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To improve the spectral efficiency in long-term evolution systems, the resource blocks (RBs) are shared among different cells/base stations (BSs) resulting in interference among the cells/BSs on each RB, although all the sub-carriers (SCs) in an RB may not be used in a cell. Defining the load of a given BS per RB as the fraction of the active SCs in that RB, in this paper, we present a generalized signal-to-interference-and-noise-ratio (SINR) model for downlink users on a given RB. This model considers both the transmit powers of the BSs and the loads of the cells over that RB. Under this load-coupled SINR model, to study the feasibility of a given rate demand vector for users, we formulate an optimization problem of minimizing the total load of the BSs on the RBs. Then, for two different scenarios of feasible and infeasible demand vectors, respectively, we study the load management problem (i.e., minimizing the total load of the BSs on the RBs) and admission control problem (i.e., finding the sub-set of users with maximum cardinality whose demands can be concurrently satisfied), respectively. Our theoretical investigations, which provide guidelines for designing radio resource management methods for load-coupled OFDMA networks, are complemented through Monte Carlo simulations. [ABSTRACT FROM PUBLISHER]

In heterogeneous cellular networks (HetNets) with macro base station (BS) and multiple small BSs (SBSs), cell association of user equipment (UE) affects UE transmission rate and network throughput. Conventional cell association rules are usually based on UE received signal-to-interference-and-noise-ratio (SINR) without being aware of other UE statistical characteristics, such as user movement and distribution. User behaviors can indeed be exploited for improving long-term network performance. In this paper, we investigate UE cell association in HetNets by exploiting both individual and clustering user behaviors with the aim to maximize long-term system throughput. We model the problem as a stochastic optimization problem, and prove that it is PSPACE-hard. For mathematical tractability, we solve the problem in two steps. In the first step, we investigate UE association for a specific SBS. We use a restless multiarmed bandit model to derive an association priority index for the SBS. In the second step, we develop an index enabled association (IDEA) policy for making the cell association decisions in general HetNets based on the indices derived in the first step. IDEA determines a set of admissible BSs for a UE based on SINR, and then associates the UE with the BS that has the smallest index in the set. We conduct simulation experiments to compare IDEA with other three cell association policies. Numerical results demonstrate the significant advantages of IDEA in typical scenarios. [ABSTRACT FROM PUBLISHER]

We investigate the performance of multiuser multiple-input-single-output (MU-MISO) downlink in the presence of the mutual coupling effect at the transmitter. Contrary to traditional approaches that aim at eliminating this effect, in this paper we propose a joint analog–digital (AD) beamforming scheme that exploits this effect to further improve the system performance. A jointly optimal AD beamformer is first obtained by iteratively maximizing the minimum received signal-to-interference-plus-noise ratio in the digital domain, followed by an optimization on the load impedance of each antenna element in the analog domain. We further introduce a decoupled low-complexity approach, with which existing closed-form beamforming schemes can also be efficiently applied. For the consideration of hardware imperfections in practice, we study the case where the analog load values are quantized, and propose a sequential search scheme based on greedy algorithm to efficiently obtain the desired quantized load values. Moreover, we also investigate the imperfect channel state information (CSI) scenarios, where we prove the optimality for closed-form beamformers, and further propose the robust schemes for two typical CSI error models. Simulation results show that with the proposed schemes the mutual coupling effect can be exploited to further improve the performance for both perfect CSI and imperfect CSI. [ABSTRACT FROM PUBLISHER]

We consider optimal linear precoder and decoder designs in a multi-cell multiple-input multiple-output system, where base stations and mobile users are both operating in full-duplex (FD) mode. Existing works on FD cellular systems focus on the maximization of overall throughput, which can result in unfairness between uplink and downlink channels depending on the self-interference power and inter-user interference levels. Therefore, to introduce fairness, in this paper, we consider the transmit and receive beamforming designs that maximize the harmonic-sum of signal-to-interference-plus-noise ratios (SINRs) in the uplink and downlink channels. We propose a low-complexity alternating optimization algorithm which converges to a stationary point. Moreover, in order to address practical system design aspects, we consider the transceiver design that enforces robustness against imperfect channel state information (CSI) while providing fair performance among the users. To this end, we formulate an optimization problem that maximizes the worst case SINR among all users under norm-bounded CSI errors. We devise a low-complexity iterative algorithm based on alternating optimization and semidefinite relaxation techniques. Numerical results verify the advantages of incorporating FD mode into cellular systems, and practical issues, such as CSI uncertainty and fairness performance. [ABSTRACT FROM PUBLISHER]

Access to the electromagnetic spectrum is an ever-growing challenge for radar. Future radar will be required to mitigate RF interference from other RF sources, relocate to new frequency bands while maintaining quality of service, and share frequency bands with other RF systems. The spectrum sensing, multioptimization (SS-MO) technique was recently investigated as a possible solution to these challenges. Prior results have indicated significant improvement in the signal-to-interference plus noise ratio at the cost of a high computational complexity. However, the optimization computational cost must be manageable in real time to address the dynamically changing spectral environment. In this paper, a bioinspired filtering technique is investigated to reduce the computational complexity of SS-MO. The proposed technique is analogous to the processing of the thalamus in the human brain in that the number of samples input to SS-MO is significantly decreased, thus, resulting in a reduction in computational complexity. The performance and computational complexity of SS-MO and the proposed technique are investigated. Both techniques are used to process a variety of measured spectral data. The results indicate a significant decrease in computational complexity for the proposed approach while maintaining performance of the SS-MO technique. [ABSTRACT FROM AUTHOR]

