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The MAC-IC-MAC is a class of multiple-access interference channels consisting of two multiple-access channels (MACs) that are mutually interfering but in which there is interference only from one transmitter of each MAC to the receiver of the other MAC. Two achievable rate regions that are within a quantifiable gap of the capacity region for the discrete-memoryless semi-deterministic MAC-IC-MAC were obtained in a previous companion work by the authors using inner and outer bounds that are unions of polytopes over admissible random coding distributions. In this paper, we obtain single-distribution—and hence explicit—inner and outer bounds that characterize the capacity region of the MIMO Gaussian MAC-IC-MAC to within a constant gap. We also evaluate and study the generalized degrees of freedom (GDoF) region via multidimensional signal-level partitioning for MIMO networks. Through its lens, the achievability of the key vertices of the GDoF region are examined. This analysis as well as the symmetric GDoF curve reveal that, at high SNR, when the ratio of the interference-to-noise to the signal-to-noise ratios, both taken in dB, is within a certain range, non-interfering transmitters in that cell can fully occupy the receivers’ signal partitions in one or more dimensions that cannot otherwise be utilized by the interfering transmitter alone. This extends the same finding in the companion paper which established the results of this work for the scalar Gaussian MAC-IC-MAC. [ABSTRACT FROM AUTHOR]

The generalized degrees of freedom (GDoF) of the two-user multiple-input multiple-output interference channel is studied under the assumption of delayed channel state information at the transmitters. In particular, with $M$ antennas at each transmitter and $N$ antennas at each receiver, and in the non-trivial case when $M>N$ (with the case of $M\leq N$ not needing any CSIT), new lower and upper bounds on the symmetric GDoF are obtained that are parameterized by $\alpha $ , which links the interference-to-noise ratio (INR) and the signal-to-noise ratio (SNR) at each receiver via $\mathrm {INR}=\mathrm {SNR}^{{\alpha }}$. A new upper bound for the symmetric GDoF is obtained by maximizing a bound on the weighted sum rate, which in turn is obtained from a combination of genie-aided side-information and an extremal inequality. The maximum weighted sum rate in the high SNR regime is shown to occur when the transmit covariance matrix at each transmitter is full rank. An achievability scheme is developed that is based on block-Markov encoding and backward decoding, and which incorporates channel statistics through interference quantization and digital multicasting. This symmetric GDoF lower bound is maximized separately for different ranges of ${\alpha }$ , by optimizing the transmit power levels in the achievability scheme separately in the very weak $[0\leq {\alpha }\leq ({1}/{2})]$ , weak $[({1}/{2}) < {\alpha }\leq 1]$ , and strong $({\alpha }>1)$ interference regimes. The lower and upper bounds coincide when ${\alpha }\geq [({{r}+1})/({{r}+2})]$ , where ${r}=\min (2,{M}/{N})$ , thus characterizing the symmetric GDoF completely for strong interference and a range of values of weak interference. It is also shown that treating interference as noise is strictly sub-optimal from a GDoF perspective even when the interference is very weak. [ABSTRACT FROM AUTHOR]

