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This paper develops a methodology for finding minimum energy per bit in networks with correlated information, without at need for finding bounds on capacity. This is used to derive the exact minimum energy per bit for some broadcast and interference channels with common and correlated messages, and bounds on the minimum energy per bit for some other channels. [ABSTRACT FROM PUBLISHER]

In the scalar dirty multiple-access channel, in addition to Gaussian noise, two additive interference signals are present, each known non-causally to a single transmitter. It was shown by Philosof et al. that for strong interferences, an independent identically distributed ensemble of codes does not achieve the capacity region. Rather, a structured-codes approach was presented that was shown to be optimal in the limit of high signal-to-noise ratios, where the sum capacity is dictated by the minimal (“bottleneck”) channel gain. In this paper, we consider the multiple-input multiple-output (MIMO) variant of this setting. In order to incorporate structured codes in this case, one can utilize matrix decompositions that transform the channel into effective parallel scalar dirty multiple-access channels. This approach, however, suffers from a “bottleneck” effect for each effective scalar channel and, therefore, the achievable rates strongly depend on the chosen decomposition. It is shown that a recently proposed decomposition, where the diagonals of the effective channel matrices are equal up to a scaling factor, is optimal at high signal-to-noise ratios, under an equal rank assumption. This approach is then extended to any number of transmitters. Finally, an application to physical-layer network coding for the MIMO two-way relay channel is presented. [ABSTRACT FROM AUTHOR]

In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers via a Gaussian multiple-input multiple-output (MIMO) broadcast channel. An eavesdropper also receives the transmitted signal via another MIMO channel. We first consider the discrete memoryless channel and obtain the capacity region of the degraded channel. The secret dirty paper coding (SDPC) region as an achievable rate region for the general discrete channel is introduced. Relying on the results for the discrete channel, we fully characterize the secrecy capacity region of MIMO broadcast channel. It is shown that the SDPC scheme is optimal. The converse part of the proof relies on the generalized Costa's entropy power inequality and a new channel enhancement strategy in which we only need to enhance the channels of the legitimate receivers, and the channel of the eavesdropper remains unchanged. [ABSTRACT FROM PUBLISHER]

Existing research on a simultaneous wireless information and power transfer (SWIPT) system is based on the assumption of Gaussian inputs. However, the optimal design on Gaussian inputs may lead to dramatic performance loss for practical systems with finite-alphabet inputs. This paper focuses on the precoder design for a SWIPT system with finite-alphabet inputs and instantaneous channel state information over a multiple-input multiple-output channel. We formulate the optimal precoder design as an optimization problem, in which the objective is to maximize the mutual information over the channel from the transmitter to the information receiver under the constraints of transmit power and harvested energy threshold. The formulated problem is NP-hard, so a global optimal solution cannot be found within the polynomial time. The main contributions of this paper are as follows: 1) By using its structure, the NP-hard problem is relaxed to a semidefinite programming problem. Then, a general solving framework for both co-located and separated receiver cases, based on the semidefinite relaxation (SDR) technique, is developed to achieve a near optimal precoder. 2) For the case of co-located receivers, we show that the optimal precoder design is a concave problem with respect to power allocation; then, a specific algorithm for co-located receivers is proposed. Compared with the general SDR-based method, the specific algorithm for co-located receivers exhibits almost the same performance but much lower complexity. 3) The performance of several practical co-located receiver designs is analyzed in SWIPT systems with finite-alphabet inputs. Finally, we provide simulation results to show the efficacy of the proposed algorithms. [ABSTRACT FROM PUBLISHER]

A common model for transmission over wireless links is that of a multiantenna system affected by an additive interfering signal. In some scenarios of interest, such as when the interferer is located close to the transmitter and performs retransmission, interference may be learned by the transmitter, but remain unknown at the receiver. In this case, it is well known that, if transmitter and receiver have perfect channel state information (CSI), then a technique called Dirty Paper Coding (DPC) is able to fully mitigate the interference. This paper studies the impact of imperfect CSI on a multiple-input multiple-output (MIMO) system with interference and compares the performance of DPC with that of a scheme where interference is decoded at the receiver, which we refer to as beamforming with joint decoding (BF-JD). Unlike DPC, which models the interference as an "unstructured" random process, BF-JD exploits the fact that the interfering signal is a codeword of the interferer's codebook. It is demonstrated by analysis and numerical results that BF-JD provides advantages over DPC when CSI is imperfect at the transmitter but perfect at the receiver, whereas this is not true for the case of imperfect CSI at both transmitter and receiver. [ABSTRACT FROM AUTHOR]

Building on the recent coded-caching breakthrough by Maddah-Ali and Niesen, the work here considers the $K$ -user cache-aided wireless multi-antenna symmetric broadcast channel with random fading and imperfect feedback, and analyzes the throughput performance as a function of feedback statistics and cache size. In this setting, this paper identifies the optimal cache-aided degrees-of-freedom (DoF) within a factor of 4, by identifying near-optimal schemes that exploit a new synergy between coded caching and delayed CSIT, as well as by exploiting the unexplored interplay between caching and feedback-quality. The DoF expressions reveal an initial gain due to current CSIT, and an additional gain due to coded caching, which is exponential in the sense that any linear decrease in the required DoF performance, allows for an exponential reduction in the required cache size. In the end, this paper reveals three new aspects of caching: a synergy between memory and delayed feedback, a tradeoff between memory and current CSIT, and a powerful ability to provide cache-aided feedback savings. [ABSTRACT FROM PUBLISHER]

In this paper, precoder designs are proposed for the wireless X networks aided by a relay and with no or very limited channel state information at the transmitters (CSIT). First, we derive the general feasibility conditions for interference alignment (IA) for a relay-aided symmetric multi-input-multi-output X channel (also called the X relay channel or XRC) without any CSI at the source transmitters. Next, we propose an IA-based joint beamforming approach with very limited feedback to the transmitters (referred to as “IA-LFB” in this paper), which can attain the maximum degrees of freedom (DoF) of the network under arbitrarily low relay power. Finally, we propose an iterative minimum-sum mean-square-error (MMSE) precoder design for the single-input-single-output XRC for throughput improvement in the finite signal-to-noise ratio (SNR) region. The proposed MMSE precoder also shows better bit error rate results than the IA precoder over a wide SNR range. Since the MMSE precoder can achieve only locally optimal solutions, we propose to initialize the iterative MMSE algorithm with the IA-LFB precoder which, unlike random initializations, not only improves the throughput in the finite SNR regions but also preserves the network DoF even under limited relay power. [ABSTRACT FROM AUTHOR]

