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In this paper, we propose three new compressive sensing-based algorithms for channel estimation in millimeter wave hybrid MIMO systems over doubly (time and frequency) selective channels. Utilizing the basis expansion model (BEM) for effectively representing doubly selective channels, we first propose a BEM-based block orthogonal matching pursuit (BBOMP) algorithm, which can work with any training sequence structure. Next, we present the second algorithm to reduce the complexity of the BBOMP method by employing a special training sequence which results in a computationally efficient block sparse sensing matrix. Finally, in order to further decrease the computational complexity, we propose the third algorithm, where the channel estimation is split into two separate steps of tap detection and gain estimation. The proposed algorithms exploit the entire available training sequence to estimate all channel parameters, and can capture channel variations across the entire training frames without requiring a feedback channel. The Cramer-Rao lower bound and the computational complexity of the proposed algorithms are also addressed. Intensive computer simulations are conducted to evaluate the accuracy of the proposed approaches, showing that they can significantly improve the mean squared error performance compared with the state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

This paper proposes a flexible pilot assignment method to jointly optimize the uplink and downlink data transmission in multi-cell Massive multiple input multiple output (MIMO) systems with correlated Rayleigh fading channels. By utilizing a closed-form expression of the ergodic spectral efficiency (SE) achieved with maximum ratio processing, we formulate an optimization problem for maximizing the minimum weighted sum of the uplink and downlink SEs subject to the transmit powers and pilot assignment sets. This combinatiorial optimization problem is solved by two sequential algorithms: a heuristic pilot assignment is first proposed to obtain a good pilot reuse set and the data power control is then implemented. Numerical results manifest that the proposed algorithm converges fast to a better minimum sum SE per user than the algorithms in previous works. [ABSTRACT FROM AUTHOR]

In this paper, we consider the downlink (DL) of a zero-forcing (ZF) precoded extra-large scale massive MIMO (XL-MIMO) system. The base-station (BS) operates with limited number of radio-frequency (RF) transceivers due to high cost, power consumption and interconnection bandwidth associated to the fully digital implementation. The BS, which is implemented with a subarray switching architecture, selects groups of active antennas inside each subarray to transmit the DL signal. This work proposes efficient resource allocation (RA) procedures to perform joint antenna selection (AS) and power allocation (PA) to maximize the DL spectral efficiency (SE) of an XL-MIMO system operating under different loading settings. Two metaheuristic RA procedures based on the genetic algorithm (GA) are assessed and compared in terms of performance, coordination data size and computational complexity. One algorithm is based on a quasi-distributed methodology while the other is based on the conventional centralized processing. Numerical results demonstrate that the quasi-distributed GA-based procedure results in a suitable trade-off between performance, complexity and exchanged coordination data. At the same time, it outperforms the centralized procedures with appropriate system operation settings. [ABSTRACT FROM AUTHOR]

With the rise of data-hungry applications and the rapid development of the Internet-of-Things (IoT), 5G and device-to-device (D2D) communications come into being. While such technologies are designed to support massive data access to meet the ever-increasing demands, the complexity and heterogeneity of the network structure bring bigger challenges for interference management. As such, downlink/uplink decoupling (DUDe) has become an attractive approach, as it offloads user equipments (UEs) to small-cells (SCells) and creates a more benign environment for D2D communication. In this paper, we investigate the application of DUDe in D2D-underlay heterogeneous networks, and propose an efficient joint cell-association, subchannel allocation, and power control scheme for network sum-rate maximization. The proposed scheme includes a minimum path-loss based DUDe to decide the uplink (UL) serving base-station, and a greedy coloring scheme with modified Munkres algorithm to cluster the UEs, and allocate subchannels. Furthermore, the difference of convex functions based programming algorithm for power control is utilized to maximize the network sum-rate while satisfying the UE transmit power and data rate constraints. The results presented show that the proposed scheme can achieve superior performance to the coupled benchmarks. [ABSTRACT FROM AUTHOR]

In multi-user downlink small cell networks, cooperative resource allocation (RA) within a small cell cluster is a key technique to enhance network capacity. However, capacity-maximizing RA in frequency-selective fading channels requires global channel state information (CSI) of users within a small cell cluster, which makes it infeasible in practical networks with limited direct link capacity. To circumvent this global CSI assumption, most of the existing studies on RA have been based on several CSI assumptions such as local CSI and local CSI at the transmitters (CSIT). Nevertheless, cost functions with local CSI or local CSIT in the literature rely on heuristic formulations, because the sum-rate cannot be computed if without global CSI. In this paper, we propose a deep reinforcement learning-based RA algorithm to maximize the sum-rate for any given limited information on instantaneous CSI or sum-rate at the previous period. The proposed scheme is not restricted to certain CSI assumptions, but attempts to find the best RA for any given information such as quantized local CSI and quantized local CSIT; thus, it is applicable to any given direct link capacity. The proposed algorithm is self-adaptive in time-varying channels, since it is not divided into training and test phases. We modify the target neural network (TNN) scheme to enhance the sum-rate and the convergence speed. Numerical simulations confirm that: i) the proposed algorithm outperforms the conventional algorithms even under the same CSI assumption such as local CSI and local CSIT; ii) a flexible trade-off between the amount of CSI and the sum-rate is realizable in practical systems. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of detector design in the frequency-selective fading channels for unique-word-based single-carrier spatial modulation (UWSC-SM) systems. We propose to precede the conventional M-algorithm with an appropriately designed frequency-domain prefilter to condition the equivalent channel so that the number of the survivor paths needed for a satisfactory performance can be significantly reduced. By exploiting the block circulant channel induced by the UWSC-SM block format, the prefilter can be computed, and carried out efficiently using the fast Fourier transforms. Simulation results demonstrate that, compared to the conventional M-algorithm, the proposed algorithm achieves essentially the same error-rate performance with a considerably lower overall complexity in systems where the number of receive antennas is no smaller than that of transmit antennas. [ABSTRACT FROM AUTHOR]

