1. Introduction
Coordinated multipoint (CoMP) techniques reduce intercell interference and increase the cell-edge throughput by integrating numerous evolved node base stations’ (eNBs) transmissions. Specifically, the CoMP methodology involves joint transmission (JT), dynamic point selection (DPS), coordinated scheduling (CS), and coordinated beamforming (CB). Additionally, CoMP can be used on homogeneous as well as heterogeneous networks. In densely deployed small-cells, the CoMP with CS method is applied to maximize the radio network’s ability within the macrocell region covered by the macro eNB [
1,
2,
3], as portrayed in
Figure 1. Besides, diversity and interference suppression are also associated with CoMP [
4]. To accomplish the features of the future generation wireless communication systems, such as speedy data rate with outstanding link quality and unlimited access, priority is being given to the implementation of CoMP ultra-dense, small-cell network (SCN)-based transmission, where SCN allows the additional flexible establishment and excellent communication link quality.
To achieve better throughput and vigorous mobility, the dual connectivity (DC) technique is presented in 3rd generation partnership project (3GPP) release 12 by utilizing radio resources from different eNBs. In comparison with release-11 carrier aggregation (CA), DC is an effective technique introducing standalone secondary eNB (SeNB) for small-cell deployment. For the case of DC-associated UE, it can establish concurrent connections with a master eNB (MeNB) and SeNB. Usually, both eNBs operate at different carrier frequencies and maintain an interconnection using general backhaul links [
5,
6].
Proper advancements in long-term evolution (LTE), LTE-Advanced, and LTE-Advanced Pro technology have already allowed the commercial deployment of the 5G new radio (NR) networks [
7,
8]. The utilization of centimeter wave (cmWave) as well as millimeter wave (mmWave) radio frequencies, are observed in both high-bandwidth and low-bandwidth transmissions (3.4 to 3.6 GHz below 6 GHz and then 24.25 to 27.5 GHz, 27.5 to 29.5 GHz, 37 GHz, 39 GHz, and 57 to 71 GHz) [
9]. With the help of both frequency division duplexing (FDD) and time division duplexing (TDD) techniques, the multiple access schemes use cyclic prefixed orthogonal frequency division multiplexing (OFDM) in downlink and cyclic prefixed discrete Fourier transform-spread-OFDM (DFT-s-OFDM) in uplink transmission for the NR physical layer [
10]. In addition, multiple OFDM-scalable numerologies are supported in 5G NR with various subcarrier spacings (15 KHz, 30 KHz, 60 KHz, 120 KHz, and 240 KHz) and utilization of both low- and higher-order digital modulations (256-QAM, 64-QAM, 16-QAM, QPSK, BPSK, and
-BPSK modulation) [
11]. In general, the use of CP in OFDM is the most popular way to suppress intersymbol interference (ISI); however, its waste of spectrum resources cannot be neglected when considering the ever-growing high-speed demand [
12].
1.1. Related Works
Several studies on signal detection and channel estimation in CP-free OFDM systems and massive multiple-input multiple-output (MIMO) have been reported in the literature. The authors in [
13] used single bit analog-to-digital converters (ADCs) for both single-input single-output (SISO) and MIMO systems in frequency selective channel to accurately obtain the maximum likelihood sequence estimation channel equalizer in mmWave massive MIMO (mMIMO) communications. Their observations revealed that the acute nonlinear distortion of single bit ADCs can be successfully nullified using an adequate number of receive antennas. The authors in [
14] formulate such a repetitive receiver for an mMIMO system that utilizes Bayesian theory as well as a strategy for the neutralization of parallel intrusion. The consequence of their work proves that the performance of the minimum mean square error (MMSE) signal detection technique was not satisfying in terms of bit error rate (BER) and latency processing performances.
