Gaussian MIMO channel under total transmit and interference power constraints (TPC and IPC) is considered. A closed-form solution for the optimal transmit covariance matrix in the general case is obtained using the KKT-based approach (up to dual variables). While closed-from solutions for optimal dual variables are possible in special cases, an iterative bisection algorithm (IBA) is proposed to find the optimal dual variables in the general case and its convergence is proved for some special cases. Numerical experiments illustrate its efficient performance. Bounds for the optimal dual variables are given, which facilitate numerical solutions. An interplay between the TPC and IPC is studied, including the transition from power-limited to interference-limited regimes as the total transmit power increases. Sufficient and necessary conditions for each constraint to be redundant are given. A number of explicit closed-form solutions are obtained, including full-rank and rank-1 (beamforming) cases as well as the case of identical eigenvectors (typical for massive MIMO settings). A bound on the rank of optimal covariance is established. A number of unusual properties of optimal covariance matrix are pointed out.
Faster-than-Nyquist (FTN) signaling is a non-orthogonal transmission technique, which has the potential to provide significant spectral efficiency improvement. This paper studies the capacity of FTN signaling for both frequency-flat and for frequency-selective multiple-input multiple-output (MIMO) channels. We show that precoding in time and waterfilling in space is capacity achieving for frequency-flat MIMO FTN. For frequency-selective fading, joint waterfilling in time, space and frequency is required.
Capacity-achieving signaling strategies for the Gaussian wiretap MIMO channel are investigated without the degradedness assumption. In addition to known solutions, a number of new rank-deficient solutions for the optimal transmit covariance matrix are obtained. The case of a weak eavesdropper is considered in detail and the optimal covariance is established in an explicit, closed form with no extra assumptions. This provides lower and upper bounds to the secrecy capacity in the general case with a bounded gap, which are tight for a weak eavesdropper or/and low SNR. Closed form solutions are al…
Quantized massive multiple-input-multiple-output (MIMO) systems are gaining more interest due to their power efficiency. We present a new precoding technique to mitigate the multi-user interference and the quantization distortions in a downlink multi-user (MU) multiple-input-single-output (MISO) system with 1-bit quantization at the transmitter. This work is restricted to PSK modulation schemes. The transmit signal vector is optimized for every desired received vector taking into account the 1-bit quantization. The optimization is based on maximizing the safety margin to the decision threshold…
Optimal signalling over the Gaussian MIMO wire-tap channel is studied under the total transmit power constraint. A closed-form solution for an optimal transmit covariance matrix is obtained when the channel is strictly degraded. In combination with the rank-1 solution, this provides the complete characterization of the optimal covariance for the case of two transmit antennas. The cases of weak eavesdropper and high SNR are considered. It is shown that the optimal covariance does not converge to a scaled identity in the high-SNR regime. Necessary optimality conditions and a tight upper bound on…
We derive the optimal signaling for a multiple input multiple output (MIMO) full-duplex two-way channel under the imperfect transmit front-end chain. We characterize the two-way rates of the channel by using a game-theoretical approach, where we focus on the Pareto boundary of the achievable rate region and Nash equilibia (NE). For a MISO full-duplex two-way channel, we prove that beamforming is an optimal transmission strategy which can achieve any point on the Pareto boundary. Furthermore, we present a closed-form expression for the optimal beamforming weights. In our numerical examples we q…
Most works on cell-free massive multiple-input multiple-output (MIMO) consider non-cooperative precoding strategies at the base stations (BSs) to avoid extensive channel state information (CSI) exchange via backhaul signaling. However, considerable performance gains can be accomplished by allowing coordination among the BSs. This paper proposes the first distributed framework for cooperative precoding design in cell-free massive MIMO (and, more generally, in joint transmission coordinated multi-point) systems that entirely eliminates the need for backhaul signaling for CSI exchange. A novel ov…
The capacity and optimal signaling over a fixed Gaussian MIMO channel are considered under the joint total and per-antenna power constraints (TPC and PAC). While the general case remains an open problem, a closed-form full-rank solution is obtained along with its sufficient and necessary conditions. The conditions for each constraint to be inactive are established. The high and low-SNR regimes are studied. Isotropic signaling is shown to be optimal in the former case while rank-1 signaling (beamforming) is not necessarily optimal in the latter case. Unusual properties of optimal covariance und…