This paper considers coordinated multicast beamforming in a multicell multigroup multiple-input single-output system. Each base station (BS) serves multiple groups of users by forming a single beam with common information per group. We propose centralized and distributed beamforming algorithms for two different optimization targets. The first objective is to minimize the total transmission power of all the BSs while guaranteeing the user-specific minimum quality-of-service targets. The semidefinite relaxation (SDR) method is used to approximate the nonconvex multicast problem as a semidefinite program (SDP), which is solvable via centralized processing. Subsequently, two alternative distributed methods are proposed. The first approach turns the SDP into a two-level optimization via primal decomposition. At the higher level, intercell interference powers are optimized for fixed beamformers, whereas the lower level locally optimizes the beamformers by minimizing BS-specific transmit powers for the given intercell interference constraints. The second distributed solution is enabled via an alternating direction method of multipliers, where the intercell interference optimization is divided into a local and a global optimization by forcing the equality via consistency constraints. We further propose a centralized and a simple distributed beamforming design for the signal-to-interference-plus-noise ratio (SINR) balancing problem in which the minimum SINR among the users is maximized with given per-BS power constraints. This problem is solved via the bisection method as a series of SDP feasibility problems. The simulation results show the superiority of the proposed coordinated beamforming algorithms over traditional noncoordinated transmission schemes, and illustrate the fast convergence of the distributed methods. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a general framework to study the tradeoff between energy efficiency (EE) and spectral efficiency (SE) in massive multiple-input-multiple-output-enabled heterogenous networks while ensuring proportional rate fairness among users and taking into account the backhaul capacity constraint. We aim at jointly optimizing user association, spectrum allocation, power coordination, and the number of activated antennas, which is formulated as a multi-objective optimization problem maximizing EE and SE simultaneously. With the help of weighted Tchebycheff method, it is then transformed into a single-objective optimization problem, which is a mixed-integer non-convex problem and requires unaffordable computational complexity to find the optimum. Hence, a low-complexity effective algorithm is developed based on primal decomposition, where we solve the power coordination and number of antenna optimization problem and the user association and spectrum allocation problem separately. Both theoretical analysis and numerical results demonstrate that our proposed algorithm can fast converge within several iterations and significantly improve both the EE-SE tradeoff performance and rate fairness among users compared with other algorithms. [ABSTRACT FROM AUTHOR]

Analog transmission of correlated information over Gaussian broadcast channels (BCs) using analog joint source–channel coding (JSCC) is addressed. This communication strategy has attractive advantages, such as low complexity, minimal delay, graceful degradation, and adaptation to time-varying environments. In this paper, we focus on the optimization of parametric continuous mappings that satisfy individual quality of service requirements over Gaussian BCs. This optimization is based on the balancing of the user distortions to ensure the feasibility of the resulting optimization problems. An analysis of the overall distortion corresponding to the considered mappings is carried out to design algorithms that determine the optimal values for the mappings parameters. Results show that the proposed analog JSCC scheme provides near optimal performance and an adequate balancing of the individual distortions. [ABSTRACT FROM AUTHOR]

The exponential growth in data traffic and dramatic capacity demand in fifth generation (5G) have inspired the move from traditional single-tier cellular networks toward heterogeneous cellular networks (HCNs). To face the coming trend in 5G, the high availability requirement in new applications needs to be satisfied to achieve low latency service. Usually, these applications require an availability of six nines or even higher. In this paper, we present a tractable multitier multiband availability model for spectrum aggregation-based HCNs. We first derive a closed-form expression for the availability of spectrum aggregation-based HCNs using the signal-to-interference-plus-noise model. By doing so, we formulate two optimization problems, one is to maximize the average availability, and the other one is to minimize the average power consumption. These two optimization problems are both nonconvex problems, which are challenging to solve. To cope with them, we propose to apply genetic algorithm for the joint user equipment (UE) association, subcarrier assignment, and power allocation problem. Our results show that the average availability in spectrum aggregation-based HCNs improves with decreasing number of UEs, as well as increasing power budget ratio. We also show that increasing the maximum number of aggregated subcarriers decreases the average power consumption, but cannot guarantee the substantial improvement of average availability. [ABSTRACT FROM PUBLISHER]

This paper introduces a fair and energy-efficient resource allocation framework in spectrum-sharing wireless networks with quality-of-service guarantees. Consider the tradeoff between energy efficiency and spectral efficiency, the multiobjective problem of spectral efficiency and energy efficiency is transformed into a problem that minimizes the total power consumption and maximizes the achievable utility, subject to power constraints and rate outage probability constraints. We then analyze the complexity of the considered problem; particularly, the optimization problem is NP-Hard when $0 < \alpha < 1$ and $\alpha =0$ and is convex for other values of the fairness index $\alpha$. After that, we adopt the successive convex approximation (SCA) approach to approximate and transform the NP-hard nonconvex optimization problem into a sequence of convex programs and propose two iterative SCA-based resource allocation algorithms. Extensive simulation results are presented to demonstrate the effectiveness and outperformance of the proposed algorithms over existing frameworks. [ABSTRACT FROM PUBLISHER]

In this paper, we design an irregular low-density parity-check (LDPC) codes for unequal inter-symbol interference channels based on the modified extrinsic information transfer chart. During transmission, each LDPC codeword will be divided and transmitted to the different channels. The aim of this scheme is to avoid transmitting the whole codeword in a high error rate channel. The simulation results show that the proposed code optimized for both PR1 and PR2 channels can achieve a 0.2 coding gain over the codes designed specifically for each individual channel. When this simple code is applied to a perpendicular channel with these two targets, the coding gains of the proposed code is about 0.08 dB at the frame error rate of 10^-3 . [ABSTRACT FROM AUTHOR]

In this paper, the problem of the waveform design for colocated multiple-input multiple-output (MIMO) radars is considered in two parts. In the first part, we design transmit waveform in order to approximate the desired beampattern with low number of samples in the transmitter. Unlike the traditional waveform design methods, in our solution, waveforms are designed for a specific number of samples. Also, the constant envelope constraint that is an important practical constraint is considered. In the second part, we jointly design the transmit waveform and receive filter by a sequential algorithm, considering a priori information of target and interference angle locations. We have evaluated the performance of the proposed algorithms via numerical simulations and shown that the proposed algorithm in the first part is able to approximate the desired beampattern with low number of samples. Also, our method in the second part achieves better signal-to-interference-plus-noise ratio performance compared with the existing active sensing array methods (e.g., phased-array and correlated MIMO radars). [ABSTRACT FROM AUTHOR]

In heterogeneous networks (HetNets), load balancing among different tiers can be effectively achieved by a biased user association scheme with which each user chooses to associate with one base station (BS) based on the biased received power. In contrast to previous studies, where a BS always has packets to transmit, we assume in this paper that incoming packets intended for all the associated users form a queue in the BS. In order to find the delay limit of the network to support real-time service, we focus on the delay optimization problem by properly tuning the biasing factor of each tier. By adopting a thinned Poisson point process model to characterize the locations of BSs in the busy state, an explicit expression of the average traffic intensity of each tier is obtained. On that basis, an optimization problem is formulated to minimize a lower bound of the network mean queuing delay. By showing that the optimization problem is convex, the optimal biasing factor of each tier can be obtained numerically. When the mean packet arrival rate of each user is small, a closed-form solution is derived. The simulation results demonstrate that the network queuing performance can be significantly improved by properly tuning the biasing factor. It is further shown that the network mean queuing delay might be improved at the cost of a deterioration of the network signal-to-interference ratio coverage, which indicates a performance tradeoff between real-time and non-real-time traffic in HetNets. [ABSTRACT FROM AUTHOR]