In the era of the fifth generation (5G) communication networks, massive multiple-input multiple-output (MIMO) systems demand even lower computation complexity and power consumption while catching up with good detection performance. In this paper, a low-complexity nonlinear detection algorithm is proposed for massive MIMO systems, which is based on partial tree search and successive interference cancellation (SIC). The proposed scheme allows us to expedite the detection process by coping with the transmit symbols group by group. As compared to vertical-Bell laboratories layered space time (V-BLAST), the major breakthrough of computation reduction lies in the fact that the partial tree search can assist the detection process to avoid the inversion of the detection matrix required in each recursion of the SIC process. Both computational complexity analysis and simulation results show that our proposed algorithm not only significantly reduces computational complexity, but also has better bit error rate (BER) performance. [ABSTRACT FROM AUTHOR]

To be differentiated from the literature, in this paper, we aim to alleviate the impact of pilot contamination (PC) on the massive MIMO systems by cooperatively scheduling users (rather than just assigning) among neighboring cells to share the limited orthogonal pilots. To this end, we develop the multi-cell cooperative scheduling (MCCS) algorithm together with the cooperative scheduling indexes (COSIs) for maximizing the data rate, maximizing the Jain's fairness index and reaching a better tradeoff in-between. For convenience, they are denoted by the COSIs for the CMDR, CMMF and CPF schedulers, respectively. However, its high computational complexity may somehow resists its from practical applications. Thus, a low-complexity cooperative proportional fairness (LC-CPF) algorithm is designed to well approach the MCCS algorithm using the CPF COSI; and at the meantime, the order of computational complexity can be significantly reduced. Moreover, its ability to reach a better tradeoff can still be maintained under the impact of high spectrum-sharing interference. In addition, it is interesting to find that using the proposed cooperative scheduling methods, the open-loop power control mechanism is no longer required for compensating the differences of received signal quality between users. [ABSTRACT FROM AUTHOR]

In this paper, we propose an optimal random beamforming technique in mmWave MIMO-NOMA transmission systems. In our model, we consider a NOMA system with a user pairing scheme that works based on the distance between the cellular base station (BS) and the active mobile users. The aim of this is to reduce the system overall overhead for massive connectivity and achieve the desired Quality of Service (QoS). We present an optimization problem with the aims to find the optimal random beamforming coefficients by minimizing the outage probability. We analyze the convexity of the outage probability for three user pairing schemes and prove that the proposed optimal random beamforming is convex in high signal-to-noise ratio (SNR). We utilize the gradient-based algorithm namely the gradient descent algorithm to find optimal random beamforming coefficients. Our simulation results demonstrate that the proposed transmission schemes reduce the outage probability and improve network performance compared to previous works. [ABSTRACT FROM AUTHOR]

In this paper, a calibration of multiple-input multiple-output (MIMO) channel sounders with internal crosstalk is considered.The objective is to minimize the number of back-to-back (B2B) connections required to estimate the transmitter (Tx) and receiver (Rx) response matrices that convey the information about linear distortion and internal crosstalk. A signal and system model is developed for the B2B measurements, where only some pairs of the Tx and Rx ports of the sounder are utilized among all pairs of the ports. Using the measurement model, a least-square estimation problem is then formulated and converted in the frequency domain to weighted rank-one approximation problems. The notion of system identifiability of a MIMO channel sounder is introduced and some optimal sets of B2B connections are proposed. Given a proposed optimal set of B2B connections, the alternate convex search (ACS) algorithm with a proper initialization is also proposed to solve the weighted rank-one approximation problems. Finally, it is shown how to calibrate field measurement data by using the estimated response matrices. Numerical results show that, only after a couple of iterations, the ACS algorithm with the proposed initialization achieves a comparable identification and calibration performance to the conventional method that requires the B2B connections of all port pairs. [ABSTRACT FROM AUTHOR]

Non-orthogonal multiple access (NOMA) has been deemed a promising technology to achieve high spectral efficiency. This paper investigates transmit power optimization for a multi-user multiple-input single-output (MISO) NOMA downlink system endowed with energy harvesting and physical layer security. More specifically, the system is designed to satisfy the data-link security requirements of its legitimate users while charging energy harvesting devices. To achieve that goal, we investigate a joint design on beamforming vectors and artificial noise (AN) covariance matrix. Then, an iterative difference-of-two-convex-function (D.C.) algorithm is proposed by applying the successive convex approximation (SCA) approach. To further reduce the computational complexity, a sub-optimal alternating D.C. (ADC) algorithm is devised by decoupling beamforming and mapping the AN to the null space of legitimate users. In the ADC algorithm, optimal null space and beamforming vectors are alternately solved by convex programming. Furthermore, the convergence of the proposed D.C. and ADC algorithms is derived. Extensive simulation results show that the two proposed AN-aided algorithms significantly reduce the transmit power cost over OMA and NOMA scheme without AN, especially when there are more eavesdroppers. [ABSTRACT FROM AUTHOR]

In intelligent transportation systems (ITSs), the communication between the base station (BS) and the vehicles can form a virtual multiple-input multiple-out put (VMIMO) vehicle communication system. This paper addresses the issue of channel estimation in a virtual MIMO system that simultaneously adopt a smart antenna (SA). First, based on quaternion theory, a novel algorithm named quaternion noncircular MUSIC (QNC-MUSIC) is proposed, and direction of arrival (DOA) estimation is achieved for circular and noncircular signals. Then, a dimension reduction procedure is performed for the parameter search by employing the partial derivative of the spectrum function with respect to the noncircular phase; thus, a novel dimensional reduction noncircular MUSIC (DRNC-MUSIC) algorithm with a low computational complexity is proposed for DOA and polarization estimation of circular signals and noncircular signals. Finally, numerical examples are provided to demonstrate the parameter estimation performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new beam allocation strategy aiming to maximize the average successful tracking probability (ASTP) of a single user time-varying millimeter-wave MIMO system. In contrast to most existing works that employ one transmitting-receiving (Tx-Rx) beam pair once only, we investigate a more general framework, where the Tx-Rx beam pairs are allowed to be used repeatedly in each beam training period to improve the received signal powers in specific directions. In the case of orthogonal Tx-Rx beam pairs, a power-based estimator is employed to track the time-varying AoA and AoD of the channel, and the resulting training beam pair sequence design problem is formulated as an integer nonlinear programming (I-NLP) problem. By dividing the feasible region into a set of subregions, the formulated I-NLP is decomposed into a series of concave sub I-NLPs, which can be solved by recursively invoking a nonlinear branch-and-bound algorithm. To reduce the computational cost, we relax the integer constraints of each sub I-NLP and obtain a low-complexity solution via solving the Karush-Kuhn-Tucker conditions of their relaxed problems. For the case when the Tx-Rx beam pairs are overlapped in the angular space, we estimate the updated AoA and AoD via an orthogonal matching pursuit (OMP) algorithm. Moreover, since no explicit expression for the ASTP exists for the OMP-based estimator, we derive a closed-form lower bound of the ASTP, based on which a favorable beam pair allocation strategy can be obtained. Numerical results demonstrate the superiority of the proposed beam allocation strategy over existing benchmarks. [ABSTRACT FROM AUTHOR]

