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This paper studies MIMO relays with non-identical link coherence times, a frequently occurring condition when, e.g., the nodes in the relay channel do not all have the same mobility, or the scatterers around some nodes have different mobility compared with those around other nodes. Despite its practical relevance, this condition, known as coherence diversity, has not been studied in the relay channel. This paper studies the performance of MIMO relays and proposes efficient transmission strategies under coherence diversity. Since coherence times have a prominent impact on channel training, we do not assume channel state is available to the decoder for free; all channel training resources are accounted for in the calculations. A product superposition technique is employed at the source, which allows a more efficient usage of degrees of freedom when the relay and the destination have different training requirements. Varying configurations of coherence times are studied. The interesting case where the different link coherence intervals are not a multiple of each other, and therefore the coherence intervals do not align, is studied. Relay scheduling is combined with the product superposition to obtain further gains in degrees of freedom. The impact of coherence diversity is further studied in the presence of multiple parallel relays.

Reconfigurable intelligent surfaces (RIS) are passive controllable arrays of small reflectors that direct electromagnetic energy towards or away from the target nodes, thereby allowing better management of signals and interference in a wireless network. The RIS has the potential for significantly improving the performance of wireless networks. Unfortunately, RIS also multiplies the number of Channel State Information (CSI) coefficients between the transmitter and receiver, which magnifies the challenges in estimating and communicating the channel state information. Furthermore, the simplicity and cost-effectiveness of the passive RIS also implies that the incoming links are not locally estimated at the RIS, and fresh pilots are not inserted into outgoing RIS links. This introduces new challenges for training and estimation of channel state information. The rapid growth of the literature on CSI acquisition in RIS-aided systems has been accompanied by variations in the underlying assumptions, models, and notation, which can obscure the similarities and differences of various techniques, and their relative merits. This paper presents a comprehensive exposition of principles and approaches in RIS channel estimation. The basic ideas underlying each class of techniques are reduced to their simplest form under a unified model and notation, and various approaches within each class are discussed. Several open problems in this area are identified and highlighted.

Empirical observations suggest that in practice, community membership does not completely explain the dependency between the edges of an observation graph. The residual dependence of the graph edges are modeled in this paper, to first order, by auxiliary node latent variables that affect the statistics of the graph edges but carry no information about the communities of interest. We then study community detection in graphs obeying the stochastic block model and censored block model with auxiliary latent variables. We analyze the conditions for exact recovery when these auxiliary latent variables are unknown, representing unknown nuisance parameters or model mismatch. We also analyze exact recovery when these secondary latent variables have been either fully or partially revealed. Finally, we propose a semidefinite programming algorithm for recovering the desired labels when the secondary labels are either known or unknown. We show that exact recovery is possible by semidefinite programming down to the respective maximum likelihood exact recovery threshold.

Compress-forward (CF) relays can improve communication rates even when the relay cannot decode the source signal. Efficient implementation of CF is a topic of contemporary interest, in part because of its potential impact on wireless technologies such as cloud-RAN. There exists a gap between the performance of CF implementations in the high spectral efficiency regime and the corresponding information theoretic achievable rates. We begin by re-framing a dilemma causing this gap, and propose an approach for its mitigation. We utilize trellis coded quantization (TCQ) at the relay together with multi-level coding at the source and relay, in a manner that facilitates the calculation of bit LLRs at the destination for joint decoding. The contributions of this work include designing TCQ for end-to-end relay performance, since a distortion-minimizing TCQ is suboptimum. The reported improvements include a 1dB gain over prior results for PSK modulation.

This paper produces an efficient Semidefinite Programming (SDP) solution for community detection that incorporates non-graph data, which in this context is known as side information. SDP is an efficient solution for standard community detection on graphs. We formulate a semi-definite relaxation for the maximum likelihood estimation of node labels, subject to observing both graph and non-graph data. This formulation is distinct from the SDP solution of standard community detection, but maintains its desirable properties. We calculate the exact recovery threshold for three types of non-graph information, which in this paper are called side information: partially revealed labels, noisy labels, as well as multiple observations (features) per node with arbitrary but finite cardinality. We find that SDP has the same exact recovery threshold in the presence of side information as maximum likelihood with side information. Thus, the methods developed herein are computationally efficient as well as asymptotically accurate for the solution of community detection in the presence of side information. Simulations show that the asymptotic results of this paper can also shed light on the performance of SDP for graphs of modest size., Comment: 15 pages

When the users in a MIMO broadcast channel experience different spatial transmit correlation matrices, a class of gains is produced that is denoted transmit correlation diversity. 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 partially and fully overlapping 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 $K$-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.

