, high CR results in the clipping noise falling in-band, and out-of-band radiation. The countermeasure for such impairment is the implementation of the hybrid clipping-filtering scheme as illustrated in Fig. 7.
It is observed that the addition of the filtering scheme decreases the PAPR more significantly, as compared to the first case where only clipping was used. This is due to the elimination of the reshaped noise and out-of-band radiation caused by clipping, and hence the PAPR effects get further reduced.

Selective Mapping
The CCDF of the PAPR for the original signal, as well as other signals obtained by varying the number of phase sequences U is investigated for the SLM model.
It can be noted from Fig. 8 that as the number of phase sequences increases from 2 to 16, there is a substantial reduction in PAPR. This is due to the fact that as U increases, it becomes more probable to obtain a signal with a very low PAPR that can be transmitted.

Partial Transmit Sequence
The last considered technique in the taxonomy of multiple signalling and probabilistic techniques is implemented, namely PTS, with the number of sub-blocks M set to 4.
Application of the peak power optimizer and transmitting the weighted signal with the lowest PAPR certainly improves the PAPR performance with number of sub-blocks M = 4 as shown in Fig. 9.

Active Constellation Extension
The ACE algorithm described is implemented. The number of sub-vectors U in the ACE technique is varied from 1 to 256.
The shapes of the plots obtained from Fig. 10 are similar to the work of Theodoros Tsiligkaridis and Douglas L. Jones, whereby an ACE-SGP STBC MIMO-OFDM algorithm has been employed which uses an iteration count to obtain an acceptable PAPR. Nonetheless, similar to the performance when increasing U to 256, it has been tested that further iterations provide nearly negligible performance increases.  Table 3 summarizes some of the PAPR reduction values achieved by each of the techniques.

• Both the Clipping and Hybrid Clipping-Filtering techniques show the highest values in
PAPR reduction compared to the other techniques. This is because the clipper works directly at limiting the signal envelope to the predefined clipping level in case the signal exceeds that level. Moreover, the hybrid scheme smoothened and reduced the overall peak power regrowth, and thus decreased the PAPR effect further and achieved the largest reduction value. • The SLM scheme showed the least reduction value in PAPR. The fact that this method is based on probable events of attaining minimum PAPR, the PAPR below a specified level cannot be guaranteed. Additionally, it may have taken the redundant bits (Side Information) into consideration during transmission which result in high peak signals.  • The PTS scheme showed better performance of PAPR reduction than SLM simply because the effect of distortions occurring in the signal and a loss of subcarrier orthogonality have been greatly suppressed through adoption of the peak value optimisation process and pseudo-random partitioning respectively. • A relatively lower value of PAPR decrease has been achieved using the ACE technique as compared to Clipping and PTS. Despite this strategy produced optimal rather than suboptimal results compared to its classical approaches, however, the method causes an increase in the average transmitted signal power. Furthermore, this technique may prove to have restricted relevance in case the modulation scheme has a large constellation size. Table 4 shows the PAPR reduction values for some recent works. The hybrid filtering technique is seen to perform better than the FNN-APTS technique [12]. It is slightly better PAPR reduction than the DE-TR technique with the same type of QPSK modulation and number of subcarriers. It is also slightly better than the SLM technique with polar coding. However, the type of modulation used is BPSK. The other techniques shown in the

Efficiency of Performance
The efficiency of performance for this technique is calculated using the following equation: Using Eq. (33) and the results from Tables 3 and 4, the efficiency of performance of the different algorithms are calculated and given in Table 5.
It can be observed from Table 5 that the hybrid clipping system proposed has a similar PAPR reduction efficiency to that of the DE-TR with QPSK modulation and N=256. The proposed system efficiency is also seen to be much higher than the PTS, SLM, ACE methods simulated and tested in this work.

Conclusion
Large PAPR of the OFDM systems has proved to be a genuine hindrance for implementation of transmitter power amplifiers since it is costly and power-inefficient for the PA systems to evade nonlinear amplification of considerable signal peaks. The primary technique used was clipping which reduced the PAPR through saturation of the overshooting signal amplitude to a predetermined value. However, such methods result in severe in-band distortion and out-of-band noise. These are removed by implementing a hybrid clipping-filtering scheme to oversample and filter the clipped signal. The clipper works directly at limiting the signal envelope to the predefined clipping level in case the signal exceeds that level but the hybrid scheme smoothened and reduced the (33) Ef f iciency = 1 − PAPR new PAPR original × 100%

Further Works
The PAPR reduction can be compared with other approaches for PAPR reduction such as Tone Injection, Tone Reservation, Peak Windowing, Peak Cancellation and Artificial Bee Colony Algorithm among others, that deserve further investigations on various types of channels. Also, the BER performance and computational complexity of the system proposed could be investigated and compared with some recent techniques. Likewise, nowadays with the ongoing evolution of 5G, the performance of these PAPR reduction strategies should be analysed over massive MIMO systems in high-mobility environments.

Author Contributions
We confirm that we have contributed to the entire work carried out in this paper and we will be available to provide the software application and custom code.
Funding We wish to confirm that this research work carried out did not receive any funding from any institution.

Data Availability
We also confirm that this research work contains transparent available data and materials.

Conflict of interest
We wish to confirm that there are no known conflicts of interest associated with this publication and there has been no financial support for this work that could have influenced its outcome. FNN-APTS (QPSK) [12] 36.7 CUPSO-PTS [13] 49 DE-TR (QPSK) [14] 62.5 Polar coded OFDM [15] 40 Novel selected mapping (SLM) scheme based on a Polar coding technique [16] 48 Companding OFDM/OQAM [17] 58 Clipping noise compression (CNC) method [18] 50.9 PTS 43.5 ACE 33.9 SLM 31.9 Clipping 50.8 Hybrid clipping 62.5 Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.