In this paper, we study the distributed precoding problem for simultaneous wireless information and power transfer (SWIPT) in decode-and-forward (DF)-based multiple-input–multiple-output (MIMO) relay networks. The system model considered here consists of a source, a relay, an information decoding (ID) receiver, and an energy harvesting (EH) receiver, all mounted with multiple antennas. Since full channel state information (CSI) is usually unavailable, a practical scenario, where only local CSI is required, is considered in this paper. Such a practical scenario naturally constitutes a noncooperative game, where the source and the relay can be regarded as two rational game players. With properly designed utilities, it can be further shown that the existence and uniqueness of the pure-strategy Nash equilibrium (NE) of the proposed game can both be guaranteed under some mild conditions. Therefore, a distributed iterative precoding algorithm can be developed based on the best-response dynamic to obtain the unique NE solution for the proposed game. Moreover, a proximal-point-based regularization approach is also pursued to ensure the convergence of the proposed algorithm without requiring special restrictions on the channel ranks. Numerical simulations are also provided to demonstrate the proposed algorithm. Results show that our algorithm can converge quickly to a satisfactory solution with guaranteed convergence. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a compressive random access (CRA) scheme using multiple resource blocks (RBs) to support massive connections for machine type communications. The proposed CRA scheme is scalable. As a result, if the number of devices increases, more RBs can be added to support them. Thanks to multiple RBs, we can employ fast retrial between RBs for re-transmissions of collided packets, which can result in short access delay. For stable CRA with fast retrial, we derive conditions (with a rate control scheme), and analyze the steady-state performance to find the throughput and delay. Through analysis and simulation results, we can see that the proposed scheme can perform better than conventional multichannel ALOHA and enjoy a tradeoff between the performance and complexity in terms of the number of RBs. [ABSTRACT FROM AUTHOR]

In this paper, we propose two groups of recursive codes, namely the Hadamard recursive carrier interferometry (HRCI) codes and diagonal recursive carrier interferometry (DRCI) codes, to simultaneously reduce the peak-to-average power ratio (PAPR) and suppress the phase noises and residual carrier frequency offset (RCFO) for high-speed orthogonal frequency division multiplexing (OFDM) systems. We exploit the recursion property of the Hadamard and diagonal matrices to constitute the proposed HRCI code and DRCI code using the carrier interferometry (CI) code, and present the system model in details to spread OFDM symbols in the frequency domain. Then, we prove that both HRCI and DRCI generation matrices keep their invertibility during the recursions. As a direct result of the new code design, the phase intervals are enlarged and the signals are shifted in the time domain, thus both the PAPR and the phase noises are reduced, and the RCFO can be mitigated. Moreover, the enlarged phase intervals enable the transceiver blocks including the channel estimator, which estimate the phase noise based on the received signals, to improve the performance. Furthermore, we present the expressions for the HRCI and DRCI embedded transmitted and received signals, and derive the analytical signal-to-interference-plus-noise ratio (SINR) expressions for bit error rate (BER) performance analysis. Then, we analyze the effects of presented codes on the phase differences and provide the computational complexity analysis. Numerical simulations verify the effectiveness of our theoretical analysis of SINR. Additionally, under different parameter settings, which consider the working conditions of practical systems, we demonstrate that the presented robust HRCI and DRCI coded OFDM systems can suppress the PAPR satisfactorily and better BER performances can be achieved by the recursive CI-aided spread OFDM systems with phase noise rejection and RCFO compensation when compared with counterpart systems. [ABSTRACT FROM AUTHOR]

In millimeter wave (mm Wave) systems, the channel state fluctuates faster than that in sub-6GHz systems. Thus, the channel state dependent scheduling requires the faster feedback from a user equipment, which will generate the larger overhead. To reduce the feedback overhead, a prediction based feedback scheme is proposed under the assumption of the imperfect channel states being available at the user equipment. The proposed feedback scheme optimizes the reconstruction accuracy at a given feedback overhead. Within the scheme, the performance degradation caused by the protocol and hardware operation delay can be mitigated. The impact of the proposed scheme on improving the downlink bit rate is studied in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new constellation design for a non-coherent massive single input multiple output (m-SIMO) uplink system based on M-DPSK suitable for Rician channels. Under Rician propagation, the non-coherent systems proposed until now cannot completely remove the interference. This new design takes into account the inter user and inter symbol interferences in order to convert them into useful terms that help us in the non-coherent detection. We propose an algorithm to non coherently detect the joint symbol with the information from all users leveraging the characteristics of the new constellation. In addition, the signal-to-interference-plus-noise ratio is derived and is used to present analytical bounds for the symbol error rate. It is shown that the analytical results tightly match the numerical simulation. We show that with the proposed constellation and detection algorithm we are able to leverage the line-of-sight component of the Rician propagation, obtaining a better performance than with Rayleigh channels. [ABSTRACT FROM AUTHOR]

