Two-user MIMO Research Articles

The Generalized Degrees-of-Freedom Region of the Two-User MIMO Broadcast Channel With Delayed CSIT

The Generalized Degrees-of-Freedom Region of the Two-User MIMO Broadcast Channel With Delayed CSIT

Rate-Splitting with Hybrid Messages: DoF Analysis of the Two-User MIMO Broadcast Channel with Imperfect CSIT

Rate-Splitting with Hybrid Messages: DoF Analysis of the Two-User MIMO Broadcast Channel with Imperfect CSIT

Transmit Correlation Diversity: Generalization, New Techniques, and Improved Bounds

When the users in a MIMO broadcast channel experience different spatial transmit correlation matrices, a class of gains is produced that is denoted <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">transmit correlation diversity.</i> This idea was conceived for channels in which transmit correlation matrices have mutually exclusive eigenspaces, allowing non-interfering training and transmission. This paper broadens the scope of transmit correlation diversity to the case of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">partially and fully overlapping</i> eigenspaces and introduces techniques to harvest these generalized gains. For the two-user MIMO broadcast channel, we derive achievable degrees of freedom (DoF) and achievable rate regions with/without channel state information at the receiver (CSIR). When CSIR is available, the proposed achievable DoF region is tight in some configurations of the number of receive antennas and the channel correlation ranks. We then extend the DoF results to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -user case by analyzing the interference graph that characterizes the overlapping structure of the eigenspaces. Our achievability results employ a combination of product superposition in the common part of the eigenspaces, and pre-beamforming (rate splitting) to create multiple data streams in non-overlapping parts of the eigenspaces. Massive MIMO is a natural example in which spatially correlated link gains are likely to occur. We study the achievable downlink sum rate for a frequency-division duplex massive MIMO system under transmit correlation diversity.

BER analysis of dynamic FOV based MIMO-NOMA-VLC system

Visible Light Communication (VLC) has evolved as a breakthrough technology for beyond 5G networks by providing a wide license-free spectrum. In this paper, we build a robust NOMA-VLC Network which exploits the MIMO technique. In particular, a two-user 2 × 2 MIMO-NOMA-VLC system is proposed which considers on–off keying (OOK) modulation and L-pulse position modulation (L-PPM). The closed-form bit-error-rate (BER) expressions for the OOK and L-PPM modulated two-user MIMO based NOMA-VLC system are derived with the consideration of perfect and imperfect successive interference cancellation (SIC). The analysis shows that the proposed system marginally outperforms the single-input single-output SISO-NOMA-VLC system. The error performance of L-PPM modulated system is superior to that of OOK modulated system for L>2. Further, the increment in the number of photo detector (PD’s) at the receiver does not improve the error performance of the system significantly. To address this, two dynamic field of view (FOV) strategies are proposed for attaining the additional enhancement in error performance of OOK and L-PPM modulated MIMO-NOMA-VLC system. The 2 × 2 MIMO-NOMA-VLC system based on dynamic FOV strategy-2 completely outperforms the 2 × 2 MIMO-NOMA-VLC systems based on static FOV and strategy-1 in terms of error performance. The effect of power allocation co-efficient, α, on the error performance of the proposed systems is investigated. The best average error probability of a two-user MIMO-NOMA-VLC system is attained at α = 0.3. The simulation results are in close alignment with those of the analytical outcomes.

On the Capacity Region of the Parallel Degraded Broadcast Channel With Three Receivers and Three-Degraded Message Sets

