Virtual Multiple-input Multiple-output Research Articles

Path Loss and Auxiliary Communication Analysis of VANET in Tunnel Environments

Vehicular ad hoc network (VANET) communications face severe fading problems due to the signal reflections and diffractions within tunnels. Unlike the open road, the space of a tunnel is very limited, so VANET communication performance in a tunnel is seriously affected. In the process of signal transmission, the reflected signal is symmetrical with the incident signal after it is reflected by the road and the wall. In this paper, we establish a mathematical model of path loss for V2V (Vehicle-to-Vehicle) communication based on the principle of signal reflection symmetry in tunnels and considering several factors, such as the tunnel surface and the color of the tunnel wall. In addition, we use cooperative communication to form a virtual multiple-input multiple-output (V-MIMO) system, to improve the communication quality in tunnels. In the proposed system, the OBU (On-Board-unit) and RSU (Road-Side-Unit) share each other’s antennas, so that wireless cooperative communication can be employed, without increasing the number of antennas in a one-way tunnel. Therefore, this multipath fading internal electromagnetic wave propagation model can be used to improve performance. A deep reinforcement learning algorithm was used to solve the pairing problem to obtain a more accurate OBU and RSU pair, to form a V-MIMO system. Here, the RSU is regarded as an agent and interacts with the OBU in the tunnel. The optimal strategy was learned in a real-time changing simulation environment, and the experiment verified the convergence of the algorithm. The simulation results showed that, compared with the Q-learning based scheme, the optimal matching algorithm based on V-MIMO and a DQN (Deep Q-network) could effectively reduce the probability of transmission outages and improve the communication efficiency in tunnels.

Adaptive LDPC coded high data rate based IR-UWB combined with VMIMO system for vehicular communication links

The automotive industry is developing significantly with the evolution of vehicular networks, intelligent transportation systems, and autonomous cars. These technologies are made achievable by recent advances in software, hardware, and communication systems, along with various applications and standardization efforts. On the other side, many impairments have existed due to these evolving, limiting the process of vehicular networks. So, this paper proposes an implementation of adaptive LDPC-coded, high data rate-based Impulse Radio-Ultra Wide Band (IR-UWB) combined with Virtual Multiple Input Multiple Output (VMIMO) systems for Vehicle-to-Vehicle (V2V) and Vehicle-to-Infrastructure (V2I) wireless communications. Furthermore, they are merged with orthogonal pulse shaping using a modified Hermite pulse. Besides, the paper compares Zero-Forcing (ZF) and Minimum Mean Square Error (MMSE) detection techniques. To enhance and mitigate the existing impairments facing the vehicular networks. The proposed system’s performance is evaluated using both techniques, utilizing Bit Error Rate (BER), processing time, and resultant throughput analysis for both channel models. The simulation results include Non-Line of Sight (NLoS) and Line of Sight (LoS) scenarios for both channel models. Moreover, the simulation considers the effect of path loss and noise on the transmitted signal. In addition, the recent LDPC decoding algorithm termed “Modified Implementation Efficient Reliability Ratio Weighted Bit Flipping” (MIERRWBF) is evaluated through all latter channel models. At last, a novel adaptive LDPC decoder is proposed to further enhance the performance of all vehicular communication links under study. Consequently, the paper proposed an integrated adaptive LDPC-coded high data rate communication system to enhance vehicular communications using VMIMO mixed with modified Hermite orthogonal pulse shaping and deploying the MMSE recommended detection technique.

Configurable virtual MIMO via UAV swarm: Channel modeling and spatial correlation analysis

Air-to-ground wireless channel modeling for unmanned aerial vehicle (UAV) communications has been widely studied. However, channel modeling for UAV swarm-enabled cooperative communication still needs investigation, where the impact of UAV positions on the spatial channel characteristics is of particular importance. In this paper, we consider a UAV swarm-enabled virtual multiple input multiple output (MIMO) system, where multiple single-antenna UAVs cooperatively transmit to multiple ground users (GUs). We establish a common coordinate system, as well as a UAV swarm-oriented coordinate system, to describe the relative positions of the GUs and the UAV elements, respectively. Based on the established coordinate systems, geometric ray superposition method is applied to describe the spatial channel matrix. The proposed modeling framework can be directly used to describe the line-of-sight and two-ray propagations, and can be extended for including more practical spatial features such as multipath scattering, inter-UAV blockage, and random UAV jittering, etc. Based on the proposed model, we further analyze the spatial correlation among the virtual MIMO links of GUs located at different positions. Via extensive simulations, we show that thanks to the flexible deployment of UAVs, the virtual MIMO array structure can be conveniently configured to get desired channel properties, such as the channel capacity, eigenvalue and condition number distribution, and spatial correlation distribution. This shows the possibility and importance of exploiting a new design dimension, i.e., the UAV swarm pattern, in such cooperative virtual MIMO systems.