This paper proposes a widely linear processing framework for multiple-input multiple-output non-orthogonal multiple access (MIMO-NOMA) downlink systems. In the framework, a widely linear MIMO-NOMA (WL-MIMO-NOMA) model is derived by assuming that the base station transmits real-valued downlink signals. WL-MIMO-NOMA adopts complex-valued power allocation coefficients to stagger the user signals in phase. The main features of WL-MIMO-NOMA are the following: first, in general case, WL-MIMO-NOMA can remove all the inter-cluster interference and at least half of the intra-cluster interference; and second, in user pairing case, both interferences can be completely eliminated. This is distinct from the existing work where real power coefficients are used, which cannot guarantee the complete separation of the paired user signals because the signals transmitted to the paired users are overlapped in phase. In addition, the closed-form expressions of outage probabilities are derived. The phase difference of the complex power coefficients is optimized to minimize the outage probability. It is proven that, with the optimal phase difference, successive interference cancellation is unnecessary in user pairing case. Finally, the framework is extended to the mixed case of real/complex circular signals. Simulation results show that the proposed framework outperforms the existing work, and the numerical results agree well with the analytical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we develop a novel layered coding scheme for the multiple-input multiple-output multicast channel. In this scheme, information is encoded in two layers, a base low-resolution (LR) layer and refining high-resolution (HR) one. The LR layer is encoded using Grassmannian noncoherent codes and the HR layer is encoded in the indices of the active transmitter antennas using the so-called space shift keying modulation. An efficient algorithm is proposed to optimize the HR codebook. The LR information can be detected noncoherently without invoking any channel state information (CSI), whereas the HR information must be detected coherently and, thus, requires accurate CSI. Hence, receivers with perfect CSI can decode both the LR and HR information, whereas those with no CSI can only decode the LR information. For receivers with accurate CSI, we propose a computationally efficient two-step detector and we show that the noncoherent detector performance is not affected by the transmission of the incremental HR information encoded in the transmit antenna indices. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive study of underwater visible light communications (UVLC), from channel characterization, performance analysis, and effective transmission and reception methods. To this end, we first simulate the fading-free impulse response (FFIR) of UVLC channels using Monte Carlo numerical procedure to take into account the absorption and scattering effects; and then to characterize turbulence effects, we multiply the aforementioned FFIR by a fading coefficient modeled as a lognormal random variable (RV) for weak oceanic turbulence. Based on this general channel model, we analytically study the bit error rate (BER) performance of UVLC systems with binary pulse position modulation (BPPM). In the next step, to mitigate turbulence effects, we employ multiple transmitters and/or receivers, i.e., we apply spatial diversity technique over UVLC links. Closed-form expressions for the system BER are provided, when an equal gain combiner is employed at the receiver side, thanks to the Gauss–Hermite quadrature formula as well as approximation to the sum of lognormal RVs. We further apply saddle-point approximation, an accurate photon-counting method, to evaluate the system BER in the presence of shot noise. Both laser-based collimated and light emitting diode based diffusive links are investigated. Additionally, in order to reduce the intersymbol interference (ISI), introduced by the multiple-scattering effect of UVLC channels on the propagating photons, we also obtain the optimal multiple-symbol detection (MSD) algorithm, as well as the suboptimal generalized MSD (GMSD) algorithm. Our numerical analysis indicate good matches between the analytical and photon-counting results implying the negligibility of signal-dependent shot noise, and also between the analytical results and numerical simulations confirming the accuracy of our derived closed-form expressions for the system BER. Besides, our results show that spatial diversity significantly mitigates fading impairments while (G)MSD considerably alleviates ISI deterioration. [ABSTRACT FROM AUTHOR]

In this paper, we study the downlink resource assignment problem of maximizing the total data rate subject to minimum satisfaction guarantees in multiservice scenarios assuming the use of multiuser (MU) multiple-input–multiple-output (MIMO) techniques. With the use of MU MIMO techniques, the same frequency resource can be shared by different terminals at the same time by assigning different spatial channels to each terminal. Different from single-user (SU) access per frequency resource where the resource assignment problem consists of searching for the best association between frequency resources and terminals, with MU access per resource, we aim at finding which space-division multiple-access (SDMA) group should be associated with each frequency resource. The first contribution of this paper is the formal presentation of this generalized problem as an optimization problem. Then, after some mathematical manipulations, we managed to convert this problem from a nonlinear integer to an integer linear problem (ILP) that can be optimally solved by standard techniques instead of resorting to brute-force methods. Motivated by the high computational complexity of the optimal solution, we propose a low-complexity algorithm. By analyzing outage rate and total data rate performance metrics, we show that the proposed solution presents a good performance–complexity tradeoff compared with the method for obtaining the optimal solution. [ABSTRACT FROM PUBLISHER]

In this paper, we study the energy efficiency (EE) optimization for simultaneous wireless information and power transfer in multiple-input-multiple-output two-way amplify-and-forward relay networks, where the energy-constrained relay harvests energy from two sources’ signals by power splitting (PS) scheme to forward the information of two sources. Our objective is to jointly design the sources and relay precoding matrices and the PS ratio to maximize the EE of the network, under the transmit power constraints at sources and relay and the minimum spectral efficiency requirement. We transform the nonconvex precoding and PS design problem into a difference of convex programming and propose an efficient iterative algorithm based on the constrained concave convex procedure to obtain a local optimum. To reduce computational complexity, we propose a generalized singular value decomposition based channel diagonalization scheme to simplify the optimization into a joint source and relay power allocation problem. The alternating optimization method is employed to solve this problem and a suboptimal solution to the EE maximization problem is obtained. Simulation results demonstrate the effectiveness of the proposed schemes. [ABSTRACT FROM AUTHOR]

The fast development of intelligent transport systems requires high-rate communications, high energy efficiency, and low latency. One promising solution to meet the requirements is to adopt the massive multiple-input multiple-output (MIMO) technique. The massive MIMO architecture is attractive to multiple vehicles on the road for vehicle-to-infrastructure access as large-scale antennas can be deployed at the roadside unit. Besides, massive MIMO systems can significantly improve the system spectrum efficiency and energy efficiency. However, the benefits are achieved at the cost of high computational complexity and long processing delay even with linear detection methods. In this paper, we propose low complexity and fast processing algorithms to address those issues. The proposed schemes transform the large-scale matrix inverse problems into solving linear equations. We then introduce iterative methods to solve linear equations. To speed up the updating process in iterative method, we utilize the properties of block matrix, and perform the updating process on a small size block independently. The independent processing progress can be paralleled, which greatly reduces the overall processing time. We also evaluate the performance of the proposed schemes in terms of the probability that the convergence conditions are met, and the system bit error rate. The results show that the proposed schemes achieve good system performance but at low complexity and latency. [ABSTRACT FROM AUTHOR]

This paper investigates space-time blind equalization (BE) of dispersive multiple-input multiple-output communication systems driven by high throughput quadrature amplitude modulation signals. Multistage processing is adopted to overcome the severe local convergence problem in BE. First, a good initial value for the equalizer is obtained by forcing one of the system inputs with desired delay to be recovered. Then, the fast multimodulus algorithm (MMA) is used to roughly equalize the communication system. After that, an improved MMA (IMMA) is developed to effectively search for a fine equalizer for the system. Moreover, the novel modified Newton method (MNM) proposed in our previous work is employed to fast optimize the MMA and IMMA cost functions, which significantly reduces the computational load. Furthermore, the proposed algorithm has an additional benefit that once a signal is recovered, its corresponding single-input multiple-output channel impulse response is estimated by the classical least squares methods. Then, the influence of the recovered signal to the original received signals is removed to avoid extracting this recovered signal repeatedly. The quadratic rate of convergence of the MNM is theoretically analyzed, and the good equalization performance of the IMMA is explained. Finally, simulation results are provided to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