In this paper, we consider a cellular downlink multiple-input-single-output (MISO) nonorthogonal multiple access (NOMA) secure transmission system, where users are grouped as multiple clusters. Each cluster consists of a central user and a cell-edge user. The central user is an entrusted user, and the cell-edge user is a potential eavesdropper. We focus on the secure beamforming and power allocation design optimization problem which maximizes the sum achievable secrecy rate of central users subject to the transmit power constraint at the base station and transmission rate requirements at cell-edge users. The problem is nonconvex because of coupling optimization variables in the considered fractional quadratically constrained quadratic programming. We propose an alternating optimization-based solution and a constrained concave–convex procedure-based solution to the considered problem. Simulation results demonstrate that our proposed NOMA schemes outperform the conventional orthogonal multiple access scheme. [ABSTRACT FROM AUTHOR]

This paper studies the achievable rates of Gaussian interference channels with additive white Gaussian noise (AWGN), when improper or circularly asymmetric complex Gaussian signaling is applied. For the Gaussian multiple-input multiple-output interference channel (MIMO-IC) with the interference treated as Gaussian noise, we show that the user's achievable rate can be expressed as a summation of the rate achievable by the conventional proper or circularly symmetric complex Gaussian signaling in terms of the users' transmit covariance matrices, and an additional term, which is a function of both the users' transmit covariance and pseudo-covariance matrices. The additional degrees of freedom in the pseudo-covariance matrix, which is conventionally set to be zero for the case of proper Gaussian signaling, provide an opportunity to further improve the achievable rates of Gaussian MIMO-ICs by employing improper Gaussian signaling. To this end, this paper proposes widely linear precoding, which efficiently maps proper information-bearing signals to improper transmitted signals at each transmitter for any given pair of transmit covariance and pseudo-covariance matrices. In particular, for the case of two-user Gaussian single-input single-output interference channel (SISO-IC), we propose a joint covariance and pseudo-covariance optimization algorithm with improper Gaussian signaling to achieve the Pareto-optimal rates. By utilizing the separable structure of the achievable rate expression, an alternative algorithm with separate covariance and pseudo-covariance optimization is also proposed, which guarantees the rate improvement over conventional proper Gaussian signaling. [ABSTRACT FROM PUBLISHER]

This paper presents a new unmixing methodology of multispectral fluorescence lifetime imaging microscopy (m-FLIM) data, in which the spectrum is defined as the combination of time-domain fluorescence decays at multiple emission wavelengths. The method is based on a quadratic constrained optimization (CO) algorithm that provides a closed-form solution under equality and inequality restrictions. In this paper, it is assumed that the time-resolved fluorescence spectrum profiles of the constituent components are linearly independent and known a priori. For comparison purposes, the standard least squares (LS) solution and two constrained versions nonnegativity constrained least squares (NCLS) and fully constrained least squares (FCLS) (Heinz and Chang, 2001) are also tested. Their performance was evaluated by using synthetic simulations, as well as imaged samples from fluorescent dyes and ex vivo tissue. In all the synthetic evaluations, the CO obtained the best accuracy in the estimations of the proportional contributions. CO could achieve an improvement ranging between 41% and 59% in the relative error compared to LS, NCLS, and FCLS at different signal-to-noise ratios. A liquid mixture of fluorescent dyes was also prepared and imaged in order to provide a controlled scenario with real data, where CO and FCLS obtained the best performance. The CO and FCLS were also tested with 20 ex vivo samples of human coronary arteries, where the expected concentrations are qualitatively known. A certainty measure was employed to assess the confidence in the estimations made by each algorithm. The experiments confirmed a better performance of CO, since this method is optimal with respect to equality and inequality restrictions in the linear unmixing formulation. Thus, the evaluation showed that CO achieves an accurate characterization of the samples. Furthermore, CO is a computational efficient alternative to estimate the abundance of components in m-FLIM data, since a global optimal solution is always guaranteed in a closed form. [ABSTRACT FROM PUBLISHER]

With macro and micro base stations (BSs) of different transmission and processing capabilities jointly deployed, heterogeneous networks effectively extend the coverage and capacity of wireless networks and have been adopted as one of the key technologies in Fourth-Generation-Long-Term Evolution (4G-LTE). To fully exploit the benefits of heterogeneous networks, proper mobile association, interference management, and radio resource management schemes need to be developed. In this paper, we investigate radio resource allocation for heterogeneous networks with cooperative relays, where the relay nodes (RNs) with in-band backhaul act as micro BSs and are able to serve user equipment (UE) either independently or cooperatively with the BSs. In such a network, radio resource-allocation schemes need to decide for each resource block: 1) whether a UE is served by a BS or an RN, and 2) whether a UE should be cooperatively served or not. In making these decisions, radio resource consumption on RN's in-band backhaul links and fairness among the UEs should be taken into consideration, which further complicates the resource-allocation problem. In this paper, we propose a radio resource-allocation framework and derive a resource-allocation strategy that is asymptotically optimal on the proportional fairness metric. The derived resource-allocation scheme gives insights on the optimal radio resource allocation for the heterogeneous networks with cooperative RNs using in-band backhauls. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate a max–min weighted signal-to-interference-plus-noise-ratio (SINR) problem in a full-duplex multiuser multiple-input-multiple-output system, where a full-duplex-capable base station (BS) equipped with multiple antennas communicates with multiple half-duplex downlink and uplink users under the same system resources. Specifically, we consider a practical scenario where the downlink minimum weighted SINR is maximized under specific SINR constraints for uplink users. Moreover, the optimization is conducted by jointly considering the BS transmit power, the transmit power of uplink users, and BS transmit and receive beamforming. This optimization problem is, therefore, subject to multiple uplink SINR constraints and multiple transmit power constraints. Due to the SINR constraints, negative matrix components arise and hence the optimization problem cannot be directly solved by the standard approach, i.e., Perron–Frobenius theory. We have provided an explicit iterative scheme to solve this joint optimization problem with a strict proof. The proposed algorithm is proved to converge to Karush–Kuhn–Tucker points. Simulation results show that our proposed algorithm has a fast convergence rate and leads to a better performance compared with other optimization techniques that do not jointly consider all parameters. [ABSTRACT FROM PUBLISHER]