The capacity of the point-to-point vector Gaussian channel under the peak power constraint is not known in general. This paper considers a simpler scenario in which the input signal vector is forced to have a constant envelope (or norm). The capacity-achieving distribution for the non-identity $2\times 2$ MIMO channel when the input vector lies on a circle in $\mathbb{R}^2$ is obtained and is shown to have a finite number of mass points on the circle. Subsequently, it is shown that the degrees of freedom (DoF) of a full-rank $n$ by $n$ channel with constant envelope signaling is $n-1$ and it c…
This paper studies the problem of linear precoding for multiple-input multiple-output (MIMO) communication channels employing finite-alphabet signaling. Existing solutions typically suffer from high computational complexity due to costly computations of the constellation-constrained mutual information. In contrast to existing works, this paper takes a different path of tackling the MIMO precoding problem. Namely, a data-driven approach, based on deep learning, is proposed. In the offline training phase, a deep neural network learns the optimal solution on a set of MIMO channel matrices. This a…
This paper investigates the linear precoder design for $K$-user interference channels of multiple-input multiple-output (MIMO) transceivers under finite alphabet inputs. We first obtain general explicit expressions of the achievable rate for users in the MIMO interference channel systems. We study optimal transmission strategies in both low and high signal-to-noise ratio (SNR) regions. Given finite alphabet inputs, we show that a simple power allocation design achieves optimal performance at high SNR whereas the well-known interference alignment technique for Gaussian inputs only utilizes a pa…
Multi-user Gaussian MIMO wiretap channel is considered under interference power constraints (IPC), in addition to the total transmit power constraint (TPC). Algorithms for \textit{global} maximization of its secrecy rate are proposed. Their convergence to the secrecy capacity is rigorously proved and a number of properties are established analytically. Unlike known algorithms, the proposed ones are not limited to the MISO case and are proved to converge to a \textit{global} rather than local optimum in the general MIMO case, even when the channel is not degraded. In practice, the convergence i…
Most recently, there has been a flurry of research activities on studying how massive MIMO precoding should be designed when the digital-to-analog conversion at the transmitter side is operated by cheap one-bit digital-to-analog converters (DACs). Such research is motivated by the desire to substantially cut down the hardware cost and power consumption of the radio-frequency chain, which is unaffordable in massive MIMO if high-resolution DACs are still used. One-bit MIMO precoding design problems are much harder to solve than their high-resolution DAC counterparts. In our previous work, we dev…
Presence of multiple antennas on both sides of a communication channel promises significant improvements in system throughput and power efficiency. In effect, a new class of large multiple-input multiple-output (MIMO) communication systems has recently emerged and attracted both scientific and industrial attention. To analyze these systems in realistic scenarios, one has to include such aspects as co-channel interference, multiple access and spatial correlation. In this paper, we study the properties of correlated MIMO multiple-access channels in the presence of external interference. Using th…
In this paper, we study the achievable rate region of 1-layer rate splitting (RS) in the presence of hardware impairment (HWI) and improper Gaussian signaling (IGS) for a single-cell reconfigurable intelligent surface (RIS) assisted broadcast channel (BC). We assume that the transceivers may suffer from an imbalance in in-band and quadrature signals, which is known as I/Q imbalance (IQI). The received signal and noise can be improper when there exists IQI. Therefore, we employ IGS to compensate for IQI as well as to manage interference. Our results show that RS and RIS can significantly enlarg…
Signaling design for secure transmission in two-user multiple-input multiple-output (MIMO) non-orthogonal multiple access (NOMA) networks is investigated in this paper. The base station broadcasts multicast data to all users and also integrates additional services, unicast data targeted to certain users, and confidential data protected against eavesdroppers. We categorize the above MIMO-NOMA with different security requirements into several communication scenarios. The associated problem in each scenario is nonconvex. We propose a unified approach, called the power splitting scheme, for optimi…