Cross layer design with extensive virtual MIMO: FS-MUP optimization model for wireless sensor network

In the wireless sensor network (WSN), wireless communication is said to be the dominant power-consuming operation and it is a challenging one. Virtual Multiple-Input–Multiple-Output (V-MIMO) technology is considered to be the energy-saving method in the WSN. In this paper, a novel multihop virtual MIMO communication protocol is designed in the WSN via cross-layer design to enhance the energy efficiency, reliability, and end-to-end (ETE) and Quality of Service (QoS) provisioning. On the basis of the proposed protocol, the optimal set of parameters concerning the transmission and the overall consumed energy by each of the packets is found. Furthermore, the modeling of ETE latency and throughput of the protocol takes place with respect to the bit-error-rate (BER). A novel hybrid optimization algorithm referred as Flight Straight Moth Updated Particle Swarm Optimization (FS-MUP) is introduced to find the optimal BER that meets the QoS, ETE requirements of each link with lower power consumption. Finally, the performance of the proposed model is evaluated over the extant models in terms of Energy Consumption and BER as well.

Secrecy Rate Maximization in Virtual-MIMO Enabled SWIPT for 5G Centric IoT Applications

In 5G centric sensors-enabled Internet of Things (IoT) applications, virtual multiple-input multiple-output (V-MIMO) technique has witnessed significant attention as physical layer security enabler. In IoT, physical layer security is potential due to the vulnerability of wireless broadcasting in low computation capability and limited power source of the sensor nodes. In this regard, this article presents a secure and energy efficient V-MIMO enabled simultaneous wireless information and power transfer framework. The security framework uses beamforming and cooperative jamming signal to maximize the secrecy rate of the IoT systems. An optimization problem is formulated by collectively optimizing the beamforming vector, power splitting ratio, and time switching ratio. Since the maximization problem is nonconvex, to find solution of the problem an iterative algorithm is presented, which inherently uses the penalty function to find the solution. It is evident from simulation results that the secrecy rate optimization of the proposed framework is better as compared to the state-of-the-art techniques considering various metrics.

Max-gain relay selection scheme for wireless networks

Next generation wireless systems are supposed to handle high amount of data with broader coverage and high quality of service (QoS). When a signal travels from a source to destination, the signal quality may suffer from the fading, which makes it difficult to receive correct messages. To handle the impact of fading, various diversity techniques are performed with Multiple Input Multiple Output (MIMO). Considering cooperative wireless networks, virtual MIMOs are being used, which also called cooperative diversity. In this paper, we propose a max-gain relay selection scheme (MGRS) for buffer-aided wireless cooperative networks. This scheme determines the best link using the maximum gain based on quality of link and available buffer size. The time slot is divided into two parts, one is used to choose the best link from the source to relay transmission (odd slot) and another time slot (even) is used based on the selection of the best link from the relay to destination. Markov chain model is use to measure buffer status and QoS parameters to evaluate the performance. The proposed scheme provides better QoS (12%) compared to the existing relay selection schemes with respect to throughput, end-to-end delay and outage probability.

Energy efficient wireless sensor network using optimum hops and virtual MIMO technique

The virtual multiple-input multiple-output (V-MIMO) configuration provide the reliable broadband wireless communication that raises the data rate and reduce the energy consumption, for long range communication in the wireless sensor network (WSN). Generally in the WSN, the source node does not have sufficient power and transmission range to transmit data packets directly to the sink node. Therefore, the multihop technique is necessary to transmit data from source node to sink node. In this paper, multihop V-MIMO technique is used for long range communication in the WSN. In this technique, the source-to-sink route divides into many optimum hops, following which the 2 × 2 V-MIMO technique is applied to all the hops. The simulation results show that for long range communication, the multihop MIMO technique provides better energy saving than the MIMO technique or multihop single-input single-output (SISO) technique in a WSN, while satisfying the throughput and delay. The paper also presents the effect of path loss exponent on energy consumption. The simulation results clearly indicate that the energy consumption increases with an increase in the path loss exponent in the SISO, MIMO, single and multihop communication techniques. The result reveals that the network reliability is inversely proportional to the number of hops.