The comprehensive study in [
15] proposed a system with a virtual carrier using the MIMO–OFDM concept to identify proper the repetition index scheme-oriented subspace channel. Such a study was carried out for the conversion of the white noise into nonwhite noise using the repetition index scheme as well as the conversion of nonwhite noise back to white noise using Cholesky factorization. The numerical simulation shows the superiority of the repetition index scheme-oriented channel identification over other compared methods. Another study in [
16] introduced a reservoir computing structure for MIMO–OFDM symbol detection, known as a windowed echo state network (WESN). Their numerical evaluations propose that only a certain number of training symbols can be utilized for the effective reduction of model mismatch and improvement in symbol identification performance by WESN. The authors in [
17] proposed two neural networks, one for channel estimation and another one for signal detection. Both the networks are associated with a CP-free OFDM system utilizing a novel artificial intelligence (AI)-supported receiver. Such a receiver provided low complexity and significant robustness over the existing algorithms. In [
18], authors explored a model-driven neural network for CP-free MIMO–OFDM data detection.
The authors in [
19] investigated the linear MMSE channel estimator for CP-free single carrier MIMO (SC-MIMO) under frequency-selective channel and also proposed a new iterative receiver for quantized CP-free uplink wideband SC-MIMO for uncorrelated or correlated Rayleigh and Rician fading channels. In [
20], authors proposed a generalized sidelobe canceller equalizer using QR decomposition for CP-Free MIMO–OFDM systems and also reduced the complexity of maximum likelihood detection. Another study [
21] proposed a CP-free MIMO generalized frequency division multiplexing system for high data rate transmission in frequency selective fading channels. A brief summary of these works is illustrated in
Table 1.
Despite the limited number of researches and applications, there are many challenges in CP-free multiuser OFDM communication systems. Due to the multiuser interference, the performance of CP-free multiuser OFDM is quite limited. Thus, the CoMP-JT transmission method and complex Hadamard transform (CHT) with block diagonalization (BD) channel precoding are very important. The CHT codes are orthogonal spreading codes whose applications are very much effective in reducing user’s interfering signals. It is known from the literature that the Hadamard matrices have been considered as a very promising tool and are applicable in MIMO systems, due to its simple and efficient implementation with the use of fast algorithm [
22]. The computational complexity is
for an
N-point CHT matrix [
23]. Besides, BD is a well-known linear precoding scheme that usually provides good performance. In this study, CHT technique is introduced with the help of the Hadamard matrix in addition to BD precoding for multiuser interference (MUI) reduction.
Moreover, to the best of authors’ knowledge, the CP-free multiuser OFDM system utilizing the CoMP-JT transmission method has not been well investigated.
1.2. Contribution and Organization
The major concern of this paper lies in developing a novel framework for a CP-free multiuser OFDM system utilizing the CoMP-JT transmission method at mmWave. The main contributions of this paper are outlined below:
Proposed CHT with BD channel precoding to reduce multiuser interference in the CP-free multiuser OFDM system.
Properly designed subcarrier mapping for out-of-band (OOB) reduction and input back-off (IBO)-aided high-power amplifier (HPA) for the peak-to-average power ratio (PAPR) reduction are also carried out in this work for cell-edge users at mmWave frequency.
Conducted a numerical study to evaluate the BER, PAPR, and ergodic achievable rate performance of the proposed system. The proposed system also ratifies the effectiveness in terms of BER, PAPR, and ergodic achievable rate.
The rest of this paper is organized as follows. In
Section 2, the system model including network description, block diagram, and signal model are introduced. In
Section 3, simulation results and discussions are described. A brief discussion on concluding remarks and future challenges in
Section 4 ends the paper.
3. Simulation Results
In this section, a MATLAB-based simulation is conducted to evaluate the system performance in terms of BER, PAPR, and PSD. Different types of channel coding and ZF signal detection technique on the performance of CoMP-JT-based downlink mmWave CP-free multiuser OFDM wireless communication systems has been properly investigated. It is verified from [
34] that federal communications commission (FCC) rules allowed a 5G BS operating in the millimeter range to emit an effective radiated power (ERP) of up to 30,000 W; further, one of the leading telecommunications equipment company, Huawei, is supporting an antenna port ERP of 65 dBm for their mmWave products [
35]. In this simulation study, a transmission power of 5000 W (66.9897 dBm) is considered. Additionally, the current study is carried out with the speculation that the channel state information (CSI) of the mmWave path loss incorporated MIMO Rayleigh fading channel is easily accessible from the receiver and the nature of the flat fading channel coefficients is unaltered during the period of simulation. To understand the work in a better way, it is represented in a concise form using a flow-chart in
Figure 4.