The degrees of freedom (DoFs) of the $K$ -user multiple-input multiple-output (MIMO) interference channel are studied when perfect, but delayed channel state information is available at the transmitter side (delayed CSIT). Recent works have proposed schemes improving the DoF knowledge of the interference channel, but at the cost of developing transmission involving many channel uses (long delay), thus increasing the complexity at both transmitter and receiver side. This paper proposes three linear precoding strategies, limited to at most three phases, based on the concept of interference alignment, and built upon three main ingredients: delayed CSIT precoding, user scheduling, and redundancy transmission. In this respect, the interference alignment is realized by exploiting delayed CSIT to align the interference at the non-intended receivers along the space-time domain. Moreover, a new framework is proposed where the number of transmitted symbols and duration of the phases is obtained as the solution of a maximization problem, and enabling the introduction of complexity constraints, which allows deriving the achievable DoF as a function of the transmission delay, i.e., the achievable DoF-delay trade-off. Finally, the latter part of this paper settles that the assumption of time-varying channels common along all the literature on delayed CSIT is indeed unnecessary. [ABSTRACT FROM PUBLISHER]

In this paper, we propose regularized block diagonalization (RBD) precoding using artificial noise (AN) for physical layer security in downlink multi-user MIMO wireless networks. We derive secrecy sum rate and asymptotic secrecy sum rate for the proposed scheme. The optimum power allocation for legitimate users and the AN signal are derived in closed form for optimal asymptotic secrecy sum rate. Our analysis shows that to achieve best performance, it is more efficient to degrade the performance of the eavesdropper than improving legitimate users’ rates. We also study the impact of error in channel estimation on the system and derive closed-form SINR and secrecy sum-rate expressions for this case. Simulations show that the secrecy sum rate of RBD precoding outperforms the secrecy sum rate of regularized channel inversion by 0.5 bits/s/Hz. We also show that in the presence of channel estimation error, our approximate closed forms for secrecy sum rate are very closed to the actual secrecy sum rate over a wide range of SNR and channel estimation error values. [ABSTRACT FROM AUTHOR]

The beamforming techniques have been recently studied as possible enablers for underlay spectrum sharing. The existing beamforming techniques have several common limitations: they are usually system model specific, cannot operate with arbitrary number of transmit/receive antennas, and cannot serve arbitrary number of users. Moreover, the beamforming techniques for underlay spectrum sharing do not consider the interference originating from the incumbent primary system. This paper extends the common underlay sharing model by incorporating the interference originating from the incumbent system into generic combined beamforming design that can be applied on interference, broadcast, or multiple access channels. This paper proposes two novel multiuser beamforming algorithms for user fairness and sum rate maximization, utilizing newly derived convex optimization problems for transmit and receive beamformers calculation in a recursive optimization. Both beamforming algorithms provide efficient operation for the interference, broadcast, and multiple access channels, as well as for arbitrary number of antennas and secondary users in the system. Furthermore, this paper proposes a successive transmit/receive optimization approach that reduces the computational complexity of the proposed recursive algorithms. The results show that the proposed complexity reduction significantly improves the convergence rates and can facilitate their operation in scenarios, which require agile beamformer computation. [ABSTRACT FROM AUTHOR]

This paper investigates the symmetric degrees of freedom (DoF) of multiple-input multiple-output (MIMO) cellular networks with $G$ cells and $K$ users per cell, having $N$ antennas at each base station and $M$ antennas at each user. In particular, we investigate techniques for achievability that are based on either decomposition with asymptotic interference alignment or linear beamforming schemes and show that there are distinct regimes of $(G,K,M,N)$ , where one outperforms the other. We first note that both one-sided and two-sided decomposition with asymptotic interference alignment achieve the same DoF. We then establish specific antenna configurations under which the DoF achieved using decomposition-based schemes is optimal by deriving a set of outer bounds on the symmetric DoF. Using these results, we completely characterize the optimal DoF of any $G$ -cell network with single-antenna users. For linear beamforming schemes, we first focus on small networks and propose a structured approach to linear beamforming based on a notion called packing ratios. Packing ratio describes the interference footprint or shadow cast by a set of transmit beamformers and enables us to identify the underlying structures for aligning interference. Such a structured beamforming design can be shown to achieve the optimal spatially normalized DoF (sDoF) of two-cell two-user/cell network and the two-cell three-user/cell network. For larger networks, we develop an unstructured approach to linear interference alignment, where transmit beamformers are designed to satisfy conditions for interference alignment without explicitly identifying the underlying structures for interference alignment. The main numerical insight of this paper is that such an approach appears to be capable of achieving the optimal sDoF for MIMO cellular networks in regimes where linear beamforming dominates asymptotic decomposition, and a significant portion of sDoF elsewhere. Remarkably, polynomial identity test appears to play a key role in identifying the boundary of the achievable sDoF region in the former case. [ABSTRACT FROM AUTHOR]

The degrees of freedom (DoF) of the 3-user multiple-input multiple-output (MIMO) interference channel (IC) with full channel state information and constant channel coefficients are investigated when $(p,p+1)$ antennas are deployed at the transmitters and receivers, respectively. The point of departure of this paper is the work of Wang et al., which conjectured but did not prove the DoF for the antenna settings with $p>1$. Here the achievability of the DoF outer bound is formally proved using linear methods, thereby avoiding the use of the rational dimensions framework. The proposed transmission scheme exploits asymmetric complex signaling together with symbol extensions in time and space interference alignment concepts. While the paper deals with the $p=2,3,\ldots,6$ cases, providing the specific transmit and receive filters, there are also provided the tools needed for proving the achievability of the optimal DoF for $p>6$, whose DoF characterization is conjectured. [ABSTRACT FROM PUBLISHER]