In this paper, we investigate the design of linear precoders for multiple-input multiple-output (MIMO) multiple access channels (MAC). We assume that statistical channel state information (CSI) is available at the transmitters and consider the problem under the practical finite alphabet input assumption. First, we derive an asymptotic (in the large-system limit) weighted sum rate (WSR) expression for the MIMO MAC with finite alphabet inputs and general jointly-correlated fading. Subsequently, we obtain necessary conditions for linear precoders maximizing the asymptotic WSR and propose an itera…
In this paper, we propose an optimization framework for rate splitting (RS) techniques in multiple-input multiple-output (MIMO) reconfigurable intelligent surface (RIS)-assisted systems, possibly with I/Q imbalance (IQI). This framework can be applied to any optimization problem in which the objective and/or constraints are linear functions of the rates and/or transmit covariance matrices. Such problems include minimum-weighted and weighted-sum rate maximization, total power minimization for a target rate, minimum-weighted energy efficiency (EE) and global EE maximization. The framework may be…
Resource coordination and interference management is the key to achieving the benefits of femtocell networks. Over-the-air signaling is one of the most effective means for distributed dynamic resource coordination and interference management. However, the design of this type of signal is challenging. In this letter, we address the challenges and propose an effective solution, referred to as coded single-tone signaling (STS). The proposed coded STS scheme possesses certain highly desirable properties, such as no dedicated resource requirement (no overhead), no near-and-far effect, no inter-sign…
In this work, we prove that a positive secure degree of freedom is achievable for a large class of Gaussian channels as long as the channel is not degraded and the channel is fully connected. This class includes the MAC wire-tap channel, the 2-user interference channel with confidential messages, the 2-user interference channel with an external eavesdropper. Best known achievable schemes to date for these channels use Gaussian signaling. In this work, we show that structured codes outperform Gaussian random codes at high SNR when channel gains are real numbers.
In a two-user broadcast channel where one user has full CSIR and the other has none, a recent result showed that TDMA is strictly suboptimal and a product superposition requiring non-coherent signaling achieves DoF gains under many antenna configurations. This work introduces product superposition in the domain of coherent signaling with pilots, demonstrates the advantages of product superposition in low-SNR as well as high-SNR, and establishes DoF gains in a wider set of receiver antenna configurations. Two classes of decoders, with and without interference cancellation, are studied. Achievab…
This paper tackles the problem of single-user multiple-input multiple-output communication with 1-bit digital-to-analog and analog-to-digital converters. With the information-theoretic capacity as benchmark, the complementary strategies of beamforming and equiprobable signaling are contrasted in the regimes of operational interest, and the ensuing spectral efficiencies are characterized. Various canonical channel types are considered, with emphasis on line-of-sight settings under both spherical and planar wavefronts, respectively representative of short and long transmission ranges at mmWave a…
This paper studies the achievable rate region of the K-user Gaussian multiple-input single-output interference channel (MISO-IC) with the interference treated as noise, when improper or circularly asymmetric complex Gaussian signaling is applied. The transmit optimization with improper Gaussian signaling involves not only the signal covariance matrix as in the conventional proper or circularly symmetric Gaussian signaling, but also the signal pseudo-covariance matrix, which is conventionally set to zero in proper Gaussian signaling. By exploiting the separable rate expression with improper Gau…
Multiple Input Multiple Output (MIMO) Orthogonal Frequency Division Multiplexing (OFDM) is a promising transmission scheme for high performance broadband wireless communications. However, this technique suffers from a major drawback which is the high Peak to Average Power Ratio (PAPR) of the output signals. In order to overcome this issue, several methods that require the transmission of explicit Side Information (SI) bits have been proposed. In fact, the transmitted bits must be channel-encoded as they are particularly critical to the performance of the considered OFDM system. This channel-en…
This paper studies the achievable rate region of the two-user single-input-single-output (SISO) Gaussian interference channel, when the improper Gaussian signaling is applied. Under the assumption that the interference is treated as additive Gaussian noise, we show that the user's achievable rate can be expressed as a summation of the rate achievable by the conventional proper Gaussian signaling, which depends on the users' input covariances only, and an additional term, which is a function of both the users' covariances and pseudo-covariances. The additional degree of freedom given by the pse…