Zero-Forcing-Based Downlink Virtual MIMO–NOMA Communications in IoT Networks

To support massive connectivity and boost spectral efficiency for Internet of Things (IoT), a downlink scheme combining virtual multiple-input–multiple-output (MIMO) and nonorthogonal multiple access (NOMA) is proposed. All the single-antenna IoT devices in each cluster cooperate with each other to establish a virtual MIMO entity, and multiple independent data streams are requested by each cluster. NOMA is employed to superimpose all the requested data streams, and each cluster leverages zero-forcing detection to demultiplex the input data streams. Only statistical channel state information (CSI) is available at the base station to avoid the waste of the energy and bandwidth on frequent CSI estimations. The outage probability and goodput of the virtual MIMO–NOMA system are thoroughly investigated by considering the Kronecker model, which embraces both the transmit and receive correlations. Furthermore, the asymptotic results facilitate not only the exploration of physical insights but also the goodput maximization. In particular, the asymptotic outage expressions provide quantitative impacts of various system parameters and enable the investigation of diversity–multiplexing tradeoff (DMT). Moreover, power allocation coefficients and/or transmission rates can be properly chosen to achieve the maximal goodput. By favor of the Karush–Kuhn–Tucker conditions, the goodput maximization problems can be solved in closed form, with which the joint power and rate selection is realized by using alternately iterating optimization. Besides, the optimization algorithms tend to allocate more power to clusters under unfavorable channel conditions and support clusters with a higher transmission rate under benign channel conditions.

MIMO-OFDM in a Cooperative Frequency Selective Fading Channel: An Analysis

Diversity is an integral technique in the advancement of wireless communications. Multiple-input multiple-output (MIMO) technology continues to occupy a pivotal position in the fourth-generation (4G) standards and beyond. With the advent of full-dimension (FD) MIMO and massive MIMO, new paradigms are being targeted in the disruptive technology. Third-generation partnership project (3GPP) has also emphasized the advanced MIMO technology for achieving its vision of International Mobile Telephony (IMT) 2020. However, implementing multiple antennas can be cumbersome due to limiting factors such as size, cost, and hardware limitations. In such a scenario, where implementing many antennas is not feasible, the benefits of diversity can be reaped by employing cooperative communication. Single antenna mobiles can share their mobile stations giving rise to a virtual MIMO system. In this paper, the authors have analyzed the performance of cooperative mobile stations in a frequency selective channel. Orthogonal frequency division multiplexing (OFDM), known for its robustness against multipath fading, is the modulation technique employed to circumvent the hazardous effects of intersymbol interference (ISI). MIMO is the key technology for achieving capacity advantage and improving link reliability. The blend of these two cutting edge technologies in a cooperative relay system presents encouraging results and inferences. Maximal Ratio Combining (MRC) is employed at the relay and the receiver to maximize the signal-to-noise ratio (SNR). Decode and forward (DF) protocol is used at the relay node owing to its regenerative nature and adaptability. The closed-form expressions for bit error rate (BER) and outage probability (Pout) are derived and compared with the experimental results. The effect of power decay factor is analyzed and simulation is done for 2 × 2, 2 × 3, and 2 × 4 transmit and receive antennas. The number of antennas at the relay is kept as 2. The analytical results agree with the simulation results.

Virtual MIMO Wireless Sensor Networks: Propagation Measurements and Fusion Performance

In this paper, we investigate the practical implications of employing virtual multiple-input multiple-output (MIMO) systems for prototyping future-generation wireless sensor networks (WSNs), especially in the light of recently proposed distributed detection based decision fusion (DF) rules. In order to do that, an indoor-to-outdoor measurement campaign has been conducted recently for investigating the propagation characteristics of an $8 \times 8$ virtual MIMO system. The campaign is conducted with transmit antennas representing the sensors deployed in different indoor environments and receiver antennas mounted on an outside tower representing the DF center. Channel measurements are reported when a 20 MHz wide signal is transmitted at 2.53 GHz. Measurements are collected for different spatial combinations of the transmit antennas. After analyzing the collected data, the performance of different DF rules is compared and tested over the measured channel. The results show that the fusion rules perform differently over different sets of measured channels. The results obtained here are important for maximizing performance and enabling the air-interface design of next-generation WSNs.