The suggested framework is simulated to derive the system performance by considering the parameters in
Table 2. Before presenting simulated results for BER, PAPR, and PSD, a comprehensive idea can be obtained from
Table 3 on estimated signal power at both the BS and user end.
The presented BER simulation results in
Figure 5,
Figure 6,
Figure 7 and
Figure 8 show the impact of implementing various channel coding under two higher-order digital modulation schemes (16-QAM and 16-PSK) and the ZF signal detection techniques on system performance for each of the four users. In all cases, the simulated CoMP-JT-based downlink mmWave CP-free multiuser OFDM wireless communication system shows improved performance in the case of 16-QAM compared with 16-PSK.
It is clearly visible in
Figure 5 for user 1 that the system shows better response under the repeat and accumulate (RA) channel coding technique and worst response under the Quasi LDPC channel coding technique in both 16-QAM and 16-PSK higher-order digital modulation techniques. It is observable that the evaluated BER values are 0.0439, 0.002, and 0.3071 in the case of (3,2) SPA, RA, and Quasi LDPC channel coding techniques under 16-QAM, respectively, for a customarily accepted SNR value of −5 dB. At this sort of customarily considered SNR value, the performance of the system using RA channel coding is improved by 13.414 dB and 21.862 dB in comparison with (3,2) SPA and Quasi LDPC channel coding techniques for 16-QAM. In the case of 16-PSK digital modulation, the overall performance of the RA channel coding technique is much better compared with other utilized channel coding techniques. However, a critical observation of the system under 16-PSK depicts that the BER values for (3,2) SPA and RA channel coding techniques are almost identical at 0 dB SNR value.
Figure 6 is for user 2, where it is seen that the estimated BERs under 16-QAM are found to have values of 0.0572, 0.0117, and 0.3394 in the cases of (3,2) SPA, RA, and Quasi LDPC channel coding techniques, respectively, with identical consideration of the SNR value. All these are pointing towards improved performance of the system by 6.892 dB and 14.625 dB in RA compared with (3,2) SPA and Quasi LDPC channel coding techniques. With 16-PSK, it is observable that the BER values evaluated for the case of (3,2) SPA, RA, and Quasi LDPC channel coding techniques are 0.0786, 0.0320, and 0.1960, respectively, which confirms an improvement in the performance of the system by 3.903 dB and 7.871 dB in RA compared with (3,2) SPA and Quasi LDPC channel coding techniques.
Figure 7 is for user 3 and in such case, the system provides significant BER performance compared with other implemented channel coding techniques. The evaluated values representing BER are 0.1153, 0.0001, and 0.4146 in the cases of (3,2) SPA, RA, and the Quasi LDPC channel coding techniques under 16-QAM, respectively, at a customarily accepted SNR value of −6 dB, which signifies the improvement in system performance by 30.618 dB and 36.176 dB in RA compared with (3,2) SPA and Quasi LDPC channel coding techniques. In the case of 16-PSK, overall system performance utilizing the RA channel coding technique provides better BER performance compared with the other two techniques. Over a significant range of higher SNR values, the system performance with (3,2) SPA and RA channel coding techniques are not well discriminated. At a customarily accepted SNR value of −5 dB, the evaluated values representing BER are 0.1716, 0.1597, and 0.3687 for the cases of (3,2) SPA, RA, and Quasi LDPC channel coding techniques, respectively, which confirm an insignificant improvement of 0.312 dB and significant improvement of 3.634 dB in RA compared with (3,2) SPA and Quasi LDPC channel coding techniques.