In community detection, the exact recovery of communities (clusters) has been mainly investigated under the general stochastic block model with edges drawn from Bernoulli distributions. This paper considers the exact recovery of communities in a complete graph in which the graph edges are drawn from either a set of Gaussian distributions with community-dependent means and variances, or a set of exponential distributions with community-dependent means. For each case, we introduce a new semi-metric that describes sufficient and necessary conditions of exact recovery. The necessary and sufficient conditions are asymptotically tight. The analysis is also extended to incomplete, fully connected weighted graphs.

The nodes of a graph existing in a cluster are more likely to connect to each other than with other nodes in the graph. Then revealing some information about some nodes, the structure of the graph (graph edges) provides this opportunity to know more information about other nodes. From this perspective, this paper revisits the node classification task in a semi-supervised scenario by graph convolutional networks (GCNs). The goal is to benefit from the flow of information that circulates around the revealed node labels. The contribution of this paper is twofold. First, this paper provides a method for extracting side information from a graph realization. Then a new GCN architecture is presented that combines the output of traditional GCN and the extracted side information. Another contribution of this paper is relevant to non-graph observations (independent side information) that exists beside a graph realization in many applications. Indeed, the extracted side information can be replaced by a sequence of side information that is independent of the graph structure. For both cases, the experiments on synthetic and real-world datasets demonstrate that the proposed model achieves a higher prediction accuracy in comparison to the existing state-of-the-art methods for the node classification task.

We consider the problem of covert communication over a state-dependent channel when the channel state is available either non-causally, causally, or strictly causally, either at the transmitter alone or at both transmitter and receiver. Covert communication with respect to an adversary, called "warden," is one in which, despite communication over the channel, the warden's observation remains indistinguishable from an output induced by innocent channel-input symbols. Covert communication involves fooling an adversary in part by a proliferation of codebooks; for reliable decoding at the legitimate receiver, the codebook uncertainty is typically removed via a shared secret key that is unavailable to the warden. In contrast to previous work, we do not assume the availability of a shared key at the transmitter and legitimate receiver. Instead, shared randomness is extracted from the channel state in a manner that keeps it secret from the warden, despite the influence of the channel state on the warden's output. When channel state is available at the transmitter and receiver, we derive the covert capacity region. When channel state is only available at the transmitter, we derive inner and outer bounds on the covert capacity. We provide examples for which the covert capacity is positive with knowledge of channel state information but is zero without it.

Motivated in part by the problem of secure multicast distributed storage, we analyze secrecy rates for a channel in which two transmitters simultaneously multicast to two receivers in the presence of an eavesdropper. Achievable rates are calculated via extensions of a technique due to Chia and El Gamal and the method of output statistics of random binning. Outer bounds are derived for both the degraded and non-degraded versions of the channel, and examples are provided in which the inner and outer bounds meet. The inner bounds recover known results for the multiple-access wiretap channel, broadcast channel with confidential messages, and the compound MAC channel. An auxiliary result is also produced that derives an inner bound on the minimal randomness necessary to achieve secrecy in multiple-access wiretap channels.

This paper employs the extrinsic information transfer (EXIT) method, a technique imported from the analysis of the iterative decoding of error control codes, to study the performance of belief propagation in community detection in the presence of side information. We consider both the detection of a single (hidden) community, as well as the problem of identifying two symmetric communities. For single community detection, this paper demonstrates the suitability of EXIT to predict the asymptotic phase transition for weak recovery. More importantly, EXIT analysis is leveraged to produce useful insights such as the performance of belief propagation near the threshold. For two symmetric communities, the asymptotic residual error for belief propagation is calculated under finite-alphabet side information, generalizing a previous result with noisy labels. EXIT analysis is used to illuminate the effect of side information on community detection, its relative importance depending on the correlation of the graphical information with node labels, as well as the effect of side information on residual errors.