A windowing-based joint user pairing and resource allocation algorithm for V-MIMO systems

In this paper, we investigate the user pairing and resource allocation (UP-RA) problem which is a critical step in uplink virtual multiple input multiple output (V-MIMO) systems. It becomes a joint problem under the framework of Long Term Evolution (LTE) where single carrier frequency division multiple access (SC-FDMA) is adopted in uplink due to the intrinsic consecutive resource allocation constraint imposed therein. Traditional two-step algorithms tackle this joint problem by separating the UP step and the RA step and turning them into two independent and successive procedures. Different from them, in this paper a windowing-based UP-RA algorithm is developed in which the user pairs are selected by maximizing their performance on a series of contiguous RBs rather than a single one as discussed in those traditional algorithms. With the windowing technique introduced in the new algorithm heuristically, improved performance in uplink V-MIMO systems can be achieved. In addition, we provide the relationship between the performance and the window size, and present that the window size can be selected adaptively to further exploit the diversity gain. Furthermore, to corroborate the universal validity of the proposed windowing technique, another algorithm named pairing and extension (P&E) is also modified accordingly by it. Corresponding simulation results manifest the great potential of the windowing technique to be applied to other general two-step algorithms in V-MIMO systems and improve their performances.

Joint VMIMO and LDPC Decoders for IR-UWB Wireless Body Area Network

A complete impulse radio-ultra wide band (IR-UWB) system is proposed to mitigate the impairments concerning on-body to off-body Wireless Body Area Networks (WBAN). The proposed system maintains the practical communication link between on-body sensors to the fusion center or the monitoring device held by the medical representative. Also, these sensors are assigned a recently proposed pulse shaping to mitigate the noise that existed in the IR-UWB WBAN channel. Furthermore, virtual multiple-input multiple-output (VMIMO) is proposed to perform spatial multiplexing between various sensors transmitted data. Moreover, low complex low density parity check (LDPC) encoding/decoding algorithms, including a new low complex hybrid LDPC decoding algorithm, are proposed to reduce the complexity and to enhance the bit error rate of the on-body sensors. Interestingly, low energy consumption at every sensor participating in the on-body to off-body WBAN was achieved by adopting the combination between LDPC decoders and VMIMO technique. According to simulation results, the new system enhanced the BER performance and reduced the complexity of the on-body to off-body IR-UWB communication system effectively.

Effective joint DOA-DOD estimation for the coexistence of uncorrelated and coherent signals in massive multi-input multi-output array systems

This paper deals with the joint direction-of-arrival (DOA) and direction-of-departure (DOD) estimation when the uncorrelated and coherent (i.e., fully correlated) narrowband signals coexist in multiple-input multiple-output (MIMO) array systems. Two new approaches based on weighted subspace fitting and oblique projection for two-dimensional direction estimation, i.e., WSFOPDE and improved WSFOPDE, are proposed. In the WSFOPDE approach, the basic procedure includes three stages. First, the DOA of all signals can be directly acquired by minimizing a reduced-dimensional weighted subspace fitting function. Then, the DOA information of uncorrelated signals are discerned by a classifying indicator; and subsequently, their auto-paired transmit steering vectors with respect to DOD information are derived. Finally, via a new Toeplitz-structured oblique projection, an virtual MIMO array data with only coherent signals remaining is constructed to assist the corresponding auto-paired DOD estimation. In order to promote the accuracy of angle estimation, we also design an improved version. It inherits the above basic procedure and, meanwhile, introduces one-dimensional local DOA spectrum searching to refine the DOA-DOD estimation. Compared with some existing strategies, WSFOPDE and its improved version perform better from the united perspective of computational complexity and estimation accuracy. Numerical simulations verify the advantages and also demonstrate that both can be served as a better alternative to the competitors.