Figure 8 presents characteristic features of the system for user 4. As the transmitter–receiver distance from BS 1 in the case of user 4 is comparatively higher, the signal attenuation in mmWave transmission has an impact on BER performance. With the SNR value observed earlier, the estimated values representing BER under 16-QAM are 0.0679, 0.0083, and 0.4640 for (3,2) SPA, RA, and Quasi LDPC channel coding techniques, respectively. For this case, improvement in the performance of the system by 9.128 dB and 17.474 dB are achieved in RA compared with (3,2) SPA and Quasi LDPC channel coding techniques. In the case of 16-PSK with an identical SNR value (−5 dB), the evaluated values corresponding to BER are 0.1194, 0.0730, and 0.3603 for (3,2) SPA, RA, and Quasi LDPC channel coding techniques, respectively, which confirm an improvement in system performance by 2.137 dB and 6.933 dB in RA compared with (3,2) SPA and Quasi LDPC channel coding techniques.
It is observable from
Figure 9 that under a scenario of transmitted power from a single BS, the estimated average minimum and maximum SINR values for user 1 through user 4 are 7.5464 dB and 17.5464 dB, 8.4224 dB and 18.4224 dB, −1.4506 dB and 8.5494 dB, and −3.5121 dB and 6.4879 dB, respectively. In
Figure 10, estimated ergodic achievable rate values are presented in the absence of CoMP-JT-based mmWave signal transmission and show that the estimated average received minimum and maximum ergodic achievable rate values for user 1 through user 4 are 2.7407 bps/Hz and 5.854 bps/Hz, 2.9917 bps/Hz and 6.1404 bps/Hz, 0.7791 bps/Hz and 3.0287 bps/Hz, and 0.5315 bps/Hz and 2.4474 bps/Hz, respectively.
It is noticeable from
Figure 11 that under a scenario of identical transmitted power from both BSs, the estimated average received minimum and maximum SINR values for user 1 through user 4 are 8.8834 dB and 18.8834 dB, 8.3532 dB and 18.3532 dB, 7.5883 dB and 17.5883 dB, and −0.2019 dB and 9.7981 dB, respectively. In
Figure 12, estimated ergodic achievable rate values are presented under a scenario of identical transmitted power from both BSs and it shows that the estimated average received minimum and maximum ergodic achievable rate values for user 1 through user 4 are 3.126 bps/Hz and 6.2915 bps/Hz, 2.9716 bps/Hz and 6.1177 bps/Hz, 2.7525 bps/Hz and 5.8676 bps/Hz, and 0.9669 bps/Hz and 3.3986 bps/Hz, respectively.
By analyzing estimated values in
Figure 9,
Figure 10,
Figure 11 and
Figure 12, it is quite obvious that the implementation of CoMP-JT-based mmWave signal transmission improves both SINR and ergodic achievable rate.
Complementary cumulative distribution functions (CCDFs) of PAPR for our proposed system with utilization of higher-order 16-QAM digital modulation are presented in
Figure 13 and
Figure 14. There is a clear illustration estimating that values of PAPR relative to their respective threshold values are greater in the case of the system without a PAPR reduction scheme using IBO-aided HPA. The probability of the output signals in different channels of BS 1 is
with PAPR greater than the threshold ranges from 12.5 dB to 15 dB. In such a case for
CCDF of PAPR, the output signals of all the channels are found to have almost identical 4 dB PAPR values. It is obvious from
Figure 13 that in the case of
CCDF of PAPR with the application of IBO-based HPA, the output signal of the typically assumed first channel has PAPR (greater than the threshold) values of 3.0 dB, 2.2 dB, 1.5 dB, and 0 dB in the cases of 0 dB, 4 dB, 8 dB, and 12 dB IBO values. The probability of the output signals at different channels of BS 2 is
with PAPR greater than the threshold ranges from 12.2 dB to 15.9 dB. In such a case, for
CCDF of PAPR, the output signals of all the channels are found to have almost identical 4 dB PAPR values. It is quite obvious from
Figure 14 that in case of
CCDF of PAPR with the application of IBO-based HPA, the output signal of the typically assumed first channel has PAPR (greater than the threshold) values of 2.9 dB, 2.0 dB, 1.5 dB, and 0 dB in the cases of 0 dB, 4 dB, 8 dB, and 12 dB IBO values.