We study channel resolvability for the discrete memoryless multiple-access channel with cribbing, i.e., the characterization of the amount of randomness required at the inputs to approximately produce a chosen i.i.d. output distribution according to KL divergence. We analyze resolvability rates when one encoder cribs (i) the input of the other encoder; or the output of the other encoder, (ii) non-causally, (iii) causally, or (iv) strictly-causally. For scenarios (i)-(iii), we exactly characterize the channel resolvability region. For (iv), we provide inner and outer bounds for the channel resolvability region; the crux of our achievability result is to handle the strict causality constraint with a block-Markov coding scheme in which dependencies across blocks are suitably hidden. Finally, we leverage the channel resolvability results to derive achievable secrecy rate regions for each of the cribbing scenarios under strong secrecy constraints.

We study the effect of the quality and quantity of side information on the recovery of a hidden community of size $K=o(n)$ in a graph of size $n$. Side information for each node in the graph is modeled by a random vector with the following features: either the dimension of the vector is allowed to vary with $n$, while log-likelihood ratio (LLR) of each component with respect to the node label is fixed, or the LLR is allowed to vary and the vector dimension is fixed. These two models represent the variation in quality and quantity of side information. Under maximum likelihood detection, we calculate tight necessary and sufficient conditions for exact recovery of the labels. We demonstrate how side information needs to evolve with $n$ in terms of either its quantity, or quality, to improve the exact recovery threshold. A similar set of results are obtained for weak recovery. Under belief propagation, tight necessary and sufficient conditions for weak recovery are calculated when the LLRs are constant, and sufficient conditions when the LLRs vary with $n$. Moreover, we design and analyze a local voting procedure using side information that can achieve exact recovery when applied after belief propagation. The results for belief propagation are validated via simulations on finite synthetic data-sets, showing that the asymptotic results of this paper can also shed light on the performance at finite $n$.

This paper addresses point-to-point communication over block-fading channels with independent fading blocks. When both channel state information at the transmitter (CSIT) and receiver (CSIR) are available, most achievable schemes use separable coding, i.e., coding independently and in parallel over different fading states. Unfortunately, separable coding has drawbacks including large memory requirements at both communication ends. In this paper a lattice coding and decoding scheme is proposed that achieves the ergodic capacity without separable coding, with lattice codebooks and decoding decision regions that are universal across channel realizations. We first demonstrate this result for fading distributions with discrete, finite support whose sequences are robustly typical. Results are then extended to continuous fading distributions, as well as multiple-input multiple-output (MIMO) systems. In addition, a variant of the proposed scheme is presented for the MIMO ergodic fading channel with CSIR only, where we prove the existence of a universal codebook that achieves rates within a constant gap to capacity for finite-support fading distributions. The gap is small compared with other schemes in the literature. Extension to continuous-valued fading is also provided., Comment: To appear in IEEE Transactions on Communications

The community detection problem involves making inferences about node labels in a graph, based on observing the graph edges. This paper studies the effect of additional, non-graphical side information on the phase transition of exact recovery in the binary stochastic block model (SBM) with $n$ nodes. When side information consists of noisy labels with error probability $\alpha$, it is shown that phase transition is improved if and only if $\log(\frac{1-\alpha}{\alpha})=\Omega(\log(n))$. When side information consists of revealing a fraction $1-\epsilon$ of the labels, it is shown that phase transition is improved if and only if $\log(1/\epsilon)=\Omega(\log(n))$. For a more general side information consisting of $K$ features, two scenarios are studied: (1)~$K$ is fixed while the likelihood of each feature with respect to corresponding node label evolves with $n$, and (2)~The number of features $K$ varies with $n$ but the likelihood of each feature is fixed. In each case, we find when side information improves the exact recovery phase transition and by how much. The calculated necessary and sufficient conditions for exact recovery are tight except for one special case. In the process of deriving inner bounds, a variation of an efficient algorithm is proposed for community detection with side information that uses a partial recovery algorithm combined with a local improvement procedure.