Due to the use of an appropriately designed pulse shaping prototype filter, filter bank multicarrier (FBMC) system can achieve low out of band (OoB) emissions and is also robust to the channel and synchronization errors. However, it comes at a cost of long filter tails, which may reduce the spectral efficiency significantly when the block size is small. Filter output truncation (FOT) can reduce the overhead by discarding the filter tails but may also significantly destroy the orthogonality of FBMC system, by introducing intercarrier interference (ICI) and intersymbol interference (ISI) terms in the received signal. As a result, the signal-to-interference ratio (SIR) is degraded. In addition, the presence of intrinsic interference terms in FBMC also proves to be an obstacle in combining multiple-input multiple-output (MIMO) with FBMC. In this paper, we present a theoretical analysis on the effect of FOT in an MIMO-FBMC system. First, we derive the matrix model of MIMO-FBMC system, which is subsequently used to analyze the impact of finite filter length and FOT on the system performance. The analysis reveals that FOT can avoid the overhead in the time domain but also introduces extra interference in the received symbols. To combat the interference terms, we then propose a compensation algorithm that considers odd and even overlapping factors as two separate cases, where the signals are interfered by the truncation in different ways. The general form of the compensation algorithm can compensate all the symbols in a MIMO-FBMC block and can improve the SIR values of each symbol for better detection at the receiver. It is also shown that the proposed algorithm requires no overhead and can still achieve a comparable bit error rate (BER) performance to the case with no filter truncation. [ABSTRACT FROM AUTHOR]

In practical massive MIMO systems, a substantial portion of system resources are consumed to acquire channel state information (CSI), leading to a drastically lower system capacity compared with the ideal case, where perfect CSI is available. In this paper, we show that the overhead for CSI acquisition can be largely compensated by the potential gain due to the sparsity of the massive MIMO channel in a certain transformed domain. To this end, we propose a novel blind detection scheme that simultaneously estimates the channel and data by factorizing the received signal matrix. We show that by exploiting the channel sparsity, our proposed scheme can achieve a degree of freedom (DoF) very close to the ideal case, provided that the channel is sufficiently sparse. Specifically, the achievable DoF has a fractional gap of only $1/T$ from the ideal DoF, where $T$ is the channel coherence time. This is a remarkable advance for understanding the performance limit of the massive MIMO system. We further show that the performance advantage of our proposed scheme in the asymptotic SNR regime carries over to the practical SNR regime. Numerical results demonstrate that our proposed scheme significantly outperforms its counterpart schemes in the practical SNR regime under various system configurations. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the transceiver design for nonregenerative multicasting multiple-input multiple-output (MIMO) relay systems, where one transmitter broadcasts common message to multiple receivers with the aid of a relay node. The transmitter, relay, and receivers are all equipped with multiple antennas. We assume that the true (unknown) channel matrices have Gaussian distribution, with the estimated channels as the mean value, and the channel estimation errors follow the well-known Kronecker model. We first develop an iterative robust algorithm to jointly design the transmitter, relay, and receiver matrices to minimize the maximal mean-squared error (MSE) of the signal waveform estimation among all receivers. Then, we derive the optimal structure of the relay precoding matrix and show that the MSE at each receiver can be decomposed into the sum of the MSEs of the first-hop and second-hop channels. Based on this MSE decomposition, we develop a simplified transceiver design algorithm with a low computational complexity. Numerical simulations demonstrate the improved robustness of the proposed transceiver design algorithms against the mismatch between the true and estimated channels. Interestingly, compared with the iterative algorithm, the simplified transceiver design has only negligible performance loss with significantly reduced computational complexity. [ABSTRACT FROM PUBLISHER]

Virtual multiple-input–multiple-output (MIMO) systems using multiple antennas at the transmitter and a single antenna at each of the receivers have recently emerged as an alternative to point-to-point MIMO systems. This paper investigates the relationship between energy efficiency (EE) and spectral efficiency (SE) for a virtual-MIMO system that has one destination and one relay using compress-and-forward (CF) cooperation. To capture the cost of cooperation, the power allocation (between the transmitter and the relay) and the bandwidth allocation (between the data and cooperation channels) are studied. This paper derives a tight upper bound for the overall system EE as a function of SE, which exhibits good accuracy for a wide range of SE values. The EE upper bound is used to formulate an EE optimization problem. Given a target SE, the optimal power and bandwidth allocation can be derived such that the overall EE is maximized. Results indicate that the EE performance of virtual-MIMO is sensitive to many factors, including resource-allocation schemes and channel characteristics. When an out-of-band cooperation channel is considered, the performance of virtual-MIMO is close to that of the MIMO case in terms of EE. Considering a shared-band cooperation channel, virtual-MIMO with optimal power and bandwidth allocation is more energy efficient than the noncooperation case under most SE values. [ABSTRACT FROM PUBLISHER]

In this paper, we treat the combined signal and spectrum coordination problem in digital subscriber line (DSL) networks with linear design for transmitters and receivers. The transmission is modeled as a multitone MIMO system where each user has a number of transceivers and there is coordination between sets of users on the transmitter and on the receiver sides. We consider the possibility of an asynchronous transmission, i.e. when the transmission of DMT blocks for different users is not aligned in time. This gives rise to inter-carrier interference. Our objective is the maximization of the weighted sum of users' data rates subject to power constraints. Although this problem is well known in the literature, previous works have always based their designs on strong assumptions about the network infrastructure. In this paper, we propose a general framework and algorithm that apply for any infrastructure, including any number of users, any number of transceivers, any number of tones, any kind of coordination on both the transmitter and on the receiver sides, and synchronous or asynchronous transmission. We also do not assume any special structure of the channel matrix. Our algorithm is seen to perform very well and is polynomial time solvable. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the design of linear precoders for simultaneously wireless information and power transfer (SWIPT) in a multi-input multi-output (MIMO) broadcasting system with discrete input signals. The considered system model consists of one base station (BS), one information receiver (IR), and one energy receiver (ER). The design objective is to maximize the input–output mutual information of the IR subject to the power constraint and the harvested energy requirement for the ER. We derive the structure of the optimal linear precoder by using manifold optimization, and propose an algorithm to find the optimal precoder. Simulation results show that the proposed algorithm can achieve better performance than the time sharing scheme and the Gaussian optimal precoder when Gaussian inputs are replaced by discrete input signals. [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]

Along with the ongoing evolution of multiple antenna communication systems, new physical layer security techniques are continuing to achieve higher levels of secrecy. Most physical layer approaches, however, concern time division duplex (TDD) channels which rely on using the channel reciprocity feature as a shared randomness and tend to be associated with a large computational burden. In this paper, we propose a new physical layer method which utilizes private random precoding for exchanging the secret key bits in multiple-input–multiple-output (MIMO) systems. The principle of this method is to exploit the precoding matrix index in a manner that produces low correlation at the adversary. A robust key exchange between the transmitter and the receiver is established by uniquely relating the secret key bits to the channel precoding matrix using a private version of the universal codebooks. What is more is that the proposed method is applicable in both frequency division duplex (FDD) and TDD channels. The results demonstrate that the proposed method can offer superior performance in terms of the key agreement, secrecy level, and computational load. [ABSTRACT FROM AUTHOR]