Second order cone (SOC) restrictions have been widely employed in the design of wireless communication systems to recast precoding optimizations in convex form. This paper highlights the flexibility of this framework to handle various transmit power and interference limitations also in the multistream multiple-input multiple-output broadcast channel with imperfect channel state information at the transmitter. In particular, we propose an iterative solution for mean square error (MSE) balancing with such constraints via the Lagrangian dual formulation. The MSE balancing criteria, contrary to signal-to-interference plus-noise ratio and rate criteria, exhibit an interesting property when considering different targets for the receivers. Users with low target values are strictly prioritized in comparison to users with large MSE targets that can even be switched off. Therefore, only a subset of the receivers is served at the solution with stringent limitations for the precoders. An example of such stringent limitations are small power constraints and probabilistic interference temperature constraints that set a measurable threshold on the generated interference in a cognitive radio system. We provide four different approaches to approximate these probabilistic constraints with deterministic SOC constraints, and compare their accuracy. [ABSTRACT FROM PUBLISHER]

The characterization of the global maximum of energy efficiency (EE) problems in wireless networks is a challenging problem due to their nonconvex nature in interference channels. The aim of this paper is to develop a new and general framework to achieve globally optimal solutions. First, the hidden monotonic structure of the most common EE maximization problems is exploited jointly with fractional programming theory to obtain globally optimal solutions with exponential complexity in the number of network links. To overcome the high complexity, we also propose a framework to compute suboptimal power control strategies with affordable complexity. This is achieved by merging fractional programming and sequential optimization. The proposed monotonic framework is used to shed light on the ultimate performance of wireless networks in terms of EE and also to benchmark the performance of the lower-complexity framework based on sequential programming. Numerical evidence is provided to show that the sequential fractional programming framework achieves global optimality in several practical communication scenarios. [ABSTRACT FROM PUBLISHER]

Traditional cellular networks are moving toward heterogeneous cellular networks (HetNets) to satisfy the stringent demand for data rates and capacity. To enable the new applications in 5G, such as haptic communications, we face new challenges of achieving high availability with low latency in HetNets. In this paper, we introduce coordinated multi-point (CoMP) and carrier aggregation (CA) techniques in HetNets to guarantee the availability of all user equipment (UE), where the CoMP improves the single-path availability, and the CA enhances availability via multi-carrier gain combining. To characterize the availability, we first derive an exact closed-form expression for the availability of a random UE in a CoMP and CA-enabled HetNets. To achieve the maximum UE availability, we formulate a max-min optimization problem. To solve it, we then propose a two-step optimization algorithm (TSOA) and a joint (JTOA). The TSOA is based on heuristic algorithm for the optimal subcarrier assignment and UE association, and based on the Lagrangian dual method for the power allocation. The JTOA is based on genetic algorithm to achieve the interaction between the first step and the second step. Our results showcase the effective of our proposed JTOA, and the effective of the CoMP in availability improvement in HetNets. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate a coding strategy devised to increase the throughput in hybrid ARQ (HARQ) transmission over a block fading channel. In our approach, the transmitter jointly encodes a variable number of bits for the each round of HARQ. The parameters (rates) of this joint coding can vary and may be based on the negative acknowledgment provided by the receiver or, on the past (outdated) information about the channel states. These new degrees of freedom allow us to improve the match between the codebook and the channel states experienced by the receiver. The results indicate that gains obtained using the proposed cross-packet coding strategy are particularly notable for the large values of the throughput. In this region, the conventional HARQ fails to offer throughput improvement even if the number of transmission rounds is increased. We implement the proposed cross-packet HARQ using turbo codes, where we show that the theoretically predicted throughput gains materialize in practice; the implementation challenges are also discussed. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the power-allocation problem in orthogonal frequency-division multiplexing (OFDM)-based bidirectional cognitive radio (CR) relay networks. A joint optimization under the amplify-and-forward (AF) relaying protocol is formulated to maximize the throughput of secondary users (SUs) via power loading over different subcarriers at the three (two transceivers and a relay) nodes. For compatibility with practical systems, separate power constraints are considered at each transmitting node. Furthermore, to provide high-level protection to primary users (PUs) in underlay CR transmission, per-subcarrier-based interference constraints are assumed. For tractability of the solution, we adopt a decomposition framework where the joint power optimization (JPO) is split into two subproblems. Later, each subproblem is solved by exploiting the convex optimization techniques. Moreover, a low-complexity suboptimal solution of the joint power allocation at all nodes is also proposed. Simulation results are presented to validate the effectiveness of the proposed schemes. [ABSTRACT FROM AUTHOR]

In this paper, the problem of optimal power allocation over flat fading additive white Gaussian noise channels is considered for maximizing the average detection probability of a signal emitted from a power constrained transmitter in the Neyman–Pearson framework. It is assumed that the transmitter can perform power adaptation under peak and average power constraints based on the channel state information fed back by the receiver. Using results from measure theory and convex analysis, it is shown that this optimization problem, which is in general nonconvex, has an equivalent Lagrangian dual that admits no duality gap and can be solved using dual decomposition. Efficient numerical algorithms are proposed to determine the optimal power allocation scheme under peak and average power constraints. Furthermore, the continuity and monotonicity properties of the corresponding optimal power allocation scheme are characterized with respect to the signal-to-noise ratio for any given value of the false alarm probability. Simulation examples are presented to corroborate the theoretical results and illustrate the performance improvements due to the proposed optimal power allocation strategy. [ABSTRACT FROM PUBLISHER]

In this paper, we propose an algorithm for robustly fusing digital surface models (DSMs) with different ground sampling distances and confidences, using explicit surface priors to obtain locally smooth surface models. Robust fusion of the DSMs is achieved by minimizing the L1-distance of each pixel of the solution to each input DSM. This approach is similar to a pixel-wise median, and most outliers are discarded. We further incorporate local planarity assumption as an additional constraint to the optimization problem, thus reducing the noise compared with pixel-wise approaches. The optimization is also inherently able to include weights for the input data, therefore allowing to easily integrate invalid areas, fuse multiresolution DSMs, and to weight the input data. The complete optimization problem is constructed as a variational optimization problem with a convex energy functional, such that the solution is guaranteed to converge toward the global energy minimum. An efficient solver is presented to solve the optimization in reasonable time, e.g., running in real time on standard computer vision camera images. The accuracy of the algorithms and the quality of the resulting fused surface models are evaluated using synthetic data sets and spaceborne data sets from different optical satellite sensors. [ABSTRACT FROM AUTHOR]