In general, the different links of a broadcast channel may experience different fading dynamics and, potentially, unequal or hybrid channel state information (CSI) conditions. The faster the fading and the shorter the fading block length, the more often the link needs to be trained and estimated at the receiver, and the more likely that CSI is stale or unavailable at the transmitter. Disparity of link fading dynamics in the presence of CSI limitations can be modeled by a multi-user broadcast channel with both non-identical link fading block lengths as well as dissimilar link CSIR/CSIT conditions. This paper investigates a MISO broadcast channel where some receivers experience longer coherence intervals (static receivers) and have CSIR, while some other receivers experience shorter coherence intervals (dynamic receivers) and do not enjoy free CSIR. We consider a variety of CSIT conditions for the above mentioned model, including no CSIT, delayed CSIT, or hybrid CSIT. To investigate the degrees of freedom region, we employ interference alignment and beamforming along with a product superposition that allows simultaneous but non-contaminating transmission of pilots and data to different receivers. Outer bounds employ the extremal entropy inequality as well as a bounding of the performance of a discrete memoryless multiuser multilevel broadcast channel. For several cases, inner and outer bounds are established that either partially meet, or the gap diminishes with increasing coherence times., Comment: 36 pages, 8 figures, submitted to IEEE Transactions on Information Theory

In the community detection problem, one may have access to additional observations (side information) about the label of each node. This paper studies the effect of the quality and quantity of side information on the phase transition of exact recovery in the binary symmetric stochastic block model (SBM) with $n$ nodes. When the side information consists of the label observed through a binary symmetric channel with crossover probability $\alpha$, and when $\log(\frac{1-\alpha}{\alpha}) =O(\log(n))$, it is shown that side information has a positive effect on phase transition; the new phase transition under this condition is characterized. When $\alpha$ is constant or approaches zero sufficiently slowly, i.e., $\log(\frac{1-\alpha}{\alpha}) = o(\log(n))$, it is shown that side information does not help exact recovery. When the side information consists of the label observed through a binary erasure channel with parameter $\epsilon$, and when $\log(\epsilon)=O(\log(n))$, it is shown that side information improves exact recovery and the new phase transition is characterized. If $\log(\epsilon)=o(\log(n))$, then it is shown that side information is not helpful. The results are then generalized to an arbitrary side information of finite cardinality. Necessary and sufficient conditions are derived for exact recovery that are tight, except for one special case under $M$-ary side information. An efficient algorithm that incorporates the effect of side information is proposed that uses a partial recovery algorithm combined with a local improvement procedure. Sufficient conditions are derived for exact recovery under this efficient algorithm., Comment: Withdrawn due to errors

A multiple-input multiple-output (MIMO) version of the dirty paper channel is studied, where the channel input and the dirt experience the same fading process and the fading channel state is known at the receiver (CSIR). This represents settings where signal and interference sources are co-located, such as in the broadcast channel. First, a variant of Costa's dirty paper coding (DPC) is presented, whose achievable rates are within a constant gap to capacity for all signal and dirt powers. Additionally, a lattice coding and decoding scheme is proposed, whose decision regions are independent of the channel realizations. Under Rayleigh fading, the gap to capacity of the lattice coding scheme vanishes with the number of receive antennas, even at finite Signal-to-Noise Ratio (SNR). Thus, although the capacity of the fading dirty paper channel remains unknown, this work shows it is not far from its dirt-free counterpart. The insights from the dirty paper channel directly lead to transmission strategies for the two-user MIMO broadcast channel (BC), where the transmitter emits a superposition of desired and undesired (dirt) signals with respect to each receiver. The performance of the lattice coding scheme is analyzed under different fading dynamics for the two users, showing that high-dimensional lattices achieve rates close to capacity., Comment: Accepted in IEEE Transactions on Wireless Communications