In this paper, we propose an algorithm to design interference alignment (IA) precoding and decoding matrices for arbitrary MIMO X networks. The proposed algorithm is rooted in the homotopy continuation techniques commonly used to solve systems of nonlinear equations. Homotopy methods find the solution of a target system by smoothly deforming the solution of a start system which can be trivially solved. Unlike previously proposed IA algorithms, the homotopy continuation technique allows us to solve the IA problem for both unstructured (i.e., generic) and structured channels such as those that arise when time or frequency symbol extensions are jointly employed with the spatial dimension. To this end, we consider an extended system of bilinear equations that include the standard alignment equations to cancel the interference, and a new set of bilinear equations that preserve the desired dimensionality of the signal spaces at the intended receivers. We propose a simple method to obtain the start system by randomly choosing a set of precoders and decoders, and then finding a set of channels satisfying the system equations, which is a linear problem. Once the start system is available, standard prediction and correction techniques are applied to track the solution all the way to the target system. We analyze the convergence of the proposed algorithm and prove that, for many feasible systems and a sufficiently small continuation parameter, the algorithm converges with probability one to a perfect IA solution. The simulation results show that the proposed algorithm is able to consistently find solutions achieving the maximum number of degrees of freedom in a variety of MIMO X networks with or without symbol extensions. Further, the algorithm provides insights into the feasibility of IA in MIMO X networks for which theoretical results are scarce. [ABSTRACT FROM PUBLISHER]

Nonlinear transceiver based on Tomlinson–Harashima (TH) precoding outperforms the linear minimum mean-square-error (MSE) architecture in terms of minimum achievable MSE. In this paper, we investigate nonlinear TH precoding design problem for simultaneous wireless information and power transfer in multiple-input-multiple-output broadcast channels, where there are one information-decoding (ID) receiver and multiple energy harvesting (EH) receivers. We consider the scenario that the transmitter knows imperfect channel state information of all links and the channel uncertainties are modeled by Gaussian random variables. Our objective is to jointly optimize TH precoding matrices and linear equalizer to minimize average MSE subject to transmit power constraint and EH constraints on average harvested power. We transform the robust transceiver design problem into a difference of convex programming and propose a constrained concave convex procedure (CCCP) based locally optimal solution. To reduce computational complexity, we propose a noniterative upper bound based suboptimal solution that minimizes the upper bound on average MSE. We also extend the CCCP-based locally optimal solution to the single group multicast scenario where there are multiple ID receivers. Simulation results demonstrate that our proposed TH precoding transceiver design achieves lower average MSE than linear precoding transceiver design. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the K -user single-input single-output interference channel with delayed channel state information at the transmitters (CSIT). Our main contribution is to show that even with delayed CSIT and distributed transmitters, the achievable degrees of freedom (DoFs) still scale with the number of users. More specifically, we propose a method that achieves K/(2\sqrt {K} - 1) \geq \sqrt {K}/2 DoF. The main idea behind the proposed method is to use interference alignment (IA) at the receiver side in conjunction with repetition coding at the transmitters. Repetition coding repeats the data R$ times while IA makes the interference generated by a given transmitter identical: 1) at all non-intended receivers and 2) all transmission repetitions. Therefore, one retransmission per transmitter is sufficient to cancel all the interference. This reduces significantly the overhead required for interference removal since the number of interference terms is reduced from $RK(K-1)$ to $K$ . [ABSTRACT FROM PUBLISHER]

The evolved multimedia broadcast multicast service ( e MBMS) system was developed to achieve higher spectrum efficiency on video traffic delivery over the long term evolution (LTE) networks. As an integrated component of the LTE, e MBMS can be deployed with great flexibility using the existing LTE infrastructure. However, the current e MBMS was designed as a supplementary subsystem, and has limited capability to deliver high-quality broadcast-type video services in a spectrum efficient manner. This paper first studies the capability and limitations of the current LTE e MBMS system to deliver broadcast services when deployed as single-frequency-network (SFN). Next, potential physical-layer enhancements are investigated for future e MBMS systems to achieve enhanced broadcast service delivery capability, higher spectrum efficiency, improved service quality, and more efficient SFN deployment options. These include wideband transmission, non-orthogonal multiplexing, e.g., layered-division-multiplexing technology, and more flexible orthogonal frequency division multiplexing system configurations, such as longer cyclic prefix and smaller subcarrier spacing. Other technologies defined in the latest next generation digital television system are also discussed that might be applicable to the development of a more capable standalone future e MBMS system. [ABSTRACT FROM AUTHOR]

This paper studies the impact of a multiple-input–multiple-output (MIMO) relay on the $K$- user multiple-input–single-output (MISO) interference channel (IC) when the relay has delayed feedback (i.e., delayed channel state information (CSI) or delayed channel output feedback) from each receiver, yet each transmitter has no knowledge about CSI. We first develop a new relay-aided retrospective interference alignment (r-RIA) and characterize the optimal sum degrees of freedom (DoFs) for the $K$- user MISO IC with a MIMO relay by providing a new matching outer bound. It is shown that the sum DoF does not decrease, even in the absence of direct links between transmitters and receivers, as long as $K$ is sufficiently large. We next show that a MIMO relay can provide a sum-DoF gain in the $K$- user MISO IC with delayed feedback to the relay in the absence of CSI at transmitter (CSIT), whereas relaying is shown to be not useful with instantaneous CSIT from the DoF perspective. [ABSTRACT FROM PUBLISHER]

Millimeter wave (mmWave) communication provides high data rates thanks to large arrays at the transmitter and receiver, coupled with large bandwidth channels. Exploiting the arrays is challenging due to the need to configure precoding at the transmitter based on the large frequency selective channel. In this paper, we exploit the power iteration principle and propose a robust analog precoding training algorithm that can be applied in both frequency division duplex transmission systems and time division duplex transmission systems with or without RF calibration. We further analyze the convergence of the proposed algorithm and show how it converges to the singular value decomposition optimality exponentially. We propose null space projection on top of the power iteration to form multiple orthogonal beams at the transmitter and receiver. Strongest tap selection with proper energy pruning is used to collect as much precoding gain as possible from a frequency selective fading channel. The exponential effective SINR mapping performance is evaluated and demonstrates that the overall approach works smoothly. Numerical simulation results demonstrate algorithm robustness and the algorithm works not only for the simplified mmWave directional channels, but also for more general rich scattering channels. [ABSTRACT FROM PUBLISHER]