In
Figure 15, the estimated ergodic achievable rate for randomly distributed users over the study area of 2000 m
is presented both in a two-dimensional surface and three-dimensional contour plots (
Figure 15a,b). The maximum and minimum values of the ergodic achievable rate are found to have values of 5.9635 bps/Hz and 0.1893 bps/Hz, respectively. In most parts of the studied area, the estimated average ergodic achievable rate is 3.2652 bps/Hz.
From
Figure 16, it is observable that at a comparatively low base station antenna height, the estimated ergodic achievable rate values are increased in comparison with the scenario of base station antenna height. At the central location, 100 m away from the BS1, the estimated ergodic achievable rate with a transmission power of 500 W is found to have values of 0.6572 bps/Hz and 1.6679 bps/Hz in the cases of high and low base station antenna height. On the other hand, with a high transmission power of 5000 W, the estimated values of achievable ergodic are 2.7487 bps/Hz and 3.9008 bps/Hz for high and low base station antenna height.
The results in
Figure 17 clearly indicate that an acceptable OOB reduction is achieved under 16-QAM higher-order digital modulation, RA channel coding, and CHT schemes. The OOB power reduction of 311.99 dB, 312.40 dB, 312.67 dB, and 312.34 dB are achieved in the cases of user 1, user 2, user 3, and user 4, respectively.
From
Table 4, it is observable that a significant amount of PAPR reduction occurs with the application of IBO-based HPA. The estimated values of PAPR for different transmitting channels of serving BSs and IBO values under consideration of nonlinear HPA are shown in
Figure 18. It is quite obvious from the figure that the PAPR performance of the system improves with low values of IBO.
By observing the nature of BER curves shown in
Figure 19,
Figure 20,
Figure 21 and
Figure 22, it can be clearly understood that the implementation of comparatively higher IBO produces an improvement of BER performance. To meet up a typically assumed BER of
, −2.5 dB and 4 dB SNR are required for a linear amplifier and 12 dB IBO with HPA, respectively, in the case of user 1, as shown in
Figure 19. In the case of user 2, for the same BER of
, −1.7 dB and 3.8 dB SNR are required for linear amplifier and 12 dB IBO with HPA, respectively, as depicted in
Figure 20. For user 3 in
Figure 21, the SNR requirement is found to have values of −2.2 dB and 4.2 dB. In comparison with the systems without IBO-based HPA linearity, the BER performance in the case of user 4 for different values of IBO is moderate, as shown in
Figure 22.
The authors in [
36] made a comparative study on the suitability of a Walsh–Hadamard transformed (WHT) universal-filtered multicarrier (UFMC) system with classical OFDM and UFMC systems in terms of BER and SNR performance. The authors in [
37] established improved performance of a double-tree complex wavelet transform (DTCWT)-based OFDM system in combination with the fast WHT (FWHT) and eliminated the drawbacks of the OFDM system. In [
38], authors recommended a zero tail inverse lifting wavelet transform spread FWHT OFDM (ZT-ILWTs FWHT OFDM) system as an alternative to the conventional OFDM and presented better performance of their proposed system in terms of BER, PAPR, and OOB emission. In
Figure 23, a comparative analysis has been illustrated in terms of BER against SNR between our proposed CoMP-JT-based mmWave CP-free multiuser OFDM system, WHT UFMC/fast WHTs and DTCWT-based OFDM, and ZT-ILWTs FWHT OFDM multicarrier signaling technique implemented systems. For a better view of the obtained values,
Table 5 is also added. Under the scenario of systems without any channel coding scheme, the presented numerical results of our proposed uncoded system for a typically assumed case of user 1 is reasonably acceptable in comparison with the works of the other systems for BPSK, QAM, and 16-QAM digital modulations.