For ergodic fading, a lattice coding and decoding strategy is proposed and its performance is analyzed for the single-input single-output (SISO) and multiple-input multiple-output (MIMO) point-to-point channel as well as the multiple-access channel (MAC), with channel state information available only at the receiver (CSIR). At the decoder a novel strategy is proposed consisting of a time-varying equalization matrix followed by decision regions that depend only on channel statistics, not individual realizations. Our encoder has a similar structure to that of Erez and Zamir. For the SISO channel, the gap to capacity is bounded by a constant under a wide range of fading distributions. For the MIMO channel under Rayleigh fading, the rate achieved is within a gap to capacity that does not depend on the signal-to-noise ratio (SNR), and diminishes with the number of receive antennas. The analysis is extended to the K-user MAC where similar results hold. Achieving a small gap to capacity while limiting the use of CSIR to the equalizer highlights the scope for efficient decoder implementations, since decision regions are fixed, i.e., independent of channel realizations., Comment: Accepted at IEEE Transactions on Communications

The capacity of the AWGN broadcast channel is achieved by superposition coding, but superposition of individual coded modulations expands the modulation alphabet and distorts its configuration. Coded modulation over a broadcast channel subject to a specific channel-input modulation constraint remains an important open problem. Some progress has been made in the related area of unequal-error protection modulations which can be considered single-user broadcast transmission, but it does not approach all points on the boundary of the capacity region. This paper studies broadcast coded modulation using multilevel coding (MLC) subject to a specific channel input constellation. The conditions under which multilevel codes can achieve the constellation-constrained capacity of the AWGN broadcast channel are derived. For any given constellation, we propose a pragmatic multilevel design technique with near constellation-constrained-capacity performance where the coupling of the superposition inner and outer codes are localized to each bit-level. It is shown that this can be further relaxed to a code coupling on only one bit level, with little or no penalty under natural labeling. The rate allocation problem between the bit levels of the two users is studied and a pragmatic method is proposed, again with near-capacity performance. In further pursuit of lower complexity, a hybrid MLC-BICM is proposed, whose performance is shown to be very close to the boundary of the constellation-constrained capacity region. Simulation results show that good point-to-point LDPC codes produce excellent performance in the proposed coded modulation framework.

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. Achievable rates are established by analysis and illustrated by simulations., Comment: IEEE Trans. Wireless Communications, 2015

Individual links in a wireless network may experience unequal fading coherence times due to differences in mobility or scattering environment, a practical scenario where the fundamental limits of communication have been mostly unknown. This paper studies broadcast and multiple access channels where multiple receivers experience unequal fading block lengths, and channel state information (CSI) is not available at the transmitter(s), or for free at any receiver. In other words, the cost of acquiring CSI at the receiver is fully accounted for in the degrees of freedom. In the broadcast channel, the method of product superposition is employed to find the achievable degrees of freedom. We start with unequal coherence intervals with integer ratios. As long as the coherence time is at least twice the number of transmit and receive antennas, these degrees of freedom meet the upper bound in four cases: when the transmitter has fewer antennas than the receivers, when all receivers have the same number of antennas, when the coherence time of one receiver is much shorter than all others, or when all receivers have identical block fading intervals. The degrees of freedom region of the broadcast under identical coherence times was also previously unknown and is settled by the results of this paper. The disparity of coherence times leads to gains that are distinct from those arising from other techniques such as spatial multiplexing or multi-user diversity; this class of gains is denoted coherence diversity. The inner bounds are further extended to the case of multiple receivers experiencing fading block lengths of arbitrary ratio or alignment. Also, in the multiple access channel with unequal coherence times, achievable and outer bounds on the degrees of freedom are obtained., Comment: 45 pages, 13 figures, submitted to IEEE Transactions on Information Theory

This paper studies the interference channel with a cognitive relay (ICCR) under delayed feedback. Three types of delayed feedback are studied: delayed channel state information at the transmitter (CSIT), delayed output feedback, and delayed Shannon feedback. Outer bounds are derived for the DoF region of the two-user multiple-input multiple-output (MIMO) ICCR with delayed feedback as well as without feedback. For the single-input single-output (SISO) scenario, optimal schemes are proposed based on retrospective interference alignment. It is shown that while a cognitive relay without feedback cannot extend the sum-DoF beyond $1$ in the two-user SISO interference channel, delayed feedback in the same scenario can extend the sum-DoF to $4/3$. For the MIMO case, achievable schemes are obtained via extensions of retrospective interference alignment, leading to DoF regions that meet the respective upper bounds.