This paper investigates a new analog beamforming architecture for massive multiple-input multiple-output (MIMO) systems, where each of the multiple transmit antennas is switched to be on or off to form a beam according to the channel state information at transmitters. This on–off analog beamforming (OABF) scheme has the advantages in terms of both hardware complexities and algorithmic complexities. OABF can completely remove the high-cost, power-consuming, and bulky analog phase shifters that are extensively employed by traditional analog beamforming schemes; it only requires the deployment of low-cost analog switches that are easy to implement. Moreover, we show that the beams formed by such simple antenna on–off switch operations can achieve rather good performances with low-complexity beamforming algorithms. Specifically, we first propose two optimal signal-to-noise ratio maximization algorithms to determine the on–off state of each switch under the per-antenna power constraint and the total power constraint, respectively. After that, we theoretically prove that OABF can achieve the full diversity gain and the full array gain with complexities up to a polynomial order. Numerical results are consistent with our theoretical analysis. We believe that the simple structure of OABF makes massive MIMO much easier to implement in real systems. [ABSTRACT FROM PUBLISHER]

In this paper, we explore low-complexity probabilistic algorithms for soft symbol detection in high-dimensional multiple-input multiple-output (MIMO) systems. We present a novel algorithm based on the expectation consistency (EC) framework, which describes the approximate inference problem as an optimization over a nonconvex function. EC generalizes algorithms such as belief propagation and expectation propagation. For the MIMO symbol detection problem, we discuss feasible methods to find stationary points of the EC function and explore their tradeoffs between accuracy and speed of convergence. The accuracy is studied, first in terms of input–output mutual information and show that the proposed EC MIMO detector greatly improves state-of-the-art methods, with a complexity order cubic in the number of transmitting antennas. Second, these gains are corroborated by combining the probabilistic output of the EC detector with a low-density parity-check channel code. [ABSTRACT FROM PUBLISHER]

In this paper, the performance of an underlay multiple-input multiple-output (MIMO) cognitive radio system is analytically studied. In particular, the secondary transmitter operates in a spatial multiplexing transmission mode, while a zero-forcing detector is employed at the secondary receiver. Additionally, the secondary system is interfered by multiple randomly distributed single-antenna primary users (PUs). To enhance the performance of secondary transmission, optimal power allocation is performed at the secondary transmitter with a constraint on the interference temperature (IT) specified by the PUs. The outage probability of the secondary receiver is explicitly derived in an exact closed-form expression. Also, some special cases of practical interest, including colocated PUs and massive MIMO, are discussed. Further, to mitigate instantaneous excessive interference onto PUs caused by the time-average IT, an iterative antenna reduction algorithm is developed for the secondary transmitter and, accordingly, the average number of transmit antennas is analytically computed. Extensive numerical and simulation results corroborate the effectiveness of our analysis. [ABSTRACT FROM PUBLISHER]

This paper considers the antenna selection (AS) problem for a multiple-input multiple-output nonorthogonal multiple access system. In particular, we develop new computationally efficient AS algorithms for two commonly used scenarios: NOMA with fixed power allocation (F-NOMA) and NOMA with cognitive radio-inspired power allocation (CR-NOMA). For the F-NOMA scenario, a new max–max–max AS (A$^3$ -AS) scheme is first proposed to maximize the system sum-rate. This is achieved by selecting one antenna at the base station (BS) and corresponding best receive antenna at each user that maximizes the channel gain of the resulting strong user. To improve the user fairness, a new max–min–max AS (AIA-AS) scheme is subsequently developed, in which we jointly select one transmit antenna at BS and corresponding best receive antennas at users to maximize the channel gain of the resulting weak user. For the CR-NOMA scenario, we propose another new AS algorithm, termed maximum-channel-gain-based antenna selection (MCG-AS), to maximize the achievable rate of the secondary user, under the condition that the primary user's quality-of-service requirement is satisfied. The asymptotic closed-form expressions of the average sum-rate for A $^3$-AS and AIA-AS and that of the average rate of the secondary user for MCG-AS are derived. Numerical results demonstrate that the AIA-AS provides better user fairness, whereas the A$^3$-AS achieves a near-optimal sum-rate in F-NOMA systems. For the CR-NOMA scenario, MCG-AS achieves a near-optimal performance in a wide signal-to-noise-ratio regime. Furthermore, all the proposed AS algorithms yield a significant computational complexity reduction, compared to exhaustive search-based counterparts. [ABSTRACT FROM PUBLISHER]

For massive MIMO public channel with any sector size in either microwave or millimeter wave (mmwave) band, this paper studies the beamforming design to minimize the transmit power while guaranteeing the quality of service for randomly deployed users. First the ideal beampattern is derived via Parseval Identity, based on which a beamforming design problem is formulated to minimize the gap with the idea beampattern. The problem is transformable to a multiconvex one and an iterative optimization algorithm is used to obtain the full-digital beamformer. In addition, with the help of same beampattern theorem, the power amplifier efficiency of the beamformer is improved with unchanged beampattern. Finally, the practical hybrid implementation is obtained that achieves the full-digital beamformer solution. Simulations verify the advantages of the proposed scheme over existing ones. [ABSTRACT FROM PUBLISHER]

The doubly selective (DS) channel estimation in the large-scale multiple-input multiple-output (MIMO) systems is a challenging problem due to the large number of the channel coefficients to be estimated, which requires unaffordable and prohibitive pilot overhead. In this paper, first we conduct the analysis about the common sparsity of the basis expansion model (BEM) coefficients among all the BEM orders and all the transmit–receive antenna pairs. Then, a novel pilot pattern is proposed, which inserts the guard pilots to deal with the intercarrier interference under the superimposed pilot pattern. Moreover, by exploiting the common sparsity of the BEM coefficients among different BEM orders and different antennas, we propose a block distributed compressive sensing-based DS channel estimator for the large-scale MIMO systems. Its structured sparsity leads to the reduction of the pilot overhead under the premise of guaranteeing the accuracy of the estimation. Furthermore, taking consideration of the block structure, a pilot design algorithm referred to as block discrete stochastic optimization is proposed. It optimizes the pilot positions by reducing the coherence among different blocks of the measurement matrix. Besides, a linear smoothing method is extended to large-scale MIMO systems to improve the accuracy of the estimation. Simulation results verify the performance gains of our proposed estimator and the pilot design algorithm compared with the existing schemes. [ABSTRACT FROM PUBLISHER]