In this paper, we consider a distributed multiple-input–multiple-output (D-MIMO) system, where the channel is flat fading and may be correlated, and experiences both small- and large-scale fading. We assume that full knowledge of channel state information (CSI) is available at the receiver and that only the first-and second-order statistics of the channel are available at the transmitter. For such a system with square quadrature amplitude modulation (QAM), an asymptotic symbol error probability (SEP) is derived for the linear zero-forcing (ZF) receiver. Then, we propose an optimal diagonal power loading (PL) strategy that minimizes the dominant term of the asymptotic SEP subject to either a total transmission power constraint when the total power normalization coefficient can be fed back to the transmitter from the receiver or an individual transmission power constraint. A simple closed-form solution is obtained. Computer simulations show that our presented optimal system attains significant performance gains over the currently available equal PL system. [ABSTRACT FROM PUBLISHER]

Time-varying channels destroy the orthogonality among subcarriers in orthogonal frequency division multiplexing (OFDM) systems, and introduce intercarrier interference (ICI). Lots of efforts have been devoted to mitigate ICI in OFDM systems, with different frame structures and channel models, but the computational complexity of the methods is usually very high. In multiple-input multiple-output (MIMO) systems, the complexity is even higher. In this paper, a low-complexity ICI mitigation method is proposed for MIMO-OFDM systems under the assumption of linear time-varying channels. It reduces the complexity of ICI compensation from O(K^3(N^3+MN^2+MN)+NK\log (K)) to O(K(N^3+2MN^2+2MN+2M^2+N\log (K))) , where K is the number of subcarriers, M the number of transmitters, and N the number of receivers. It requires channel estimation based on the linear time-varying channel model, and no transmission overhead is needed. The proposed algorithm applies to all OFDM systems as long as linear time-varying channel estimation is applicable. Time-domain synchronous-OFDM naturally suits for the proposed ICI mitigation algorithm because its receiver is able to easily estimate linear time-varying channels. Simulation with QPSK and 16QAM modulation demonstrates the performance of the proposed method, in comparison with no ICI mitigation case. It shows that 2 dB signal to noise gain is achieved when the uncoded bit error rate is 10^-3 and the normalized Doppler frequency is 0.1. [ABSTRACT FROM AUTHOR]

In this paper, we consider a Partial Interference Alignment and Interference Detection (PIAID) design for K-user quasi-static MIMO interference channels with discrete constellation inputs. Each transmitter has M antennas and transmits L independent data streams to the desired receiver with N receive antennas. We focus on the case where not all K-1 interfering transmitters can be aligned at every receiver. As a result, there will be residual interference at each receiver that cannot be aligned. Each receiver detects and cancels the residual interference based on the constellation map. However, there is a window of unfavorable interference profile at the receiver for Interference Detection (ID). In this paper, we propose a low complexity Partial Interference Alignment scheme in which we dynamically select the user set for IA so as to create a favorable interference profile for ID at each receiver. We first derive the average symbol error rate (SER) by taking into account of the non-Guassian residual interference due to discrete constellation. Using graph theory, we then devise a low complexity user set selection algorithm for the PIAID scheme, which minimizes the asymptotically tight bound for the average end-to-end SER performance. Moreover, we substantially simplify interference detection at the receiver using Semi-Definite Relaxation (SDR) techniques. It is shown that the SER performance of the proposed PIAID scheme has significant gain compared with various conventional baseline solutions. [ABSTRACT FROM PUBLISHER]

In a companion paper, we have studied the zero-forcing (ZF) transceiver with decision feedback equalizer (DFE) over slowly time-varying narrowband multiinput multioutput (MIMO) channels. The space-time generalized triangular decomposition (ST-GTD) was used for the design of ZF-DFE transceivers. The space-time geometric mean decomposition (ST-GMD) ZF transceiver minimizes both the arithmetic mean square error (MSE) at the feedback detector and the average uncoded bit error rate (BER) in moderate high signal-to-noise ratio (SNR). This paper addresses the design problem of DFE transceiver without zero-forcing constraint. In the first part, a channel independent temporal precoder is superimposed on the conventional block-wise GMD-based minimum mean square error (MMSE) DFE transceiver to take advantage of the temporal diversity. In the second part, ST-GTD is applied for the design of MMSE DFE transceivers. With accurate channel prediction and space-time powerloading, the proposed ST-GMD MMSE transceiver minimizes the arithmetic MSE at the feedack detector, and maximizes Gaussian mutual information. For practical applications, the ST-GTD MMSE transceiver which does not require channel prediction but shares the same asymptotic BER performance with the ST-GMD MMSE system is also developed. In the convex region, our analysis shows that the proposed MMSE transceivers has better BER performance than the conventional GMD-based MMSE transceiver; the average BERs of the proposed systems are nonincreasing functions of the ST-block size. The superior performance of ST-GMD MMSE transceiver over the ST-GMD ZF transceiver is also verified analytically. [ABSTRACT FROM PUBLISHER]

In this paper, we design robust precoders, under the minimum mean square error (MMSE) criterion, for different types of channel state information (CSI) in multiple-input multiple-output (MIMO) channels. We consider low-complexity pre-fixed receivers that may adapt to the channel but are oblivious to the existence of a precoder at the transmitter. In particular, three types of CSI are taken into account: i) perfect CSI, ii) statistical CSI in the form of mean feedback, and iii) deterministic imperfect CSI assuming that the actual channel is within the neighborhood of a nominal channel, which leads to the worst-case robust design that is the focus of this paper. Interestingly, it is found that, under some mild conditions, the optimal transmit directions, i.e., the left singular vectors of the precoder, are equal to the right singular vectors of the channel, the channel mean, and the nominal channel for perfect CSI, statistical CSI, and the worst-case design, respectively. Consequently, the matrix-valued problems can be simplified to scalar power allocation problems that either admit closed-form solutions or can be efficiently solved by the proposed algorithm. [ABSTRACT FROM PUBLISHER]