We consider a broadcast channel with three receivers and three-degraded message sets, i.e., the transmitter has a common message intended for all three receivers, a message intended for receivers 2 and 3, and a private message intended only for receiver 3. The messages are transmitted over a family of parallel degraded broadcast channels. In the most general case, the broadcast channel consists of the product of six parallel degraded broadcast channels, each with a different order of degradedness. We first consider an achievable rate region of Nair and El Gamal, by appropriately choosing independent input random variables and auxiliary random variables for each subchannel. We then show that the achievable rate region attains the capacity region for two different classes of such broadcast channels, one consisting of the product of five parallel degraded broadcast channels and another consisting of the product of three parallel degraded broadcast channels. To accomplish this, we make use of an information-theoretic inequality that may be proven using the Csiszar-sum identity. Next, we extend the result to the Gaussian case. We consider the aligned Gaussian MIMO broadcast channel consisting of the product of six parallel degraded Gaussian broadcast channels, where the Gaussian noise vectors for each of the users in each of the subchannels follow a degradedness order, i.e., the noise covariance matrices may be ordered in a positive semi-definite sense. We show that the Nair–El Gamal achievable rate region considered in this paper is maximized by Gaussian inputs. To prove that Gaussian inputs are optimal, we prove an extremal entropy inequality employing a new method recently introduced by Geng and Nair to prove the capacity region of the two-user Gaussian MIMO broadcast channel with common and private messages.

A Relay Can Increase Degrees of Freedom in Bursty Interference Networks

We investigate the benefits of incorporating relays in future multi-user wireless networks that seek to exploit unexplored bands of very high frequency spectrum, where transmitted signals are known to be highly susceptible to outages. To this end, we examine a two-user bursty MIMO Gaussian interference channel with an in-band relay, where Bernoulli random states conceptually capture signal outages. As our main result, we show that an in-band relay can provide a degrees of freedom (DoF) gain in this bursty channel. This beneficial role of in-band relays in the bursty channel is in direct contrast to their role in the non-bursty channel which is not as significant to provide a DoF gain. More importantly, we demonstrate that in certain antenna configurations, an in-band relay can help achieve interference-free performances with increased DoF. We find the benefits particularly substantial in high-outage circumstances, as the DoF gain can grow linearly with the number of antennas at the relay. In this paper, first we derive an outer bound from which we obtain a necessary condition for interference-free DoF performances. Then we develop a novel scheme that exploits information of the bursty channel states to achieve them.

Antenna Selection for MIMO Nonorthogonal Multiple Access Systems

This paper considers the joint antenna selection (AS) problem for a classical two-user MIMO non-orthogonal multiple access (NOMA) system, where both the base station (BS) and users (UEs) are equipped with multiple antennas. Specifically, several computationally-efficient AS algorithms are developed for two commonly-used NOMA scenarios: fixed power allocation NOMA (F-NOMA) and cognitive radio-inspired NOMA (CR-NOMA). For the F-NOMA system, two novel AS schemes, namely max-max-max AS (A$^3$-AS) and max-min-max AS (AIA-AS), are proposed to maximize the system sum-rate, without and with the consideration of user fairness, respectively. In the CR-NOMA network, a novel AS algorithm, termed maximum-channel-gain-based AS (MCG-AS), is proposed to maximize the achievable rate of the secondary user, under the condition that the primary user's quality of service requirement is satisfied. The asymptotic closed-form expressions of the average sum-rate for A$^3$-AS and AIA-AS and that of the average rate of the secondary user for MCG-AS are derived, respectively. Numerical results demonstrate that the AIA-AS provides better user-fairness, while the A$^3$-AS achieves a near-optimal sum-rate in F-NOMA systems. For the CR-NOMA scenario, MCG-AS achieves a near-optimal performance in a wide SNR regime. Furthermore, all the proposed AS algorithms yield a significant computational complexity reduction, compared to exhaustive search-based counterparts.

Robust Transceiver Design for Two-User MIMO Interference Channel With Simultaneous Wireless Information and Power Transfer

For two-user multiple-input–multiple-output interference channels with simultaneous wireless information and power transfer, we investigate robust transceiver design problem where channel uncertainties are modeled by worst case model. Our objective is to minimize worst case sum mean square error under individual transmit power constraints and worst case energy harvesting (EH) constraints. We propose to transform the quadratic EH constraints into linear matrix inequalities combined with two equality constraints. Furthermore, we propose to employ an algorithm based on constrained concave–convex procedure to alternatively optimize precoding matrices and postprocessing matrices. Simulation results demonstrate that our proposed robust transceiver design has significant performance gain over the nonrobust one.