Multiple-input–multiple-output (MIMO) technology can efficiently use the spectrum to increase the communication throughput. Designing low-complexity detection algorithms with high performance for the MIMO system has been an important issue. In this paper, we propose efficient detection algorithms for MIMO systems based on differential metrics. We first define differential metrics and give their recursive calculation of different orders. Based on differential metrics, we give the principle of gradient search. We then propose a gradient search algorithm (GSA) that can provide a tradeoff between performance and complexity. The GSA applies the indicative functions such that we can determine in advance some maximum-likelihood (ML) bits of the initial sequence and reduce the searching range. The GSA also uses a stop condition with which we can stop the search if the proper condition is satisfied. The GSA does not need QR decomposition (QRD) or matrix inversion. The multiplicative operations are only necessary before the searching process, during which only the additive operations are needed. For large-scaled MIMO systems, we also give a simple searching algorithm based on differential metrics. Finally, we propose a fixed-complexity gradient algorithm (FCGA), which has a fixed number of operations during the searching process and is appropriate for pipelined hardware implementation. The simulation results validate the efficiency of the proposed algorithms. [ABSTRACT FROM PUBLISHER]

This paper studies generalized spatial modulation (Gen-SM) schemes in multicell multiuser massive multiple-input multiple-output (MIMO) systems as a promising high-throughput and energy-efficient technique for fifth-generation (5G) wireless networks. A detection algorithm for such systems is proposed based on linear processing techniques. By applying the concept of order statistics, a general framework for approximating the achievable sum rates with linear detection is also given. The probability of detecting antenna combinations is analyzed and is used to approximate the sum-rate performance with practical channel conditions, such as antenna correlation, imperfect channel information, and pilot contamination. The fundamental trade-off between spectral efficiency (SE) and energy efficiency (EE) is also investigated. Despite offering less SE, spatial modulation (SM) with a single active antenna per user is shown to be the most energy-efficient transmission mode among the Gen-SM class. Within the operating range of SM (i.e., in the low-to-moderate SE regime), SM is demonstrated to achieve better EE compared with conventional massive MIMO schemes. The performance in terms of economic efficiency, indicating economic profitability (in monetary unit per second), is also analyzed and is shown to serve as a complementary performance metric, enabling an implicit trade-off between SE and EE. [ABSTRACT FROM PUBLISHER]

Signal identification represents the task of a receiver to identify the signal type and its parameters, with applications to both military and commercial communications. In this paper, we investigate the identification of spatial multiplexing and Alamouti space–time block codes with single-carrier frequency-division multiple-access signals, when the receiver is equipped with a single antenna. We develop a discriminating feature based on a fourth-order statistic of the received signal as well as a constant false-alarm rate decision criterion that relies on the statistical properties of the feature estimate. Furthermore, we present the theoretical performance analysis of the proposed identification algorithm. The algorithm does not require channel or noise power estimation, modulation classification, and block synchronization. Simulation results show the validity of the proposed algorithm as well as a very good agreement with the theoretical analysis. [ABSTRACT FROM PUBLISHER]

In this paper, the downlink of a clustered coordinated multicell multiuser multiple-input multiple-output (MIMO) system is considered, and various low-complexity user scheduling algorithms to maximize the sum rate are proposed. The users' data signals are transmitted cooperatively via the base stations (BSs) of a cluster within the sectorized multicell heterogeneous cellular network. Exhaustive search as the optimal scheduling method is extremely complex, particularly for large numbers of users requesting service. We therefore propose suboptimal scheduling algorithms based on the lower complexity metaheuristic stochastic optimization techniques of simulated annealing (SA) and particle swarm (PS). Moreover, a hybrid algorithm combining the traits of PS and a greedy scheduler is also proposed. The performance and complexity of these algorithms are evaluated for a heterogeneous system model employing different precoding methods. Assessing the algorithms' performance via computer simulations, the effectiveness of the proposed schemes in terms of sum rate is demonstrated, yielding performance very close to that of the exhaustive search at much lower complexity. For each precoding method used in the employed system model, the best corresponding approach to scheduling from our proposed algorithms is determined. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the interference alignment (IA) for the multiple-input–multiple-output (MIMO) multicell downlink networks in the context of a square channel matrix. We propose a novel joint user grouping and base station (BS) association algorithm. Furthermore, we design the transmit and receive beamforming matrices in closed forms by using a generalized eigenvalue decomposition (GEVD)-based IA scheme, which can exploit the special structure of a square channel matrix against the existing algorithm. Moreover, we provide three theorems to characterize the maximum achievable degrees of freedom (DoF) of the proposed GEVD-based IA scheme. Compared with the existing IA scheme, the proposed GEVD-based IA scheme can reduce the dimension of subspace occupied by the intercell interference (ICI) more efficiently, hence providing achievable DoF higher than or equal to that of the existing IA scheme. [ABSTRACT FROM AUTHOR]

A companding-based transformation method is introduced to quasi-maximum-likelihood (ML) detectors, such as the QR-decomposition-based M-algorithm (QRD-M) and list sphere decoding, for coded multiple-input–multiple-output (MIMO) systems in this paper. The key idea of the proposed companding technique is to compress (i.e., down-weight) the dubious observation of the accumulated branch metric by taking into account its statistical characteristics so that, after companding, the estimation error of the unreliable detected information bits due to insufficient candidate size and/or channel estimation error is significantly mitigated without disproportionate compromise of the reliable information bits. By employing the proposed companding method, the original leptokurtically distributed log-likelihood ratio of the detected information bits becomes more Gaussian distributed. As an illustrative example, the QRD-M detector is employed in this paper. Numerical results show that the QRD-M detector based on the proposed companding paradigm achieves significant performance gain over the conventional method and approaches the performance of the ML detector for a 16-ary quadrature-amplitude-modulated (16-QAM) \4 \times \4 MIMO multiplexing system with lower-than-linear-detector computational complexity. [ABSTRACT FROM PUBLISHER]