Preference‐based unified criterion in virtual MIMO systems

Virtual multiple-input multiple-output (V-MIMO) is an advanced technology in uplink systems, and a well-designed user pairing and resource allocation scheme in V-MIMO systems can effectively exploit multi-user diversity to yield a significant performance gain. Recently, main attention has been devoted to the crucial user pairing issue with consideration of three key metrics, i.e. spectrum efficiency, energy efficiency and fairness. In this study, the authors investigate the unified tradeoff among all the three metrics for V-MIMO systems with user pairing and resource allocation. They first formulate the three key metrics in a united form and derive a straightforward unified criterion based on the user-specific preference to depict system performances. Through discussing several preference-based cases, they observe that a portion of spectrum efficiency is considered redundantly. Thus, a modified unified criterion is proposed to remove the partial redundancy provided by spectrum efficiency contribution to the objective function. Based on the two unified criteria, they propose a user pairing scheme in flat fading channels and a joint user pairing and resource allocation scheme in frequency-selective fading channels to balance the tradeoff flexibly. Simulation results show that, compared with existing schemes, the proposed scheme achieves a dynamical tradeoff among spectrum efficiency, energy efficiency and fairness.

Joint User Pairing and Power Allocation in Virtual MIMO Systems

Virtual multiple-input multiple-output (V-MIMO) is an effective way to achieve a diversity gain in uplink channels. A well-designed user pairing scheme in V-MIMO systems can exploit multiuser diversity to yield a significant performance gain. This paper investigates joint user pairing and power allocation problems in V-MIMO systems to maximize energy efficiency (EE) while guaranteeing spectrum efficiency (SE) under a total power consumption constraint. We formulate such a joint problem as a complex nonlinear optimization problem, which can be solved in two steps in $M\times K$ V-MIMO systems, i.e., power allocation with known user group and joint user pairing and power allocation. A multi-level water-filling method is used, and an iterative algorithm based on the outputs from the first step is employed in the second step. Finally, we propose a joint user pairing and power allocation scheme to find a user group that can achieve the maximum EE with power allocation. Simulation results and performance comparisons illustrate improved performance of the proposed scheme. Compared to the existing user pairing approaches, the proposed scheme achieves a significantly high EE gain while guaranteeing SE of a V-MIMO system.

Interference Management in Ultradense Networks: A User-Centric Coalition Formation Game Approach

Ultradense networks have been identified as a promising technology to accomplish objectives of the fifth-generation wireless networks. However, the severe mutual interference generated by the densely deployed femtocells constitutes a great challenge. Different from the most prior studies that center on femtocell access points (FAPs) and neglect the influence of users’ location when allocating subchannels, a centralized user-centric merge-and-split rule based coalition formation game, which can be well supported in the framework of the cloud/centralized radio access network, is proposed. This user-centric game makes it possible to utilize user information (e.g., distance) in estimating interuser interference so that the interference mitigation can be more accurate and effective. Besides, a novel resource allocation algorithm based on graph theory is presented. It can eliminate intratier interference efficiently by allocating users who may severely interfere each other in the conflict-graph with orthogonal subchannels as far as possible in a distance-aware sequence, and allocating subchannels in a profit-calculating method if idle subchannels are unavailable. Furthermore, in order to overcome the limitation that “only one subchannel can be allocated to each user” in previous coalitional games, a supplementary allocation algorithm is put forward to allocate remainder subchannels such that the system spectral efficiency can be improved. Simulation results show that the proposed algorithms improve the aggregate throughput up to 51.04%, 62.70%, 157.46%, and 482.42% comparing with the coalition formation game transmitted in a time-division multiple access (TDMA) manner within each coalition with virtual multiple-input multiple-output (MIMO) case, the reuse 1 case, the FAP-centric coalition formation game with modified recursive core case, and the coalition formation game transmitted in a TDMA manner among users with virtual MIMO case, respectively. The coalitional game proposed in this paper converges to a final stable partition in finite iterations.

Protocol Design and Performance Analysis of Multiuser Mixed RF and Hybrid FSO/RF Relaying With Buffers

In this paper, a multiuser mixed radio frequency (RF) and hybrid free-space optical (FSO)/RF system is considered, where multiple mobile users transmit their data to an intermediate decode-and-forward relay node through RF links using a virtual multiple-input multiple-output (MIMO) system, and the relay node forwards the multiplexed data of all users through a FSO link that is supported by a RF MIMO backup system to the destination. The relay node is equipped with a buffer in the physical layer for temporal storage of the users’ data until the best channel conditions at the relay-destination link are met. For this communication setup, we first propose a transmission protocol that achieves a multiplexing gain through a virtual MIMO system. After that, we derive closed-form expressions for the end-to-end outage probability, asymptotic outage probability, average symbol error rate, and the ergodic capacity when considering the delay-tolerant (finite buffer size) scenario. The results show that buffering in the physical layer provides a significant enhancement to the system performance (outage, error rate, and ergodic capacity). It is also found that pointing error and severe weather turbulence conditions become more tolerable with the existence of the relay’s buffer and RF backup link (in the second hop). In addition, the proposed virtual MIMO scheme shows a significant performance enhancement at a high number of receiving antennas, which introduces potential low-complexity diversity gain-based massive MIMO schemes.