This paper continues the Wu–Shamai–Verdú program on characterizing the degrees of freedom (DoF) of interference channels (ICs) through Rényi information dimension. Specifically, we find a single-letter formula for the DoF of vector ICs, encompassing multiple-input multiple-output ICs, time- and/or frequency-selective ICs, and combinations thereof, as well as scalar ICs as considered by Wu et al., 2015. The DoF-formula we obtain lower-bounds the DoF of all channels—with respect to the choice of the channel matrix—and upper-bounds the DoF of almost all channels. It applies to a large class of noise distributions, and its proof is based on an extension of a result by Guionnet and Shlyakthenko, 2007, to the vector case in combination with the Ruzsa triangle inequality for differential entropy introduced by Kontoyiannis and Madiman, 2015. As in scalar ICs, achieving full DoF requires the use of singular input distributions. Strikingly, in the vector case, it suffices to enforce singularity on the joint distribution of each transmit vector. This can be realized through signaling in subspaces of the ambient signal space, which is in accordance with the idea of interference alignment, and, most importantly, allows the scalar entries of the transmit vectors to have non-singular distributions. The DoF-formula for vector ICs we obtain enables a unified treatment of classical interference alignment à la Cadambe and Jafar, 2008, and Maddah-Ali et al., 2008, and the number-theoretic schemes proposed by Motahari et al., 2014, and by Etkin and Ordentlich, 2009. Moreover, it allows to calculate the DoF achieved by new signaling schemes for vector ICs. We furthermore recover the result by Cadambe and Jafar on the non-separability of parallel ICs, 2009, and we show that almost all parallel ICs are separable in terms of DoF. Finally, our results apply to complex vector ICs, thereby extending the main findings of Wu et al., 2015 to the complex case. [ABSTRACT FROM PUBLISHER]

In this paper, adaptive training beam sequence design for efficient channel estimation in large millimeter-wave (mmWave) multiple-input multiple-output (MIMO) channels is considered. By exploiting the sparsity in large mmWave MIMO channels and imposing a Markovian random walk assumption on the movement of the receiver and reflection clusters, the adaptive training beam sequence design and channel estimation problem is formulated as a partially observable Markov decision process (POMDP) problem that finds non-zero bins in a two-dimensional grid. Under the proposed POMDP framework, optimal and suboptimal adaptive training beam sequence design policies are derived. Furthermore, a very fast suboptimal greedy algorithm is developed based on a newly proposed reduced sufficient statistic to make the computational complexity of the proposed algorithm low to a level for practical implementation. Numerical results are provided to evaluate the performance of the proposed training beam design method. Numerical results show that the proposed training beam sequence design algorithms yield good performance. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate a codeword refinement technique called double codeword coding in the context of MIMO feedback. In the proposed method, the second codeword is fed back in addition to the best codeword as their interpolation at the transmitter improves the channel knowledge. The derivation of the optimal interpolation parameter is presented together with the derivation of an upper-bound to the interpolation parameter based on channel quality feedback available at the transmitter. We show that double codeword feedback refinement has slightly lower complexity than alternative techniques and still achieves similar performance. Furthermore, double codeword coding can be generalized to higher transmission ranks. Using extended multiuser MIMO link simulations, we verify that the double codeword feedback is able to provide significant gains in 3GPP LTE context. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the performance of a multiple-input–multiple-output (MIMO) maximal ratio combining (MRC) system with feedback delay and channel estimation error. By taking these practical imperfect factors into account, we first formulate the system model and derive the moment-generating function of the output signal-to-noise ratio (SNR), which serves as the basis for further system performance analysis. Then, we compute the probability density function (pdf) and the cumulative distribution function (cdf) of the output SNR. Furthermore, we derive the analytical expressions of the exact and approximate average symbol error rates (SERs) of the MIMO MRC system, which are used to investigate the performance loss in terms of the array gain and diversity order. Finally, computer simulations are conducted to show the efficacy of the analytical results and the effect of feedback delay and channel estimation error on the system performance. [ABSTRACT FROM PUBLISHER]

Multiuser orthogonal frequency-division multiplexing (OFDM) and multiple-output multiple-output (MIMO) have been widely adopted to enhance the system throughput and combat the detrimental effects of wireless channels. Interference alignment has been proposed to exploit interference to enable concurrent transmissions of multiple signals. In this paper, we investigate how to combine these techniques to further enhance the system throughput. We first reveal the unique characteristics and challenges brought about by using interference alignment in diagonal channels. We then derive a performance bound for the multiuser (MIMO) OFDM interference alignment system under practical constraints and show how to achieve this bound with a decomposition approach. The superior performance of the proposed scheme is validated with simulations. [ABSTRACT FROM PUBLISHER]

Tomlinson–Harashima precoded (THP) multiple-input–multiple-output (MIMO) systems are developed to cancel the intersymbol interference (ISI) at the transmitter. However, the THP at least requires perfect channel direction information (CDI) to completely mitigate the interference at the transmitter, which is not practical in the real world. The limited feedback systems are then practically developed to convey the quantized CDI to the transmitter. Using the quantized CDI to conduct the THP, an unavoidable interference degrades the performance at the receiver. In this paper, we investigate the performance degradation resulted from the random vector quantization (RVQ), which is a kind of CDI-based limited feedback mechanism. Here, we measure the performance degradation as the excess mean-squared error (EMSE). Since the formulation of the EMSE is a complicated function of the quantization error, we proposed using the second-order Taylor expansion to derive an analytical result. Simulation results have also verified our proposed analysis, showing that the derived analysis can match the actual EMSE. [ABSTRACT FROM PUBLISHER]

In this paper, we give a unified performance analysis of interference alignment (IA) over multiple-input–multiple-output (MIMO) interference channels. Rather than the asymptotic characterization, i.e., degree of freedom (DOF) at high signal-to-noise ratio (SNR), we focus on the other practical performance metrics, namely, outage probability, ergodic rate, and symbol error rate (SER). In particular, we consider imperfect IA because the transmitters usually have only imperfect channel state information (CSI) in a practical scenario. By characterizing the impact of imperfect CSI, we derive the exact closed-form expressions of outage probability, ergodic rate, and SER in terms of CSI accuracy, transmit SNR, channel condition, number of antennas, and the number of data streams of each communication pair. Furthermore, we obtain some important guidelines for performance optimization of IA under imperfect CSI by minimizing the performance loss over IA with perfect CSI. Finally, our theoretical claims are validated by simulation results. [ABSTRACT FROM PUBLISHER]