This paper investigates the network resource allocation in multiuser downlink wireless systems where the base station and the mobile stations are equipped with multiple antennas to provide fair and efficient transmission services to the mobile users. We focus on packet scheduling, given that it has a significant impact on the overall performance of a multiple-input-multiple-output (MIMO) system. Most previous schedulers designed at the packet level do not take into account the traffic characteristics (different packet lengths and the arrival process parameters); consequently, they fall short of simultaneously providing fairness and a low average packet transmission delay. We are making use of a flexible packet transmission algorithm at the medium access control (MAC) layer to develop and propose a novel scheduler, which is referred to as MIMO packet-based proportional fairness (MP-PF). The new scheduler is designed with the goal of providing high performance in terms of a low average packet transmission delay and time and service fairness among the users based on the concept of proportional fairness. The scheduler also conserves work and takes into consideration the packet length, the user queue length, the user transmission rate (related to its channel quality), and the service guarantees for heterogeneous users. The well-known ideal service fair scheduler called max-min can also significantly be improved using our framework by taking into consideration the traffic characteristics. We also provide an analysis for the fairness of the new scheduler in terms of time and service allocation, which is the key contribution of this paper. Simulations that consider the traffic characteristics and the mobility of users show the relatively low average packet transmission delay and demonstrate the time and service fairness capabilities of MP-PF, compared with other well-known MIMO schedulers. [ABSTRACT FROM AUTHOR]

Maximum-likelihood (ML) detection for higher order multiple-input-multiple-output (MIMO) systems faces a major challenge in computational complexity. This limits the practicality of these systems from an implementation point of view, particularly for mobile battery-operated devices. In this paper, we propose a modified approach for MIMO detection, which takes advantage of the quadratic-amplitude modulation (QAM) constellation structure to accelerate the detection procedure. This approach achieves low-power operation by extending the minimum number of paths and reducing the number of required computations for each path extension, which results in an order-of-magnitude reduction in computations in comparison with existing algorithms. This paper also describes the very-large-scale integration (VLSI) design of the low-power path metric computation unit. The approach is applied to a 4 x 4, 64-QAM MIMO detector system. Results show negligible performance degradation compared with conventional algorithms while reducing the complexity by more than 50%. [ABSTRACT FROM AUTHOR]

Multicell coordinated beamforming (CB) can mitigate intercell interference (ICI). However, existing work on CB focuses on systems that maximize overall throughput. This paper considers CB for systems with multiple receive antennas and further extends the CB to multiuser and multistream transmission. We consider fairness and pay close attention to cell-edge users. CB that maximizes the harmonic sum of signal-to-interference-plus-noise ratio (SINR) can be derived into a low-complexity algorithm that favors cell-edge users. Two iterative algorithms are developed. From the simulation results, the proposed algorithms can provide a better fifth-percentile user throughput compared with the CB algorithms minimizing mean square error, maximizing uplink SINR, and maximizing weighted sum rate. Furthermore, the computational complexity of the proposed algorithms is significantly lower than that maximizing the minimum SINR of users. [ABSTRACT FROM AUTHOR]

This paper focuses on precoding design for sum-rate maximization while considering the effects of residual self-interference for multiuser multiple-input–multiple-output (MU-MIMO) full-duplex (FD) systems. The problem formulation leads to a nonconvex matrix-variable optimization problem, where we develop two efficient sum-rate maximization algorithms using sequential convex programming (SCP), namely, the difference of convex functions (DC)-based and the sequential convex approximations for matrix-variable programming (SCAMP) algorithms. In addition, we derive the achievable sum rate under the effect of residual self-interference. Simulation results show that, even in cases of high self-interference and high estimation error, the SCAMP algorithm provides approximately 20%–30% sum-rate improvements over both conventional optimized half-duplex (HD) transmission and the existing state-of-the-art FD algorithm in a wide range of scenarios. Finally, the convergence results indicate that the DC-based algorithm tends to initially give the best performance; however, at convergence, the SCAMP algorithm tends to significantly outperform the other algorithms. [ABSTRACT FROM AUTHOR]

Existing full-rate transmission schemes for two-path relay networks typically cannot achieve full diversity while demanding high decoding complexity. In this paper, we present a novel low-complexity full-rate transmission scheme for two-path relay networks to harvest maximum achievable diversity. The proposed scheme adopts block transmission with small block size of four symbols, which greatly reduces the decoding complexity at the receiver. Through the performance analysis of the resulting two-path relay network in terms of the symbol error rate (SER) and diversity order, we show the proposed scheme can achieve full diversity order of four and mimic a 2 $\times$ 2 multiple-input multiple-output system. Simulations results are provided to validate the mathematical formulation. [ABSTRACT FROM PUBLISHER]

This paper investigates the uplink transmission in multicell multiuser multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems. The system model considers imperfect channel estimation, pilot contamination (PC), and multicarrier and multipath channels. Analytical expressions are first presented on the mean square error (MSE) of two classical channel estimation algorithms [i.e., least squares (LS) and minimum mean square error (MMSE)] in the presence of PC. Then, a simple H-infinity (H-inf) channel estimation approach is proposed to have good suppression to PC. This approach exploits the space-alternating generalized expectation–maximization (SAGE) iterative process to decompose the multicell multiuser MIMO (MU-MIMO) problem into a series of single-cell single-user single-input single-output (SISO) problems, which reduces the complexity significantly. According to the analytic results given herein, increasing the number of pilot subcarriers cannot mitigate PC, and a clue for suppressing PC is obtained. It is shown from the results that the H-inf has better suppression capability to PC than classical estimation algorithms. Its performance is close to that of the optimal MMSE as the length of channel impulse response (CIR) is increased. By using the SAGE process, the performance of the H-inf does not degrade when the number of antennas is large at the base station (BS). [ABSTRACT FROM PUBLISHER]