Spatial Degrees of Freedom for MIMO Interference Channel with Local Channel State Information at Transmitters

This paper discusses inner bound and outer bound for the total number of spatial degrees of freedom (DoF) of the K-user MIMO interference channel with only local channel state information at each transmitter when channel extensions are disabled over time and frequency dimensions. We firstly provide a constructive proof of the achievability of the DoF based on zero forcing for two-user MIMO interference channel with $$M_{1},M_{2}$$M1,M2 antennas at transmitter 1, 2 and $$N_{1},N_{2}$$N1,N2 antennas at the corresponding receivers when only local channel state information (CSI) is available at the transmitters. Then the total achievable DoF and interference management scheme for 3-user interference channel with specific antenna configuration is presented by comparing the number of equations and the number of variables. We apply interference zero-forcing scheme and signal subspace analysis on the generalization of the interference management for this special case to the common 3-user and K-user MIMO symmetric interference channel and establish that the the inner bound on total spatial DoF $$\min ({K\min (M_{t}, N_{r}), \max (M_{t}, N_{r})})$$min(Kmin(Mt,Nr),max(Mt,Nr)) is achievable in K-user MIMO symmetric interference channel with $$M_{t}$$Mt transmitter antennas and $$N_{r}$$Nr receiver antennas. We also provide the proof of an outer bound on spatial DoF for the K-user MIMO symmetric interference channel with only local CSI at each transmitter and indicate that the inner bound and outer bound are tight when the number of receiver antennas is not less than the number of transmitter antennas.

A Unified Scheme to Achieve the Degrees-of-Freedom Region of the MIMO Interference Channel With Delayed Channel State Information

In interference channels (ICs), channel state information (CSI) can be utilized to design transmit signals that are optimally adapted to the state of the channels. This requires feeding CSI back to the transmitters. The CSI available at the transmitters (CSIT) is usually degraded, due to the limited capacity of the feedback link and the delays involved in the channel estimation and feedback. We discuss the scenario of fast fading and delayed CSIT, which is highly relevant in mobile environments with short channel coherence times. We consider the two-user multiple-input-multiple-output (MIMO) IC where the transmitters are provided with delayed CSIT. The DoF region for this channel was characterized by Vaze and Varanasi. We devise a simple and intuitive achievable scheme, which has a unified structure for different antenna configurations. We show that the proposed scheme also achieves the DoF region of the two-user MIMO broadcast channel (BC). In the IC, our scheme does not require the knowledge of direct channels at the transmitters. Moreover, we show that the amount of feedback can be further reduced by exploiting the invariances of the problem. Our approach can be helpful when analyzing more complicated networks.

Weighted Sum Rate Maximization of MIMO Broadcast and Interference Channels With Confidential Messages

We consider two-user MIMO broadcast and interference channels in which confidential messages intended for each receiver are kept secret from the other receiver. The confidential secrecy rates are nonconvex functions of transmit covariance matrices, which makes it intractable to find optimal transmit covariance matrices analytically. In the MIMO broadcast channels, we prove the weighted secrecy sum rate maximization has zero duality gap and KKT conditions are necessary conditions for the optimal solution. We apply the block successive lower-bound maximization technique to nonconvex weighted secrecy sum rate maximization problems. We also derive numerical algorithms for MIMO interference channels and Gaussian wiretap channels with a cooperative jammer. Every limit point achieved by the proposed algorithms is a local optimal solution that satisfies the KKT conditions. Numerical results show that the proposed algorithms outperform existing suboptimal algorithms in terms of secrecy rates.