In the presence of perfect channel state information (CSI), the achievable degrees of freedom (DoF) in wireless interference networks can be linearly scaled up with the number of users. Achievability is based on the idea of interference alignment (IA). However, in the presence of imperfect CSI, the sum rate becomes degraded, and full DoF may no longer be achievable. In this paper, we propose novel least squares (LS)- and minimum mean square error (MMSE)-based IA schemes that adaptively design beamformers by relying on the availability of imperfect CSI and knowledge of the channel estimation error variance in advance. Interestingly and unlike the other robust algorithms, the proposed adaptive schemes do not impose extra computational complexity compared to their nonadaptive counterparts. It is shown that the LS-based IA is able to outperform interference leakage minimization algorithms under both perfect and imperfect CSI. Furthermore, we compare the performance of the proposed MMSE-based IA with maximum signal-to-interference-plus-noise ratio (Max-SINR) algorithm. We show that while under perfect CSI, the MMSE-based IA achieves the same performance as that of Max-SINR, the former outperforms the latter under CSI mismatch. Meanwhile, it is shown that the proposed MMSE-based IA needs less CSI to be available and has less computational complexity compared to Max-SINR. [ABSTRACT FROM PUBLISHER]

In this paper, we investigated the effect of power combining and delivering in multiinput and multioutput wireless energy transmission systems, which consist of more than one transmitter antennas as sources and more than one receiver antennas as loads and repeaters. Theoretical expressions were developed to model the system operation that can be in a large-scale wireless energy network architecture. System characteristics, such as power transfer between antennas, power losses induced in each antenna, wireless efficiency, coil misalignment, and power fluctuation due to the loss of frequency synchronization were examined by theory and verified with experiments. Measurement results matched well with the theory demonstrating the feasibility of combining and delivering power with high efficiencies in large-scale wireless energy transmission systems. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of per-stream maximum sum-rate joint precoder and minimum mean-squared error equalizer design for the multi-input multi-output interference channel. We consider the general case of more than three users with more than one stream per user. We propose a generalized iterative algorithm which directly maximizes the sum-rate without assuming the signal-to-noise ratio to be infinite. To reduce complexity, which can become prohibitive for large network size, we examine the performance-complexity tradeoffs involved in a sparse equalizer design. Joint precoder and equalizer optimization requires alternation between the forward and reverse links and assumes perfect synchronization between the transmitters and receivers at each network node, resulting in extensive overhead and spectral efficiency loss. To overcome this serious drawback, we propose a new design approach based on weighted-sum-rate maximization assuming a virtual equalizer type at the transmitter to limit the optimization process to the transmitter side. In addition, we quantify the sum-rate loss due to mismatched equalizer types and demonstrate the robustness of our proposed sum-rate weighting strategy to such mismatches with perfect or imperfect channel knowledge. Finally, we derive asymptotic performance expressions and verify their accuracy numerically even for a moderate number of users. [ABSTRACT FROM PUBLISHER]

In this paper, we study the codebook size design strategies in the multiple-input–multiple-output (MIMO) broadcast channel (BC) systems. We adopt the nonlinear Tomlinson–Harashima precoder (THP), which is designed by the imperfect channel direction information (CDI) acquired from the random vector quantization (RVQ) feedback mechanism. Under the limitation of the total feedback rate, we flexibly allocate the size of each user's codebook so that the overall channel capacity is maximized. Since the design problem is not convex, directly finding out the optimum allocation of codebook size is not attainable. However, by sophisticatedly using the discrete majorization theory, we can derive the codebook size allocation strategies for the high- and the low-signal-to-noise-ratio (SNR) regions. Interestingly, the results show that the equal size codebook is preferable in the low-SNR region, whereas the codebook allocates the whole available codebook size to a single user in the high-SNR region. Simulations certify the theoretical result of our design. [ABSTRACT FROM PUBLISHER]

Interference alignment (IA) is a precoding technique that aligns interfering signals at receivers. It is known that IA achieves the maximum degrees of freedom over an interference channel under ideal assumptions. The real-world performance of IA depends on a range of practical issues, such as imperfect synchronization, channel estimation, and feedback. Practical issues have been studied in simulations and prototypes, but fully distributed operation of IA network nodes has not been considered. In this paper, we present the first investigation of real-time IA performance on a fully distributed 2 $\times$ 2 multiple-input–multiple-output (MIMO) prototype system with three physically independent user pairs. Over-the-air algorithms for time and frequency synchronization, as well as analog feedback, are studied and implemented. Sum rates are illustrated as a function of complexity and accuracy of different alignment, synchronization, and feedback algorithms. Corresponding tradeoffs are evaluated using an iterative IA method, the injection of residual frequency offset into synchronization, and analog versus quantization-based limited feedback approaches. We demonstrate that, while considering all possible error sources in estimation, synchronization, and feedback, the theoretical multiplexing gain of IA can be reached in practical systems with a constant sum rate loss that remains within 5 bits/Hz/s compared with an ideal simulation. [ABSTRACT FROM PUBLISHER]

In this paper, we consider variable-rate transmission over a slowly varying multiple-input multiple-output (MIMO) channel with a decision feedback receiver. The transmission rate is adapted to the channel by dynamically assigning bits to the subchannels of the MIMO system. Predictive quantization is used for the feedback of bit loading to take advantage of the time correlation inherited from the temporally correlated channel. Due to the use of decision feedback at the receiver, the bit loading is related to the Cholesky decomposition of the channel Gram matrix. Assuming the channel is modeled by a slowly varying Gauss–Markov process, we show that the nested submatrices generated during the process of Cholesky decomposition can be updated as time evolves. Based on the update, we derive the optimal predictor of the next bit loading for predictive quantization. Furthermore, we derive the statistics of the prediction error, which are then exploited to design the quantizer to achieve a smaller quantization error. Simulations are given to demonstrate that the proposed predictive quantization gives a good approximation of the desired transmission rate with a low feedback rate. [ABSTRACT FROM PUBLISHER]