Coarsely quantized massive Multiple-Input Multiple-Output (MIMO) systems are gaining more interest due to their power efficiency. We present a new precoding technique to mitigate the Multi-User Interference (MUI) and the quantization distortions in a downlink Multi-User (MU) MIMO system with coarsely Quantized Constant Envelope (QCE) signals at the transmitter. The transmit signal vector is optimized for every desired received vector taking into account the QCE constraint. The optimization is based on maximizing the safety margin to the decision thresholds of the receiver constellation modulat…
This paper provides a complete characterization of the boundary of an achievable rate region, called the Pareto boundary, of the single-antenna Z interference channel (Z-IC), when interference is treated as noise and users transmit complex Gaussian signals that are allowed to be improper. By considering the augmented complex formulation, we derive a necessary and sufficient condition for improper signaling to be optimal. This condition is stated as a threshold on the interference channel coefficient, which is a function of the interfered user rate and which allows insightful interpretations in…
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…
Resource coordination and interference management is the key to achieving the benefits of femtocell networks. Over-the-air signaling is one of the most effective means for distributed dynamic resource coordination and interference management. However, the design of this type of signal is challenging. In this paper, we address the challenges and propose an effective solution, referred to as coded single-tone signaling (STS). The proposed coded STS scheme possesses certain highly desirable properties, such as no dedicated resource requirement (no overhead), no near-and-far effect, no inter-signa…
The capacity regions of multiple-input multiple-output Gaussian Z-interference channels are established for the very strong interference and aligned strong interference cases. The sum-rate capacity of such channels is established under noisy interference. These results generalize known results for scalar Gaussian Z-interference channels.
The rate maximization for the $K$-user interference channels (ICs) has been investigated extensively in the literature. However, the dual problem of minimizing the error probability with given signal modulations and/or data rates of the users is less exploited. In this paper, by utilizing the additional degrees of freedom attained from the improper signaling (versus the conventional proper signaling), we optimize the precoding matrices for the $K$-user single-input single-output (SISO) ICs to achieve minimal pair-wise error probability (PEP) and symbol error rate (SER) with two proposed algori…
The capacity region of a multiple-input-multiple-output interference channel (MIMO IC) where the channel matrices are square and invertible is studied. The capacity region for strong interference is established where the definition of strong interference parallels that of scalar channels. Moreover, the sum-rate capacity for Z interference, noisy interference, and mixed interference is established. These results generalize known results for the scalar Gaussian IC.
In this paper, we study the effect of feedback on two-user MIMO interference channels. The capacity region of MIMO interference channels with feedback is characterized within a constant number of bits, where this constant is independent of the channel matrices. Further, it is shown that the capacity region of a MIMO interference channel with feedback and its reciprocal interference channel are within a constant number of bits. Finally, the generalized degrees of freedom region for the MIMO interference channel with feedback is characterized.
Interference alignment in the K-user MIMO interference channel with constant channel coefficients is considered. A novel constructive method for finding the interference alignment solution is proposed for the case where the number of transmit antennas equals the number of receive antennas (NT = NR = N), the number of transmitter-receiver pairs equals K = N + 1, and all interference alignment multiplexing gains are one. The core of the method consists of solving an eigenvalue problem that incorporates the channel matrices of all interfering links. This procedure provides insight into the feasib…
In this paper, we propose low complexity opportunistic methods for interference alignment in $K$-transmitter MIMO interference channels by exploiting multiuser diversity. We do not assume availability of channel state information (CSI) at the transmitters. Receivers are required to feed back analog values indicating the extent to which the received interference subspaces are aligned. The proposed opportunistic interference alignment (OIA) achieves sum-rate comparable to conventional OIA schemes but with a significantly reduced computational complexity.