In practical scenarios with random arrival and departure of primary users (PUs), existing simultaneous sensing and transmission schemes allocated the same weight to each sample, and did not consider low signal-to-noise ratio (SNR) situations. This paper proposes an adaptive weighted sensing scheme with simultaneous transmission for dynamic PU traffic. It uses a power function based on the corresponding sampling sequence and could reveal the actual PU state in near real time. The power exponent is further adjusted to the sensing situations to achieve lowest false alarm probability under a certain detection probability constraint. Then, an analytical model considering all possible PU state transitions is developed to evaluate achievable interference, throughput, and energy efficiency. Furthermore, the optimal frame duration yielding both optimal false alarm probability and throughput is computed. After that, a fast search algorithm is proposed to track the optimal duration at an exponential convergence rate. Simulation results are provided to validate the analytical model and demonstrate the improvement in low SNR. The results indicate that the proposed scheme can achieve lower false alarm probability and higher energy efficiency over a wide SNR range than that of the existing weighting schemes, which are based on probability, geometric sequence, and equal weighting. [ABSTRACT FROM AUTHOR]

A full-duplex (FD) two-way relay channel (TWRC) with multiple antennas is considered. For this three-node network, the beamforming design needs to suppress self-interference (SI). While a traditional way is to apply zero forcing (ZF) for SI mitigation, it may harm the desired signals. In this paper, a design that reserves a fraction of SI is proposed by solving a quality-of-service (QoS) constrained beamforming design problem. Since the problem is challenging due to the loop SI, a convergence-guaranteed alternating optimization (AO) algorithm is proposed to jointly design the relay–user beamformers. Numerical results show that the proposed scheme outperforms ZF method and achieves a transmit power value close to the ideal case. [ABSTRACT FROM PUBLISHER]

In this paper, we conduct the joint design of transmitting sequence(s) and receiving filters subject to the Peak-to-Average Ratio (PAR) constraint in radar and communications applications. We consider optimizing the worst-case performance and the resulting optimization problem takes a maximin format. We propose two algorithms based on the MM (Majorization–Minimization or Minorization–Maximization) method as opposed to the traditional epigraph-based smooth reformulation. On top of that, both algorithms are guaranteed to converge to a B(oulingand)-stationary solution, and B-stationarity is the appropriate stationarity condition for problems with a nonconvex constraint set. The proposed algorithms successively solve a series of simple convex problems that enjoy low computational complexity. Numerical simulations have shown that the proposed algorithms empirically achieve slightly higher objective values and converge faster in terms of CPU time than the existing methods. [ABSTRACT FROM PUBLISHER]

Small cells are introduced to cellular systems to enhance coverage and improve capacity. Densely deploying small cells can not only offload the traffic of macrocells but also provide an energy- and cost-efficient way to meet the sharp increase in traffic demands in mobile networks. However, such a cell deployment paradigm also leads to heterogeneous network (HetNet) infrastructure and raises new challenges for cell planning. In this paper, we study the cell planning issue in the HetNet. Our optimization task is to select a subset of candidate sites to deploy macro or small cells to minimize the total cost of ownership (TCO) or the energy consumption of the cellular system while satisfying practical constraints. We introduce approximation algorithms to cope with two different cell-planning cases, which are both NP-hard. First, we discuss the macrocell-only case. Our proposed algorithm achieves an approximation ratio of O(\log R) in this scenario, where R is the maximum achievable capacity of macrocells. Then, we introduce an O(\log \widetildeR)-approximation algorithm to the small-cell scenario, where \widetildeR is the maximum achievable capacity of a macrocell with small cells overlaid on it. Numerical results indicate that the HetNet can significantly reduce the TCO and the energy consumption of the cellular system. [ABSTRACT FROM PUBLISHER]

Compared to the different brain signals used in brain–computer interface (BCI) paradigms, the s teady-state visually evoked potential (SSVEP) features a high signal to noise ratio, enabling reliable and fast classification of neural activity patterns without extensive training requirements. In this paper, we present methods to further increase the information transfer rates (ITRs) of SSVEP-based BCIs. Starting with stimulus parameter optimizations methods, we develop an improved approach for the use of Canonical correlation analysis and analyze properties of the SSVEP when the user fixates a target and during transitions between targets. These transitions show a negative effect on the system's ITR which we trace back to delays and dead times of the SSVEP. Using two classifier types adapted to continuous and transient SSVEPs and two control modes (fast feedback and fast input), we present a simulated online BCI implementation which addresses the challenges introduced by transient SSVEPs. The resulting system reaches an average ITR of 181 Bits/min and peak ITR values of up to 295 Bits/min for individual users. [ABSTRACT FROM AUTHOR]

MIMO radar receivers need to reliably separate waveforms originating from different transmitters while suppressing interference for effective operation. In order to achieve this goal, mismatched filters may be employed at the receivers. By using mismatched filters, it is possible to reduce the power of the interference while strictly controlling the autocorrelation sidelobe and peak cross-correlation levels of the received waveforms. In this paper, we propose a mismatched filter design method that minimizes interference and jamming power at the filter output while the peak sidelobe and cross-correlation levels for all Doppler frequencies are constrained to desired values. The proposed design method is formulated as an optimization problem employing sum-of-squares representation of non-negative polynomials and solved using semidefinite relaxation. It is demonstrated that good interference suppression performance is achieved even when using an estimated covariance matrix. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the relay selection and power allocation (RSPA) problem in amplify-and-forward (AF) relaying networks. The objective is to minimize the outage probability at the receiver, assuming that only the mean channel gain information is available. By taking advantage of its special structure, we propose to decompose the RSPA problem into two tractable subproblems, which can be implemented in a semidistributed manner. For the relay selection (RS) subproblem, a relay-ordering-based scheme is designed to incrementally select a subset of relays from the candidate nodes according to a specific metric in a centralized manner, which is dominated by the mean channel gain of each individual nodes. For the power allocation (PA) subproblem, a source-driven iterative algorithm is proposed for each relay to decide its optimal transmit power locally by exploiting the convexity of this subproblem. Simulation results are provided to evaluate the outage and signal-to-noise-ratio (SNR) performance of the proposed scheme under different channel conditions. It is shown that the proposed scheme can dynamically select relays and adjust power allocation according to the SNR and channel conditions. It outperforms the other two benchmark schemes, and the performance is close to the optimal scheme with exhaustive search, but the computational complexity is significantly reduced. [ABSTRACT FROM AUTHOR]