In this paper, we propose multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) radar with sufficient cyclic prefix (CP), where all OFDM pulses transmitted from different transmitters share the same frequency band and are orthogonal to each other for every subcarrier in the discrete frequency domain. The orthogonality is not affected by time delays from transmitters. Thus, our proposed MIMO OFDM radar has the same range resolution as single transmitter radar and achieves full spatial diversity. Orthogonal designs are used to achieve this orthogonality across the transmitters, with which it is only needed to design OFDM pulses for the first transmitter. We also propose a joint pulse compression and pulse coherent integration for range reconstruction. In order to achieve the optimal signal-to-noise ratio (SNR) for the range reconstruction, we apply the paraunitary filterbank theory to design the OFDM pulses. We then propose a modified iterative clipping and filtering (MICF) algorithm for the designs of OFDM pulses jointly, when other important factors, such as peak-to-average power ratio (PAPR) in time domain, are also considered.With our proposed MIMO OFDM radar, there is no interference for the range reconstruction not only across the transmitters but also across the range cells in a swath called inter-range-cell interference (IRCI) free that is similar to our previously proposed CP-based OFDM radar for single transmitter. Simulations are presented to illustrate our proposed theory and show that the CP-based MIMO OFDM radar outperforms the existing frequency-band shared MIMO radar with polyphase codes and also frequency division MIMO radar. [ABSTRACT FROM PUBLISHER]

Multiple-input multiple-output (MIMO) radar imaging suffers from performance degradation under carrier offsets across transmitters and receivers. This paper analyzes the impact of carrier offsets on imaging a sparse target, from the perspective of the MIMO point spread function (PSF). Conditions are established for successful support recovery using orthogonal matching pursuit (OMP), and the performance loss is characterized in terms of l2 distance. A sparse imaging algorithm taking into account the perturbation due to carrier offsets is also proposed, which improves upon the OMP algorithm. Numerical experiments corroborate this analysis. [ABSTRACT FROM PUBLISHER]

This paper studies the linear transceiver design for multi-stream multiple-input-multiple-output (MIMO) interference channels with imperfect channel state information (CSI). Two CSI error models are considered. The same coding and modulation scheme is assumed for all users and data streams. In the first model, where the CSI error is statistical, we minimize the average maximum per-stream mean square error (MSE). In the second model, where the CSI error is norm bounded, the worst-case maximum per-stream MSE is optimized. Since the problems are not jointly convex, the alternate optimization approach is adopted to obtain suboptimal transceivers. For the statistical CSI error, a low-complexity algorithm utilizing Lagrangian duality is proposed, which has a semi-closed form solution and can be implemented distributively. Compared with the classical algorithm using the second-order-cone programming, the proposed algorithm significantly reduces the computational complexity without sacrificing the performance. For the bounded CSI error, we present two approaches. One uses S-procedure to obtain an equivalent problem and the other one solves an approximated problem. Simulation results demonstrate the robustness of the proposed algorithms and their improved performance over the sum-MSE and the maximum per-user MSE based methods. The lower complexity of the Lagrangian duality based algorithm is also verified numerically. [ABSTRACT FROM PUBLISHER]

We study a number of two-user interference networks with multiple-antenna transmitters/receivers (MIMO), transmitter side information in the form of linear combinations (over an appropriate finite-field) of the information messages, and two-hop relaying. We start with a cognitive interference channel (CIC) where one of the transmitters (noncognitive) has knowledge of a rank-1 linear combination of the two information messages, while the other transmitter (cognitive) has access to a rank-2 linear combination of the same messages. This is referred to as the network-coded CIC, since such linear combination may be the consequence of some random linear network coding scheme implemented in the backbone wired network. For such channel we develop an achievable region based on a few novel concepts: precoded compute-and-forward (PCoF) with channel integer alignment (CIA), combined with standard dirty-paper coding. We also develop a capacity region outer bound and find the symmetric generalized degrees of freedom (GDoF) region of the network-coded CIC. Through the GDoF characterization, we show that knowing mixed data (linear combinations of the information messages) provides a unbounded spectral efficiency gain over the classical CIC counterpart, if the ratio (in decibel) of signal-to-noise (SNR) to interference-to-noise is larger than certain threshold. Then, we consider a Gaussian relay network having the two-user MIMO IC as the main building block. We use PCoF with CIA to convert the MIMO IC into a deterministic finite-field IC. Then, we use a linear precoding scheme over the finite-field to eliminate interference in the finite-field domain. Using this unified approach, we derive the symmetric sum rate of the two-user MIMO IC with coordination, cognition, and two-hops. We also provide finite-SNR results (not just DoF) which show that the proposed coding schemes are competitive against state-of-the-art interference avoidance scheme based on orthogonal access, for standard randomly generated Rayleigh fading channels. [ABSTRACT FROM AUTHOR]

In this paper, we propose interference alignment (IA) schemes for downlink multiple-input–multiple-output heterogeneous networks (HetNets) with partial connectivity, which is induced by the path loss and the low transmission power of small cells. Specifically, we consider two partially connected scenarios of HetNets. In the first scenario, we focus on the partial connectivity among small cells, whereas in the second scenario, we further consider the partial connectivity between the macrocell and small cells. For the first scenario, we first propose a two-stage IA scheme by exploiting the heterogeneity and partial connectivity of HetNets. Then, the influence of the number of served macro users on system degrees of freedom (DoFs) is investigated. In particular, we derive the condition under which serving one macro user achieves more DoFs than serving multiple macro users and design an algorithm to find the optimal number of served macro users to maximize the system DoFs. Afterward, we study the second scenario and extend the two-stage IA to this scenario. The simulation results show that the proposed IA schemes can significantly improve the system sum rate. Moreover, by considering the partial connectivity between the macro cell and small cells, the system performance can be further improved. [ABSTRACT FROM PUBLISHER]

In this paper, we study the Gaussian MIMO Z channel and the Gaussian MIMO X channel. The MIMO X channel (XC) consists of two multiple antenna transmit-receive pairs, where each transmitter communicates with both receivers. The MIMO Z channel (ZC) is obtained from the MIMO X channel by eliminating one of the links and its corresponding message. First, we derive a sum-rate upper bound for the MIMO Z channel and compare it with an existing bound in literature. Next, we consider the MIMO X channel and propose a new sum-rate upper bound by utilizing the sum-rate upper bound for the MIMO ZC. Subsequently, we derive another upper bound for the MIMO XC by assuming receiver cooperation and deriving the worst noise covariance matrix for the resulting two-user MAC. We compare the above two upper bounds for the MIMO XC with the MaddahAli-Motahari-Khandani (MMK) scheme. Then, we consider some consequences of the above results for the MIMO interference channel. Finally, we present some numerical results. The numerical results suggest that the proposed sum-rate capacity upper bounds are tighter than existing bounds. [ABSTRACT FROM PUBLISHER]