Recent works on MIMO interference channels have shown that interference alignment can significantly increase the achievable degrees of freedom (DoF) of the network. However, most of these works have assumed a fully connected interference graph. In this paper, we investigate how the partial connectivity can be exploited to enhance system performance in MIMO interference networks. We propose a novel interference mitigation scheme which introduces constraints for the signal subspaces of the precoders and decorrelators to mitigate "many" interference nulling constraints at a cost of "little" freed…
The use of low-resolution digital-to-analog converters (DACs) for transmit precoding provides crucial energy efficiency advantage for massive multiple-input multiple-output (MIMO) implementation. This paper formulates a quadrature amplitude modulation (QAM) constellation range and one-bit symbol-level precoding design problem for minimizing the average symbol error rate (SER) in downlink massive MIMO transmission. A tight upper-bound for SER with low-resolution DAC precoding is first derived. The derived expression suggests that the performance degradation of one-bit precoding can be interpret…
We consider interference alignment (IA) over K-user Gaussian MIMO interference channel (MIMO-IC) when the SNR is not asymptotically high. We introduce a generalization of IA which enables receive diversity inside the interference-free subspace. We generalize the existence criterion of an IA solution proposed by Yetis et al. to this case, thereby establishing a multi-user diversity-multiplexing trade-off (DMT) for the interference channel. Furthermore, we derive a closed-form tight lower-bound for the ergodic mutual information achievable using IA over a Gaussian MIMO-IC with Gaussian i.i.d. ch…
This paper investigates the performance of improper Gaussian signaling (IGS) for the $K$-user multiple-input, multiple-output (MIMO) interference channel (IC) with hardware impairments (HWI). HWI may arise due to imperfections in the devices like I/Q imbalance, phase noise, etc. With I/Q imbalance, the received signal is a widely linear transformation of the transmitted signal and noise. Thus, the effective noise at the receivers becomes improper, which means that its real and imaginary parts are correlated and/or have unequal powers. IGS can improve system performance with improper noise and/…
In this paper, we analyze the feasibility of linear interference alignment (IA) for multi-input-multi-output (MIMO) interference broadcast channel (MIMO-IBC) with constant coefficients. We pose and prove the necessary conditions of linear IA feasibility for general MIMO-IBC. Except for the proper condition, we find another necessary condition to ensure a kind of irreducible interference to be eliminated. We then prove the necessary and sufficient conditions for a special class of MIMO-IBC, where the numbers of antennas are divisible by the number of data streams per user. Since finding an inve…
This paper considers a deterministic physical model of massive multiple-input multiple-output (MIMO) systems with uniform linear antenna arrays. It is known that the maximum spatial degrees of freedom is achieved by spacing antenna elements at half the carrier wavelength. The purpose of this paper is to investigate the impacts of spacing antennas more densely than the critical separation. The achievable rates of MIMO systems are evaluated in the large-system limit, where the lengths of transmit and receive antenna arrays tend to infinity with the antenna separations kept constant. The main res…
MIMO Z Channel is investigated in this paper. We focus on how to tackle the interference when different users try to send their codewords to their corresponding receivers while only one user will cause interference to the other. We assume there are two transmitters and two receivers each with two antennas. We propose a strategy to remove the interference while allowing different users transmit at the same time. Our strategy is low-complexity while the performance is good. Mathematical analysis is provided and simulations are given based on our system.
Determining the feasibility conditions for vector space interference alignment in the K-user MIMO interference channel with constant channel coefficients has attracted much recent attention yet remains unsolved. The main result of this paper is restricted to the symmetric square case where all transmitters and receivers have N antennas, and each user desires d transmit dimensions. We prove that alignment is possible if and only if the number of antennas satisfies N>= d(K+1)/2. We also show a necessary condition for feasibility of alignment with arbitrary system parameters. An algebraic geometr…
This paper studies two-user MIMO interference channel with isotropic fading. We assume that users are equipped with arbitrary number of antennas and the channel state information (CSI) is available at receivers only. An outer bound is obtained for the degree of freedom region, which suggests the loss of degrees of freedom due to the lack of CSI at transmitters under many circumstances.