Growing attention has been paid to renewable- or hybrid-energy-powered heterogeneous networks (HetNets). In this paper, focusing on backhaul-aware joint user association and resource allocation for this type of HetNets, we formulate an online optimization problem to maximize the network utility reflecting proportional fairness. Since user association and resource allocation are tightly coupled not only on resource consumption of the base stations (BSs) but in the constraints of their available energy and backhaul as well, the closed-form solution is quite difficult to obtain. Thus, we solve the problem distributively by employing certain decomposition methods. Specifically, at first, by adopting the primal decomposition method, we decompose the original problem into a lower level resource-allocation problem for each BS and a higher level user-association problem. For the optimal resource allocation, we prove that a BS either assigns equal normalized resources or provides an equal long-term service rate to its served users. Then, the user-association problem is solved by the Lagrange dual decomposition method, and a completely distributed algorithm is developed. Moreover, applying results of the subgradient method, we demonstrate the convergence of the proposed distributed algorithm. Furthermore, to efficiently and reliably apply the proposed algorithm to the future wireless networks with an extremely dense BS deployment, we design a virtual user association and resource allocation scheme based on the software-defined networking architecture. Finally, numerical results validate the convergence of the proposed algorithm and the significant improvement on network utility, load balancing, and user fairness. [ABSTRACT FROM PUBLISHER]

In this paper, we present a joint antenna beamforming and power allocation technique to maximize the multiuser sum rate in an underlying microcellular system which reuses the same spectrum of a macrocellular system. One challenge in this kind of hierarchical cognitive radio (HCR) systems is to manage the interference between the macrocell and the microcell. The key contribution of this paper is to develop an optimization technique for antenna beamforming that can maximize the achievable sum rate of the underlying cognitive radio (CR) microcellular system and control the interference between the macrocell and the microcell with a satisfaction level. The proposed technique optimizes the sum rate performance by maximizing its lower bound and transfers the original non-convex problem into a convex optimization problem by introducing auxiliary variables to confine the intra-user interference power among the secondary system. Next, an iterative sum rate maximization (ISM) algorithm is developed to find the beamforming weights and the allocated power for each secondary user to simultaneously maximize system sum rate, coverage, and concurrent multiuser transmission probability in the HCR system. The developed joint design methodology provides valuable insights into the design of an optimal HCR system for various numbers of users as well as cell coverage, and can quantitatively optimize the performance tradeoffs in the hierarchical multiuser CR systems for current and future wireless communication applications. [ABSTRACT FROM PUBLISHER]

Non-Uniform Constellations (NUC) have been introduced in ATSC 3.0 (Advanced Television Systems Committee - Third Generation) as one of the main novelties to improve the performance compared to uniform Quadrature Amplitude Modulation (QAM) constellations. NUCs are optimized by means of signal geometrical shaping, considering the signal-to-noise ratio (SNR) and the channel model. ATSC 3.0 implements two types of NUC, depending on the number of real-valued dimensions in which they are optimized: 1D-NUC and 2D-NUC. However, the gain of NUCs becomes almost non-existent at high SNRs, especially when optimizing for fading channels. In that particular case, Rotated Constellations (RC) can be used to further improve the overall system performance. RCs may become especially effective when using multi-radio frequency (multi-RF) SNR averaging techniques such as Channel Bonding (CB) or Time-Frequency Slicing (TFS), where in-phase (I) and quadrature (Q) components are transmitted in different RF channels. 2D-NUCs can be rotated without increasing the demapping complexity, since a 2D-demapper is also needed. In this paper, we propose an optimization method designed for rotated 2D-NUCs, in which the rotation angle is considered as an additional variable, together with the symbol positions. The SNR gain obtained in fading channels is also provided for three different use cases: single-RF transmissions, CB with 2 RF channels as adopted in ATSC 3.0, and extension of multi-RF techniques to 4 RF channels. [ABSTRACT FROM PUBLISHER]

In this paper, we revisit the design of Raptor codes for binary input additive white Gaussian noise channels, where we are interested in very low signal to noise ratios (SNRs). A linear programming degree distribution optimization problem is defined for Raptor codes in the low SNR regime through several approximations. We also provide an exact expression for the polynomial representation of the degree distribution with infinite maximum output node degree in the low SNR regime, which enables us to calculate the exact value of the fractions of output nodes of small degrees. A more practical degree distribution design is also proposed for Raptor codes in the low SNR regime, where we include the rate efficiency and the decoding complexity in the optimization problem, and an upper bound on the maximum rate efficiency is derived for given design parameters. Simulation results show that the Raptor code with the designed degree distributions can approach rate efficiencies larger than 0.95 in the low SNR regime. [ABSTRACT FROM PUBLISHER]

Heterogeneous network deployment is considered to be among the most promising approaches to meet the demand for increasing communication capacity. The concept is that of increasing the number of cells while reducing their size to provide different layers of coverage. This paper proposes a coordinated method to face the interlayer and intralayer interference caused by the overlapping of heterogeneous cells. The aim is to exploit the benefits of both enhanced intercell interference coordination (eICIC) and coordinated multipoint (CoMP) approaches and to limit, at the same time, their drawbacks by means of their optimized joint use. The idea devised here is to build an ad hoc CoMP system on top of a basic eICIC mechanism. Therefore, the analysis focuses on the dynamic selection of users and cells involved in CoMP operations, with the goal of minimizing the unfulfilled data rate requests (UDRRs). Due to the computational complexity of the optimal solution, we propose a heuristic procedure and validate its accuracy by providing a comparison with the optimal numerical solution. In particular, our results show that the proposed method outperforms other benchmark solutions in terms of UDRRs and signaling overhead. [ABSTRACT FROM PUBLISHER]

In this paper, we consider a dual-hop amplify-and-forward (AF) multiple-input–multiple-output (MIMO) relay network, where the source, relay, and destination are each equipped with multiple antennas. The relay is untrusted if it is willing to forward the signal to the destination and, at the same time, acts as a potential eavesdropper to interpret the message from the source. Since there exists no direct link between the source and the destination, a positive secrecy rate cannot be obtained. Addressing this issue, we propose a joint destination-aided cooperative jamming and precoding at both the source and the relay scheme: joint source, relay, and destination precoding (JP). We target at maximizing the secrecy rate by jointly designing the source, relay, and destination precoding matrices and propose an alternating iterative optimization algorithm to tackle the nonconvex problem. Then, a comprehensive study on the asymptotic performance is conducted in a high signal-to-noise ratio (SNR) regime. In particular, we present simple closed-form expressions for the two key performance parameters in the asymptotic secrecy rate, i.e., the high-SNR slope and the high-SNR power offset. Finally, numerical results are conducted to demonstrate the validity of the proposed secure scheme and its performance analysis. [ABSTRACT FROM PUBLISHER]