Linear Precoder Design for Simultaneous Information and Energy Transfer Over Two-User MIMO Interference Channels

Communication strategies that utilize wireless media for simultaneous information and power transfer offer a promising perspective for efficient usage of energy resources. With this motivation, we focus on the design of optimal linear precoders for interference channels utilizing such strategies. We formulate the problem of minimizing the total minimum mean-square error while keeping the energy harvested at the energy receivers above given levels. Our framework leads to a non-convex problem formulation. For point-to-point multiple-input multiple-output channels, we provide a characterization of the optimal solutions under a constraint on the number of transmit antennas. For the general interference scenario, we propose two numerical approaches, one for the single antenna information receivers case, and the other for the general case. We also investigate a hybrid signalling scheme, where the transmitter sends a superposition of two signals: a deterministic signal optimized for energy transfer and an information carrying signal optimized for information and energy transfer. It is illustrated that if hybrid signalling is not incorporated into the transmission scheme, interference can be detrimental to the system performance when the number of antennas at the receivers is low.

Rate-Energy Region of Joint Information and Energy Transfer in a Two-User MIMO Interference Channel

This letter considers joint information and energy transfer in a two-user MIMO interference channel in which one receiver decodes information and the other harvests energy. We prove the energy beamforming is optimal for the energy transmitter irrespective of the operating SNR. We maximize the weighted sum of rate and energy to characterize the region of rate-energy pairs that are achievable using Gaussian signaling. We propose a numerical algorithm based on the alternating optimization technique because the maximization problem is a non-convex problem. The proposed algorithm converges to a KKT point of the maximization problem. Numerical results show that the rate-energy region of the algorithm is larger than those of the existing suboptimal algorithms. In addition, the algorithm harvests 60% more energy in the high-information transfer region than the suboptimal algorithms.

Structured Lattice Codes for Some Two-User Gaussian Networks With Cognition, Coordination, and Two Hops

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.

Joint Wireless Information and Energy Transfer with Reduced Feedback in MIMO Interference Channels

To determine the transmission strategy for the joint wireless information and energy transfer (JWIET) in the MIMO interference channel (IFC), the information access point (IAP) and energy access point (EAP) require the channel state information (CSI) of their associated links to both the information-decoding (ID) mobile stations (MSs) and energy-harvesting (EH) MSs (so-called local CSI). In this paper, to reduce the feedback overhead of MSs for the JWIET in two-user MIMO IFC, we propose a Geodesic energy beamforming scheme that requires partial CSI at the EAP. Furthermore, in the two-user MIMO IFC, it is proved that the Geodesic energy beamforming is the optimal non-cooperative strategy under local CSIT assumption. By adding a rank-one constraint on the transmit signal covariance of IAP, we can further reduce the feedback overhead to IAP by exploiting Geodesic information beamforming. Under the rank-one constraint of IAP's transmit signal, we prove that Geodesic information/energy beamforming approach is the optimal non-cooperative strategy for JWIET in the two-user MIMO IFC. We also discuss the extension of the proposed rank-one Geodesic information/energy beamforming strategies to general K-user MIMO IFC. Finally, by analyzing the achievable rate-energy performance statistically under imperfect partial CSIT, we propose an adaptive bit allocation strategy for both EH MS and ID MS.

A tight outer bound of the degrees of freedom for the MIMO interference channel with the delayed CSIT and partial local feedback

We have researched a new model for the general two-user MIMO interference channel. The model is constructed under the assumption that the instantaneous channel state information (CSI) is available to the receive nodes and the delayed CSI at transmitters (defined as CSIT) and partial local feedback are accessible to the transmit nodes. From this model, an outer bound of the degrees of freedom (DoF) region has been deduced for such channel. A special case of (6,1,5,2) interference channel is used to demonstrate the proposed interference cancellation scheme. This case shows that the limit DoF pairs (3,1) and (92,12) lied on the region boundary can be achieved. Based on this scheme, the general demonstration for the achievability of the DoF region is also presented. Our work shows that the derived outer bound is tight and under some cases, the DoF region with delayed CSIT and partial local feedback is comparable to that with instantaneous CSIT or delayed CSIT and global feedback.