We establish the optimal input signaling and the capacity of MIMO channels under per-antenna power constraint. While admitting a linear eigenbeam structure, the optimal input is no longer diagonalizable by the channel right singular vectors as with sum power constraint. We formulate the capacity optimization as an SDP problem and solve in closed-form the optimal input covariance as a function of the dual variable. We then design an efficient algorithm to find this optimal input signaling for all channel sizes. The proposed algorithm allows for straightforward implementation in practical system…
In this paper, we analyze a multiple-input multiple-output (MIMO) interference channel where nodes are randomly distributed on a plane as a spatial Poisson cluster point process. Each cluster uses interference alignment (IA) to suppress intra-cluster interference but unlike most work on IA, we do not neglect inter-cluster interference. We also connect the accuracy of channel state information to the distance between the nodes, i.e. the quality of CSI degrades with increasing distance. Accounting for the training and feedback overhead, we derive the transmission capacity of this MIMO IA ad hoc …
Femtocell networks are promising for not only improving the coverage but also increasing the capacity of current cellular networks. The interference-limited reality in femtocell networks makes interference management (IM) the key to maintaining the quality of service and fairness in femtocell networks. Over-the-air signaling is one of the most effective means for fast distributed dynamic IM. However, the design of this type of signal is challenging. In this paper, we address the challenges and propose an effective solution, referred to as single-tone signaling (STS). The proposed STS scheme po…
The degrees of freedom (DoF) of the 3-user multiple input multiple output interference channel (3-user MIMO IC) are investigated where there is delayed channel state information at the transmitters (dCSIT). We generalize the ideas of Maleki et al. about {\it Retrospective Interference Alignment (RIA)} to be applied to the MIMO IC, where transmitters and receivers are equipped with $(M,N)$ antennas, respectively. We propose a two-phase transmission scheme where the number of slots per phase and number of transmitted symbols are optimized by solving a maximization problem. Finally, we review the…
In the two-user Gaussian interference channel with Gaussian inputs and treating interference as noise (TIN), improper complex signals can be beneficial if time-sharing is not allowed or if only the data rates are averaged over several transmit strategies (convex hull formulation). On the other hand, proper (circularly symmetric) signals have recently been shown to be optimal if coded time-sharing is considered, i.e., if both the data rates and the transmit powers are averaged. In this paper, we show that both conclusions remain the same if single-input multiple-output (SIMO) systems with multi…
In this paper, we propose an iterative interference alignment (IA) algorithm for MIMO cellular networks with partial connectivity, which is induced by heterogeneous path losses and spatial correlation. Such systems impose several key technical challenges in the IA algorithm design, namely the overlapping between the direct and interfering links due to the MIMO cellular topology as well as how to exploit the partial connectivity. We shall address these challenges and propose a three stage IA algorithm. As illustration, we analyze the achievable degree of freedom (DoF) of the proposed algorithm …
A rateless transmission architecture is developed for communication over Gaussian intersymbol interference channels, based on the concept of super-Nyquist (SNQ) signaling. In such systems, the signaling rate is chosen significantly higher than the Nyquist rate of the system. We show that such signaling, when used in conjunction with good "off-the-shelf" base codes, simple linear redundancy, and minimum mean-square error decision feedback equalization, results in capacity-approaching, low-complexity rateless codes for the time-varying intersymbol-interference channel. Constructions for both sin…
This paper considers the so-called MIMO interference channel. This situation has relevance in applications such as multi-cell coordination in cellular networks as well as spectrum sharing in cognitive radio networks among others. We address the design of precoding (i.e. beamforming) vectors at each sender with the aim of striking a compromise between beamforming gain at the intended receiver (Egoism) and the mitigation of interference created towards other receivers (Altruism). Combining egoistic and altruistic beamforming has been shown previously to be instrumental to optimizing the rates in…
Using Gaussian inputs and treating interference as noise at the receivers has recently been shown to be sum capacity achieving for the two-user single-input single-output (SISO) Gaussian interference channel in a low interference regime, where the interference levels are below certain thresholds. In this paper, such a low interference regime is characterized for multiple-input multiple-output (MIMO) Gaussian interference channels. Conditions are provided on the direct and cross channel gain matrices under which using Gaussian inputs and treating interference as noise at the receivers is sum ca…