In heterogeneous networks (HetNets), the load between macrocell base stations (MBSs) and small-cell base stations (SBSs) is imbalanced due to their different transmission powers and locations. This load imbalance significantly impacts system performance and affects the experience of mobile users (MUs) with different priorities. In this paper, we aim to distributively optimize the user association in HetNets with various user priorities to solve the load balancing problem. Since the user association is a binary matching problem, which is NP-hard, we propose a distributed belief propagation (BP) algorithm to approach the optimal solution. We first develop a factor graph model, using the network topology, to represent this user association problem. With this factor graph, we propose a novel distributed BP algorithm by adopting the proportional fairness as the objective. Next, we theoretically prove the existence of the fixed point in our BP algorithm. To be more practical, we develop an approximation method to significantly reduce the computational and communication complexity of the BP algorithm. Furthermore, we analyze some properties of the factor graph relevant to the performance of the BP algorithm using the stochastic geometry. Simulation results show that 1) the proposed BP algorithm well approaches the optimal system performance and achieves a much better performance compared with other association schemes and that 2) the analytical results on the average degree distribution and sparsity of the factor graph match with those obtained from the Monte Carlo simulations. [ABSTRACT FROM PUBLISHER]

In this paper, the energy efficiency (EE) of multihop relaying over Nakagami- $m$ fading channels is investigated. The “consumption factor” (CF), which is adopted as a metric to evaluate the EE, is derived for both amplify-and-forward and decode-and-forward relaying strategies. Then, based on the obtained expressions, we propose a power-allocation (PA) strategy maximizing the CF. In addition, a suboptimal low-complexity PA algorithm is proposed and analyzed, and the obtained PA scheme is compared in terms of EE with other PA schemes from the literature. Analytical and simulation results confirm the accuracy of our derivations and assess the performance gains of the proposed approach. [ABSTRACT FROM PUBLISHER]

In this paper, we analyze the problem of power control in large, random wireless networks that are obtained by “erasing” a finite fraction of nodes from a regular $d$ -dimensional lattice of $N$ transmit-receive pairs. In this model, which has the important feature of a minimum distance between transmitter nodes, we find that when the network is infinite, power control is always feasible below a positive critical value of the users’ signal-to-interference-plus-noise ratio (SINR) target. Drawing on tools and ideas from statistical physics, we show how this problem can be mapped to the Anderson impurity model for diffusion in random media. In this way, by employing the so-called coherent potential approximation method, we calculate the average power in the system (and its variance) for 1-D and 2-D networks. This approach is equivalent to traditional techniques from random matrix theory and is in excellent agreement with the numerical simulations; however, it fails to predict when power control becomes infeasible. In this regard, even though infinitely large systems are always unstable beyond a critical value of the users’ SINR target, finite systems remain stable with high probability even beyond this critical SINR threshold. We calculate this probability by analyzing the density of low lying eigenvalues of an associated random Schrödinger operator, and we show that the network can exceed this critical SINR threshold by at least $ \mathop {{\mathcal O}}\nolimits ((\log N)^{-2/d})$ before undergoing a phase transition to the unstable regime. Finally, using the same techniques, we also calculate the tails of the distribution of transmit power in the system and the rate of convergence of the Foschini–Miljanic power control algorithm in the presence of random erasures. [ABSTRACT FROM PUBLISHER]

Direct device-to-device (D2D) links are proposed as a possible enabler for vehicle-to-vehicle (V2V) communications, where the incurred intracell interference and the stringent latency and reliability requirements are challenging issues. In this paper, we investigate the radio resource management problem for D2D-based V2V communication. First, we analyze and transform the latency and reliability requirements of V2V communication into optimization constraints that are computable using only the slowly varying channel information. This transformation opens up the possibility of extending certain existing D2D techniques to cater to V2V communication. Second, we propose a problem formulation that fulfills the different requirements of V2V communication and traditional cellular communication. Moreover, a Separate resOurce bLock and powEr allocatioN (SOLEN) algorithm is proposed to solve this problem. Finally, simulations are presented to evaluate different schemes, which illustrate the necessity of careful design when extending D2D methods to V2V communication, as well as show promising performance of the proposed SOLEN algorithm. [ABSTRACT FROM AUTHOR]

The cellular communications scenario involving the coexistence of the one-hop direct transmission and the two-hop relaying is studied in this paper. In contrast to conventional cellular systems featuring orthogonal information flows served by decoupled channel resources via, e.g., time division, we propose a novel protocol in which two information flows are served simultaneously via the shared channel resource, thus constituting a spectral-efficient solution for cellular communications. On the other hand, however, an inevitable issue associated with the proposed protocol is the interflow interference, which may lead to serious deterioration on both information flows. To tackle this issue, we develop an overhearing-based protocol that utilizes the overheard interference as useful side information in the receiver design. Specifically, depending on the interference levels, an adaptive linear minimum mean squared error (MMSE) and nonlinear MMSE successive interference cancellation (SIC) receiver exploiting the overheard interference at the direct mobile terminal is developed. To balance between the two information flows, we develop the asymptotically optimum superposition coding at the base station (BS) in the high-power regime. Furthermore, the optimum relay beamforming matrix maximizing the bottleneck of the achievable rates of the two information flows is developed subject to a finite power constraint. Finally, simulations demonstrate a remarkable throughput gain over the conventional cellular systems. [ABSTRACT FROM AUTHOR]

The ultimate efficiency of a wireless network is achieved when various resources are allocated in a joint optimization process. This paper proposes the optimal solution for a joint power allocation and relay assignment (JPARA) problem subject to the sum-power constraint at the source node. This formulation is applicable to different system models. Specifically, we assume a network consisting of one source node, one destination node, and $N$ relays, where the source node uses orthogonal frequency-division multiplexing (OFDM) to transmit its information to the destination. Each relay should be assigned to one of the subcarriers, and the source node should distribute its power among the subcarriers. We propose an algorithm to find the JPARA solution based on the max-min criterion. The optimality of the proposed algorithm is analytically proved, and its complexity is calculated to be $O(N^4)$. We show that our proposed algorithm offers significant improvement in the performance of the worst end-to-end link compared with the separate optimization case. To further improve the performance, a new approach is proposed, in which each subcarrier is assigned a predetermined initial power, and the remaining power is distributed through the proposed JPARA algorithm. [ABSTRACT FROM AUTHOR]