Approximate capacity regions are established for a class of interfering multiple access channels consisting of two multiple-access channels (MACs), each with an arbitrary number of transmitters, with one transmitter in each MAC causing interference to the receiver of the other MAC, a channel we refer to henceforth as the MAC-IC-MAC. For the discrete memory-less (DM) MAC-IC-MAC, two inner bounds are obtained that are generalizations of prior inner bounds for the two-user DM interference channel (IC) due to Chong et al. For the semi-deterministic MAC-IC-MAC, it is shown that single-user coding at the non-interfering transmitters and superposition coding at the interfering transmitter of each MAC achieves a rate region that is within a quantifiable gap of the capacity region, thereby extending such a result for the two-user semi-deterministic IC by Telatar and Tse. For the Gaussian MAC-IC-MAC, an approximate capacity region that is within a constant gap of the capacity region is obtained, generalizing such a result for the two-user Gaussian IC by Etkin et al. On contrary to the aforementioned approximate capacity results for the two-user IC, whose achievability requires the union of all admissible input distributions, our gap results on the semi-deterministic and the Gaussian MAC-IC-MAC are achievable by only a subset and one of all admissible coding distributions, respectively. The symmetric generalized degrees of freedom (GDoFs) of the symmetric Gaussian MAC-IC-MAC with more than one user per cell, which is a function of the interference strength (the ratio of INR to SNR at high SNR, both expressed in dB) and the numbers of users in each cell, are V-shaped with flat shoulders. An analysis based on signal-level partitions shows that the non-interfering transmitters utilize the signal-level partitions at the receiver where they are intended that cannot be accessed by the interfering transmitters (due to the restriction of superposition coding), thereby improving the sum symmetric GDoF of up to one degree of freedom per cell under a range of SINR exponent levels, which in turn becomes wider as the number of transmitters in each cell increases. Consequently, time-sharing between interfering and non-interfering transmitters is GDoF-suboptimal in general, as is time-sharing between the two embedded MAC-Z-MACs. [ABSTRACT FROM AUTHOR]

We establish that the capacity regions of the discrete memoryless and vector Gaussian multiple access channels with general message sets are achievable with hierarchical successive group decoding, where groups of messages are successively decoded in accordance with the following rule: for each pair of messages known to nested sets of transmitters, the message known to more transmitters is decoded prior to—and not jointly with—the message known to fewer transmitters. This conclusion requires neither rate-splitting nor time-sharing, and is agnostic to whether or not the messages were encoded dependently. For instance, with private messages, hierarchical successive group decoding includes jointly decoding all messages at once, while for degraded messages, it is successive decoding in only one order. A consequence of our main result is that the capacity region of the multiple access channel with general message sets is achievable by time-sharing between only those successive decoding vertices whose decoding order respects the rule described as earlier. [ABSTRACT FROM PUBLISHER]

Sun and Luo recently showed that if the vector-space single-beam interference alignment problem for a $K$ -user, $L$ -carrier interference channel is feasible, then $K\leq 2L-2$ . We prove the converse, that if $K\leq 2L-2$ , then the problem is feasible, i.e., that the requisite beamformers do exist. [ABSTRACT FROM PUBLISHER]

We establish the degree of freedom (DoF) regions of the two-user multiple-input multiple-output (MIMO) broadcast channel with a general message set (BC-GM), that includes private and common messages, under fast fading. Nine different channel state knowledge assumptions—collectively known as hybrid channel state information at the transmitter (CSIT) models—are considered wherein the transmitter has either perfect/instantaneous, delayed, or no CSI from each of the two receivers. General antenna configurations are addressed wherein the three terminals have arbitrary numbers of antennas. The DoF regions are established for the five hybrid CSIT models in which either both channels are unknown at the transmitter or each of the two channels is known perfectly or with delay. In the four remaining cases in which exactly one of the two channels is unknown at the transmitter, the DoF regions under the restriction of linear encoding strategies—also known as the linear DoF (LDoF) regions—are established. As the key to the converse proofs of the LDoF region of the MIMO BC-GM under such hybrid CSIT assumptions, we show that, when only considering linear encoding strategies, the CSI from the receiver with more antennas does not help if there is no CSI available from the receiver with fewer antennas. This result is conjectured to be true even without the restriction on the encoding strategies to be linear. If true, the LDoF regions obtained for the four hybrid CSIT cases herein will also be the DoF regions for those cases. Many of the results of this paper when specialized to even the two-message problems are new. These include the LDoF regions, when one of the two channels is not known, of the MIMO BC-GM when specialized to the MIMO BC with private messages. They also include the DoF/LDoF regions for all the hybrid CSIT models obtained by specializing the corresponding regions for the MIMO BC-GM to the case with degraded messages. [ABSTRACT FROM AUTHOR]