On Uplink Virtual MIMO with Device Relaying Cooperation Enforcement in 5G Networks

In this paper, a novel protocol is proposed in which mobile terminals (MT) form a virtual Multiple-input Multiple-output (MIMO) uplink by means of device relaying on Device to Device (D2D) tier in 5G Cellular Network. The competitive scenario is considered in which each of the selfish MTs tries to transmit its own data and not relay others’ data in the formed virtual MIMO. The main focus is to design an incentive for MTs to form the virtual MIMO and cooperate in relaying others data. A direct revelation on-line mechanism for the BS is designed, in order to assist forming a stable virtual MIMO. A self-punishment mechanism is also proposed in which MTs autonomously punish malicious MTs that do not cooperate in relaying. We prove that our designed direct revelation on-line mechanism and proposed self-punishment mechanism enforce all-cooperation (all-C) profile as a Nash equilibrium (NE), under uncertainty in the presence of MTs in the formed virtual MIMO. Our simulation results confirm that the proposed protocol, even in the competitive scenario, increases the bit rate and decreases power consumption at the same time. The proposed protocol can improve the energy efficiency up to 35 percent compared to a non-cooperative case, i.e., Single-Input Multiple-Output (SIMO) uplink. Moreover, if the multi-user MIMO transmission is used for the uplink medium access layer, the proposed protocol can improve the energy efficiency up to 42 percent compared to SIMO uplink with multi-user MIMO transmission. Under the proposed OCVM protocol with Shapley value fairness, the price of anarchy reaches to 0.78 in the competitive scenario. In addition, the energy efficiency improvement of our proposed protocol is almost robust to the preferences of MTs. Simulation results show that if BS employs our on-line mechanism and MTs autonomously punish malicious MTs, the malicious MTs cannot gain by defecting from relaying other MTs’ data.

Combined IEEE 802.15.4 Physical Layer and Virtual Multiple Input Multiple Output (VMIMO) Transmissions for Energy Efficient Wireless Sensor Networks

Combined IEEE 802.15.4 Physical Layer and Virtual Multiple Input Multiple Output (VMIMO) Transmissions for Energy Efficient Wireless Sensor Networks

Diversity Pulse Shaped Transmission in Ultra-Dense Small Cell Networks

In ultra-dense small cell networks, spatial multiplexing gain is a challenge because of the different propagation conditions. The channels associated with different transmit–receive pairs can be highly correlated due to the: 1) high probability of line-of-sight (LOS) communication between user equipment (UE) and base station (BS) and 2) insufficient spacing between antenna elements at both UE and BS. In this paper, we propose a novel transmission technique titled Diversity Pulse Shaped Transmission (DPST), to enhance the throughput over the correlated multiple-input multiple-output (MIMO) channels in an ultra-dense small cell network. The fundamental of DPST is to shape transmit signals at adjacent antennas with distinct interpolating filters, introducing pulse shaping diversity. In DPST, each antenna transmits its own data stream with a relative deterministic time offset—which must be a fraction of the symbol period—with respect to the adjacent antenna. The delay is interpolated with the pulse shaped signal generating a virtual MIMO channel that benefits from increased diversity from the receiver perspective. To extract the diversity, the receiver must operate in an oversampled domain, and hence, a fractionally spaced equalizer (FSE) is proposed. The joint impact of DPST and FSE helps the receiver to sense a less correlated channel, eventually enhancing the UE's throughput. Moreover, in order to minimize the spatial correlation, we aim to optimize the deterministic fractional delay. Simulation results show that applying DPST to a correlated channel can approximately enhance the UE throughput by 1.93 $\times$ and 3.76 $\times$ in ${\text{2}}\,\times\, {\text{2}}$ and ${\text{4}}\,\times \,{\text{4}}$ MIMO systems, respectively.