This paper studies the information-theoretic metric of outage probability for a half-duplex asymmetric two-way amplify-and-forward (AF) relaying. Unlike current research activities, our main purpose is to examine the impact of traffic asymmetry on system outage probability. First, an exact but two-integral-form outage probability is derived over Rayleigh fading channels. To provide more insight, a closed-form asymptotic outage probability is then obtained. It is shown that the outage probability in the system is determined only by the one-way channel or related to the two-way links, depending on the asymmetric level of the two senders' target rates and the terminals' average transmission powers. Following this analysis, optimum power allocation and opportunistic relay selection are studied to optimize the overall performance of the considered AF scenario. Next, with the aid of traffic knowledge, novel power allocation and relay selection criteria are proposed, followed by an analysis of the outage probability with the relay selection. Simulation experiments are performed to validate the proposed studies in this paper. The results show that the proposed power allocation and relay selection methods can achieve significant performance gains in terms of outage probability, regardless of symmetric or asymmetric traffic and channels. [ABSTRACT FROM PUBLISHER]

This paper considers maximizing the network-wide minimum supported rate in the downlink of a two-cell system, where each base station (BS) is endowed with multiple antennas. This is done for different levels of cell cooperation. At one extreme, we consider single cell processing where the BS is oblivious to the interference it is creating at the other cell. At the other extreme, we consider full cooperative macroscopic beamforming. In between, we consider coordinated beamforming, which takes account of inter-cell interference, but does not require full cooperation between the BSs. We combine elements of Lagrangian duality and large system analysis to obtain limiting SINRs and bit-rates, allowing comparison between the considered schemes. The main contributions of the paper are theorems which provide concise formulas for optimal transmit power, beamforming vectors, and achieved signal to interference and noise ratio (SINR) for the considered schemes. The formulas obtained are valid for the limit in which the number of users per cell, K, and the number of antennas per base station, N, tend to infinity, with fixed ratio \beta=K/N. These theorems also provide expressions for the effective bandwidths occupied by users, and the effective interference caused in the adjacent cell, which allow direct comparisons between the considered schemes. [ABSTRACT FROM AUTHOR]

This paper addresses the optimal design of limited-feedback downlink multiuser spatial multiplexing systems. A multiple-antenna base-station is assumed to serve multiple single-antenna users, who quantize and feed back their channel state information (CSI) through a shared rate-limited feedback channel. The optimization problem is cast in the form of minimizing the average transmission power at the base-station subject to users' target signal-to-interference-plus-noise ratios (SINR) and outage probability constraints. The goal is to derive the feedback bit allocations among the users and the corresponding channel magnitude and direction quantization codebooks in a high-resolution quantization regime. Toward this end, this paper develops an optimization framework using approximate analytical closed-form solutions, the accuracy of which is then verified by numerical results. The results show that, for channels in the real space, the number of channel direction quantization bits should be (M-1) times the number of channel magnitude quantization bits, where M is the number of base-station antennas. Moreover, users with higher requested quality-of-service (QoS), i.e., lower target outage probabilities, and higher requested downlink rates, i.e., higher target SINR's, should use larger shares of the feedback rate. It is also shown that, for the target QoS parameters to be feasible, the total feedback bandwidth should scale logarithmically with the geometric mean of the target SINR values and the geometric mean of the inverse target outage probabilities. In particular, the minimum required feedback rate is shown to increase if the users' target parameters deviate from the corresponding geometric means. Finally, the paper shows that, as the total number of feedback bits B increases, the performance of the limited-feedback system approaches the perfect-CSI system as 2-B/M2. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the game theoretical approach in designing the multiuser downlink beamformers in multicell systems. Sharing the same physical resource, the base-station of each cell wishes to minimize its transmit power subject to a set of target signal-to-interference-plus-noise ratios (SINRs) at the multiple users in the cell. In this context, at first, the paper considers a strategic noncooperative game (SNG) where each base-station greedily determines its optimal downlink beamformer strategy in a distributed manner, without any coordination between the cells. Via the game theory framework, it is shown that this game belongs to the framework of standard functions. The conditions guaranteeing the existence and uniqueness of a Nash Equilibrium (NE) in this competitive design are subsequently examined. The paper then makes a revisit to the fully coordinated design in multicell downlink beamforming, where the optimal beamformers are jointly designed between the base-stations. A comparison between the competitive and coordinated designs shows the benefits of applying the former over the latter in terms of each design's distributed implementation. Finally, in order to improve the efficiency of the NE in the competitive design, the paper considers a more cooperative game through a pricing mechanism. The pricing consideration enables a base-station to steer its beamformers in a more cooperative manner, which ultimately limits the interference induced to other cells. The study on the existence and uniqueness of the new game's NE is then given. The paper also presents a condition on the pricing factors that allow the new NE point to approach the performance established by the coordinated design, while retaining the distributed nature of the multicell game. [ABSTRACT FROM PUBLISHER]

This paper studies the design and optimization of a limited feedback single-user system with multiple-antenna transmitter and single-antenna receiver. The design problem is cast in form of the minimizing the average transmission power at the base station subject to the user's outage probability constraint. The optimization is over the user's channel quantization codebook and the transmission power control function at the base station. Our approach is based on fixing the outage scenarios in advance and transforming the design problem into a robust system design problem. We start by showing that uniformly quantizing the channel magnitude in dB scale is asymptotically optimal, regardless of the magnitude distribution function. We derive the optimal uniform (in dB) channel magnitude codebook and combine it with a spatially uniform channel direction codebook to arrive at a product channel quantization codebook. We then optimize such a product structure in the asymptotic regime of B \ura \infty, where B is the total number of quantization feedback bits. The paper shows that for channels in the real space, the asymptotically optimal number of direction quantization bits should be (M-1)/2 times the number of magnitude quantization bits, where M is the number of base station antennas. We also show that the performance of the designed system approaches the performance of the perfect channel state information system as 2^- 2B/(M+1). For complex channels, the number of magnitude and direction quantization bits are related by a factor of (M-1) and the system performance scales as 2^- B/M as B \ura \infty. [ABSTRACT FROM AUTHOR]