We establish the degrees of freedom (DoF) region for the multiple-input multiple-output (MIMO) two-transmitter, and two-receiver ( $2 \times 2$ ) interference network with a general message set consisting of nine messages, one for each pair of a subset of transmitters at which that message is known and a subset of receivers where that message is desired. An outer bound on the general nine-message $2 \times 2$ interference network is obtained and it is shown to be tight, thereby establishing the DoF region for the most general antenna setting wherein the four nodes have an arbitrary number of antennas each. The DoF-optimal scheme is applicable to the MIMO $2 \times 2$ interference network with constant channel coefficients, and hence, a fortiori, to time/frequency varying channel scenarios. In particular, a linear precoding scheme is proposed that can achieve all the DoF tuples in the DoF region. In it, the precise roles played by transmit zero-forcing, interference alignment, random beamforming, symbol extensions, and asymmetric complex signaling (ACS) are delineated. For instance, we identify a class of antenna settings, in which ACS is required to achieve the fractional-valued corner points. Evidently, the DoF regions of all previously unknown cases of the $2 \times 2$ interference network with a subset of the nine-messages are newly established as special cases of the general result of this paper. For instance, the DoF region of the well-known four-message (and even three-message) MIMO $X$ channel is newly established. This problem had remained open despite previous studies, which had found inner and outer bounds that were not tight in general. Hence, the DoF regions of all special cases obtained from the general DoF region of the nine-message $2\times 2$ interference network of this paper that include at least three of the four $X$ channel messages are new, among many others. This paper sheds light on how the same physical $2 \times 2$ interference network could be used by a suitable choice of message sets to take most advantage of the channel resource in a flexible and efficient manner. [ABSTRACT FROM PUBLISHER]

The generalized diversity-multiplexing tradeoff (GDMT) of the two-user, quasi-static fading, multi-input, multi-output (MIMO) Z interference channel (Z-IC) is established for the general case with an arbitrary number of antennas at each node under the assumptions of full channel state information at the transmitters (CSIT) and a short-term average power constraint. In the GDMT framework, which captures the rate versus reliability tradeoff in the high signal-to-noise ratio (SNR) regime, the direct link SNR and cross-link interference-to-noise ratio (INR) are allowed to be disparate, so that their ratios relative to a nominal SNR in the decibel scale, i.e., the SNR and INR exponents, are arbitrary and fixed. It is shown that a simple Han–Kobayashi message-splitting/partial interference decoding scheme that uses only partial CSIT—in which the second transmitter’s signal depends only on its cross-link channel matrix and the first user’s transmit signal does not need any CSIT—can achieve the full-CSIT GDMT of the MIMO Z-IC. The GDMT of the MIMO Z-IC under the No-CSIT assumption is also obtained for some range of multiplexing gains. The size of this range depends on the numbers of antennas at the four nodes and the SNR and INR exponents of the direct and cross links, respectively. For certain classes of channels including those in which the interfered receiver has more antennas than do the other nodes, or when the INR exponent is greater than a certain threshold, the GDMT of the MIMO Z-IC under the No-CSIT assumption is also completely characterized. [ABSTRACT FROM AUTHOR]

The interference channel with common information (IC-CI) consists of two transmit–receive pairs that communicate over a common noisy medium. Each transmitter has an individual message for its paired receiver, and additionally, both transmitters have a common message to deliver to both receivers. In this paper, through explicit inner and outer bounds on the capacity region, we establish the capacity region of the Gaussian IC-CI to within a bounded gap of one bit, independently of the values of all channel parameters. Using this constant-gap characterization, the generalized degrees of freedom (GDoF) region is determined. It is shown that the introduction of the common message leads to an increase in the GDoF over that achievable over the Gaussian interference channel without a common message, and hence, to an unbounded improvement in the achievable rate. A surprising feature of the capacity-within-one-bit result is that most of the available benefit (i.e., to within one bit of capacity) due to the common message is achieved through a simple and explicit coding scheme that involves independent signaling at the two transmitters so that, in effect, this scheme forgoes the opportunity for transmitter cooperation that is inherently available due to shared knowledge of the common message at both transmitters. [ABSTRACT FROM AUTHOR]