MIMO Wiretap Channels With Unknown and Varying Eavesdropper Channel States

In this paper, a class of information theoretic secrecy problems is addressed where the eavesdropper channel state is completely unknown to the legitimate parties. In particular, a Gaussian MIMO wiretap channel is considered, where the eavesdropper channel state can vary from one channel use to the next, and the overall channel state sequence is known only to the eavesdropper. When the eavesdropper has fewer antennas than the transmitter and its intended receiver, a positive secrecy rate in the sense of strong secrecy is proved to be achievable and shown to match with the converse in secure degrees of freedom. This yields the conclusion that secure communication is possible regardless of the location or channel states of the eavesdropper. Additionally, it is observed that, the present setting renders the secrecy capacity problems for some multiterminal wiretap-type channels more tractable as compared to the case with full or partial knowledge of eavesdropper channel states. To demonstrate this observation, secure degrees of freedom regions are derived for the Gaussian MIMO multiple access (MAC) wiretap channel and the two-user Gaussian MIMO broadcast (BC) wiretap channel, where the transmitter(s) and intended receiver(s) have the same number of antennas.

An Extremal Inequality and the Capacity Region of the Degraded Compound Gaussian MIMO Broadcast Channel With Multiple Users

The two-user compound Gaussian MIMO broadcast channel models the situation where each user has a finite set of possible realizations. The transmitter sends two messages, one for each user, such that each user must be able to decode its message regardless of the actual realization. This channel also models a broadcast channel (BC) with two groups of users and two messages, with one message intended for each group of users. Weingarten et al. established the capacity region for the degraded case where the realizations/users exhibit a degradedness order. The degradedness order is defined through an additional realization/user where the realizations/users from one set are degraded with respect to him and where he is degraded with respect to the realizations/users from the other set. To show that Gaussian inputs attain the capacity region, they proved a new extremal inequality and employed the use of the channel enhancement technique as well. In this paper, we extend the result to the N-user degraded compound Gaussian MIMO BC, where the N users exhibit a degradedness order similar to the two-user case. We first prove a generalization of the extremal inequality considered by Weingarten et al.; instead of considering the difference between the weighted sum of two sets of conditional differential entropies, we consider the summation of N - 1 sets of such differences, where the conditioning random variables of the N - 1 sets form a Markov chain. Our proof relies on the Gaussian perturbation approach, the necessary KKT conditions as well as a data processing inequality. Finally, we specialize the generalized extremal inequality to characterize the capacity region of the N-user degraded compound Gaussian MIMO BC. By making appropriate use of the necessary KKT conditions, we are able to do away with the use of the channel enhancement technique that was employed in the proof of the capacity region of the two-user case.

Alamouti Coded Blind Interference Alignment with Partial Interference Cancellation Group Decoding

Interference alignment is a promising technique which suppresses interference in multiuser wireless networks. Most research on interference alignment aims at deriving or realizing the maximum achievable Degrees of Freedom (DoF), as well as the diversity gain is usually one. However, achieving better diversity performance is equally important. To improve the diversity gain, this paper presents an Alamouti coded Blind Interference Alignment (BIA) scheme, which combines interference alignment with Alamouti coding. First, the Alamouti coded BIA scheme for a two-user MIMO X channel is proposed. The proposed scheme results in 4/3 DoF with no channel state information at transmitters, and an equivalent channel matrix with partly orthogonal columns. The orthogonal structure can be exploited to obtain diversity gain. Therefore, we then explore the Partial Interference Cancellation (PIC) group decoding and ZF algorithm. Simulation results show that the proposed scheme achieves a higher diversity gain of 2, while keeps the same DoF as the original BIA scheme.

On the Capacity Region and the Generalized Degrees of Freedom Region for the MIMO Interference Channel With Feedback

In this paper, we study the effect of feedback on the two-user MIMO interference channel. The capacity region of the MIMO interference channel 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 the 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.