We consider the uplink transmission in multiuser wireless systems with multiple single-antenna transmitting users and a multiantenna receiver. We address two problems in this paper. The first problem is user admission, i.e., given a large number of users, how to admit the maximum number of users that can simultaneously satisfy quality of service (QoS) and power constraints. The second problem is how to distribute the data among the users when they are allowed to share data before transmission. The aim is to minimize the total data exchange cost. Such a problem is called user clustering. We formulate those problems into sparsity-maximization problems, which are NP-hard. Inspired by compressive sensing techniques, we propose a common framework to tackle those problems by first applying the \ell1 -norm relaxation and then solving them with convex optimization methods. Simulations show that the proposed algorithms achieve excellent performance. For user admission, the numbers of admitted users by the proposed algorithms are close to the optimum numbers of admitted users obtained by exhaustive search (ES) . For user clustering, the total data exchange cost is reduced by more than 10% after only a few iterations. When the QoS requirement is low, the user data exchange can be avoided using the proposed method, which achieves the optimum result obtained by ES. [ABSTRACT FROM PUBLISHER]

This paper considers a belief propagation algorithm over pairwise graphical models to develop low-complexity iterative multiple-input multiple-output (MIMO) detectors. The pairwise graphical model is a bipartite graph where a pair of variable nodes are related by an observation node represented by the bivariate Gaussian function obtained by marginalizing the posterior joint probability density under the Gaussian input assumption. Specifically, we consider two types of pairwise models: the fully connected and ring-type. The pairwise graphs are sparse, compared with the conventional graphical model introduced by Bickson et al., insofar as the number of edges connected to an observation node (edge degree) is only two. Consequently, the computations are much easier than those of maximum likelihood (ML) detection, which are similar to the belief propagation (BP) that is run over the fully connected bipartite graph. The link level performance for non-Gaussian input is evaluated via simulations, and the results show the validity of the proposed algorithms. We also customize the algorithm with Gaussian input assumption to obtain the Gaussian BP run over the two pairwise graphical models, and for the ring-type, we prove its convergence to the linear minimum mean square error (MMSE) estimates. Since the maximum a posterior (MAP) estimator for Gaussian input is equivalent to the linear MMSE estimator, it shows the optimality of the scheme for Gaussian input. [ABSTRACT FROM PUBLISHER]

In this paper, we develop a novel joint transmit and receive design for multiuser multiple-input-multiple-output (MU-MIMO) systems. By exploiting channel temporal correlations, the proposed scheme incorporates a matched-filter (MF) combining vector into the beamformer design and enhances the performance of conventional signal-to-leakage-plus-noise ratio (SLNR) beamforming. With imperfect channel state information (CSI) available at the transmitter, we then focus on improving the robustness of the proposed algorithm against the mismatched CSI. The feedback delay effect is considered in the beamformer design first. We design a statistically robust beamforming design by maximizing the conditional expectation of the SLNR, hence alleviating the performance degradation due to CSI errors. Following that, we further encompass the imperfection caused by the quantized feedback into the beamforming design. Moreover, we also develop efficient power allocation techniques to further improve the sum-rate performance. Finally, we extend the proposed robust joint transmit and receive design to multicell MIMO systems. Simulation results verify the effectiveness of our algorithm under various scenarios. [ABSTRACT FROM PUBLISHER]

Spatial modulation (SM) is a spatial multiplexing scheme that utilizes both the signal constellation and antenna index to convey information. In the original SM, traditional modulation schemes such as quadrature amplitude modulation (QAM) are employed for constellation mapping. In this paper, we propose a novel scheme where superposition coded modulation (SCM) is employed to modulate the information onto the constellation points. We also develop a low-complexity iterative detector for our proposed SCM-SM system. Analysis and simulations demonstrate that SCM-SM significantly outperforms the original SM system with the same data rate while maintaining the relatively low complexity, particularly in the high data rate scenario. [ABSTRACT FROM PUBLISHER]

High-speed railways (HSRs) have been widely deployed all over the world in recent years. Different from traditional cellular communications, the high mobility of HSR communication makes it essential to implement power allocation (PA) along time. In the HSR case, the transmission rate greatly depends on the distance between the base station (BS) and the train. As a result, the train receives a time-varying data rate service when passing by a BS. It is clear that the most efficient PA will spend all the power when the train is nearest the BS, which will cause great unfairness along time. On the other hand, channel inversion allocation achieves the best fairness in terms of constant rate transmission. However, its power efficiency is much lower. Therefore, power efficiency and fairness along time are two incompatible objects. For the HSR cellular system considered in this paper, a tradeoff between the two is achieved by proposing a temporal proportional-fair PA scheme. In addition, a near-optimal closed-form solution and one algorithm finding \epsilon-optimal allocation are presented. [ABSTRACT FROM PUBLISHER]

The max-log list demapper has been widely employed in the implementations of a coded multiple-input–multiple-output (MIMO) receiver, where only a candidate list of signal vectors is examined in the likelihood-ratio calculation to reduce complexity. Traditionally, the candidate list is generated in the original-lattice domain, which, unfortunately, results in severe degradation in the performance of the demapper if the channel is in ill-condition. In this paper, two new lattice-reduction-aided max-log list demappers are proposed, i.e., one for an iterative receiver and the other for a noniterative receiver. With similar complexity, the proposed demappers provide significant gains over existing demappers, particularly for the cases with a small list size and/or under a spatially correlated channel, due to the new algorithms for the generation of the candidate list. In addition, for the iterative receiver, the prior information coming out of the decoder is exploited to lower the complexity of the demapper. [ABSTRACT FROM PUBLISHER]

Cognitive radio is regarded as the ideal candidate for enhancing the efficiency of spectrum usage for next-generation wireless systems. In fact, this emerging technology allows unlicensed cognitive users to transmit over frequency bands that are initially owned by license holders through the use of dynamic spectrum sharing. In this paper, we propose a novel algorithm that efficiently solves the problem of spectrum sharing and user scheduling in a cognitive downlink multi-input–multi-output system (MIMO). We study the scenario where primary receivers do not allow any interference from a multiantenna cognitive base station, which serves cognitive users. Using graph theory, we model, formulate, and develop an algorithm that finds near-optimal spectrum sharing with the objective of approaching the maximum achievable secondary sum rate. Since the formulated graph-coloring problem is shown to be \cal NP-hard, we design a low-complexity greedy algorithm. Following, we add the well-known proportional fairness to the proposed algorithm to ensure time-based fairness and to efficiently resolve the fairness/sum rate tradeoff. The problem is also formulated as a binary integer programming problem to find the optimal coloring solution. Computer simulations show that the proposed algorithm is able to achieve near-optimal performances with low computational complexity. [ABSTRACT FROM PUBLISHER]