A unified approach is developed for the study of multi-input, multi-output (MIMO) systems under fast fading with quantized covariance feedback. In such systems, the receiver computes, using perfect channel state information (CSI), the covariance matrices to be adopted by the transmitter corresponding to the current channel realization, and feeds back a quantized version of this information to the transmitter using finite, say Nf, bits per channel realization. Our analysis is based on a geometric framework we developed in a companion paper for manifolds of positive semi-definite (covariance) matrices with various trace and rank constraints. That analysis applies to MIMO systems in a unified manner to optimal as well as various suboptimal precoding methods for obtaining input covariances. These include, for example, the capacity achieving spatio-temporal water-filling strategy, the incorporation of just spatial water-filling and reduced-rank beamforming with power allocation in both cases, as well as MIMO systems with antenna selection. For a given system strategy, including the one that achieves capacity, the gap between the communication rates in the perfect and quantized covariance cases is shown to be O(2^-Nf/{N}), where N is the dimension of the particular Pn manifold used for quantization. This dimension depends on the precoding strategy adopted and strongly determines how quickly the communication rate with quantized covariance feedback approaches that with perfect CSI at the transmitter (CSIT). Our results show how the choice of covariance quantization manifold can be tailored to the available feedback rate in MIMO system design. [ABSTRACT FROM AUTHOR]

The two-user multiple-input multiple-output (MIMO) interference and cognitive radio channels are considered, where the i\th transmitter and the i\th receiver have Mi and Ni antennas, respectively. In particular, the degrees of freedom (DoF) regions of these channels are studied under the assumption of having no channel state information at the transmitters. Making certain assumptions about the distributions of channel matrices of increasing generality respectively, Huang , Zhu and Guo, and the authors of this paper characterized the DoF region of the MIMO interference channel for all values of the four-tuple (M1,M2,N1,N2), except when \min (M1,N1) > N2 > M2 or \min (M2,N2) > N1 > M1. More recently, for isotropic fading distributions, Zhu and Guo have solved this latter case by providing a tight outer bound to the DoF region. Here, a simpler and more widely applicable proof of that outer bound is given based on the idea of interference localization. Using the same idea, under Rayleigh fading, the DoF region is then also established for the MIMO cognitive radio channel (when the second transmitter is cognitive) with \min (M1+M2,N1) > N2 > M2—the only class for which the inner and outer bounds previously reported by the authors were not tight—thereby completing the DoF region characterization of this channel under Rayleigh fading for all values of (M1,M2,N1,N2). [ABSTRACT FROM PUBLISHER]

The degree-of-freedom (DoF) regions are characterized for the multiple-input multiple-output (MIMO) broadcast channel (BC), interference channels (ICs), including X and multihop ICs, and the cognitive radio channel (CRC), when there is no channel state information at the transmitter(s) (CSIT) and for fading distributions in which transmit directions are statistically indistinguishable. For the K-user MIMO BC, the exact DoF region is obtained, which shows that time division is DoF-region optimal. For the two-user MIMO IC and CRC, inner and outer bounds are obtained that coincide for a vast majority of the relative numbers of antennas at the four terminals. Finally, the DoF of the K-user MIMO IC, the CRC, and X networks are obtained for certain classes of these networks. The results herein are derived for fading distributions and additive noises that are more general than those considered in other simultaneous related works. The DoF with and without CSIT are compared and conditions under which a lack of CSIT does, or does not, result in the loss of DoF are identified, thereby 1) providing robust no-CSIT schemes that have the same DoF as their previously found CSIT counterparts and 2) identifying situations where CSI feedback to transmitters would provide gains that are significant enough that even the DoF could be improved. [ABSTRACT FROM PUBLISHER]