This letter produces a family of rate-compatible protograph-based LDPC codes approaching the independent and uniformly distributed (i.u.d.) capacity of inter-symbol interference (ISI) channels. This problem is highly nontrivial due to the joint design of structured (protograph-based) LDPC codes and the state structure of ISI channels. We describe a method to design nested high-rate protograph codes by adding variable nodes to the protograph of a lower rate code. We then design a family of rate-compatible protograph codes using the extension method. The resulting protograph codes have iterative decoding thresholds close to the i.u.d. capacity. Our results are supported by numerical simulations., Comment: 4 pages, 5 figures

This paper produces a rate-compatible protograph LDPC code at 1k information blocklength with superior performance in both waterfall and error floor regions. The design of such codes has proved difficult in the past because the constraints imposed by structured design (protographs), rate-compatibility, as well as small block length, are not easily satisfied together. For example, as the block length decreases, the predominance of decoding threshold as the main parameter in coding design is reduced, thus complicating the search for good codes. Our rate-compatible protograph codes have rates ranging from 1/3 to 4/5 and show no error floor down to $10^{-6}$ FER.

Despite encouraging advances in the design of relay codes, several important challenges remain. Many of the existing LDPC relay codes are tightly optimized for fixed channel conditions and not easily adapted without extensive re-optimization of the code. Some have high encoding complexity and some need long block lengths to approach capacity. This paper presents a high-performance protograph-based LDPC coding scheme for the half-duplex relay channel that addresses simultaneously several important issues: structured coding that permits easy design, low encoding complexity, embedded structure for convenient adaptation to various channel conditions, and performance close to capacity with a reasonable block length. The application of the coding structure to multi-relay networks is demonstrated. Finally, a simple new methodology for evaluating the end-to-end error performance of relay coding systems is developed and used to highlight the performance of the proposed codes., Comment: Accepted in IEEE Trans. Wireless Comm

Interference alignment (IA) is known to significantly increase sum-throughput at high SNR in the presence of multiple interfering nodes, however, the reliability of IA is little known, which is the subject of this paper. We study the error performance of IA and compare it with conventional orthogonal transmission schemes. Since most IA algorithms require extensive channel state information (CSI), we also investigate the impact of CSI imperfection (uncertainty) on the error performance. Our results show that under identical rates, IA attains a better error performance than the orthogonal scheme for practical signal to noise ratio (SNR) values but is more sensitive to CSI uncertainty. We design bit loading algorithms that significantly improve error performance of the existing IA schemes. Furthermore, we propose an adaptive transmission scheme that not only considerably reduces error probability, but also produces robustness to CSI uncertainty.

This paper considers the multiantenna broadcast channel without transmit-side channel state information (CSIT). For this channel, it has been known that when all receivers have channel state information (CSIR), the degrees of freedom (DoF) cannot be improved beyond what is available via TDMA. The same is true if none of the receivers possess CSIR. This paper shows that an entirely new scenario emerges when receivers have unequal CSIR. In particular, orthogonal transmission is no longer DoF-optimal when one receiver has CSIR and the other does not. A multiplicative superposition is proposed for this scenario and shown to attain the optimal degrees of freedom under a wide set of antenna configurations and coherence lengths. Two signaling schemes are constructed based on the multiplicative superposition. In the first method, the messages of the two receivers are carried in the row and column spaces of a matrix, respectively. This method works better than orthogonal transmission while reception at each receiver is still interference free. The second method uses coherent signaling for the receiver with CSIR, and Grassmannian signaling for the receiver without CSIR. This second method requires interference cancellation at the receiver with CSIR, but achieves higher DoF than the first method., Comment: 14 pages, 7 figures, accepted by IEEE Trans. Inform. Theory

We consider a spectrum-sharing network where n secondary relays are used to increase secondary rate and also mitigate interference on the primary by reducing the required overall secondary emitted power. We propose a distributed relay selection and clustering framework, obtain closed-form expressions for the secondary rate, and show that secondary rate increases proportionally to log n. Remarkably, this is on the same order as the growth rate obtained in the absence of a primary system and its imposed constraints. Our results show that to maximize the rate, the secondary relays must transmit with power proportional to n^(-1) (thus the sum of relay powers is bounded) and also that the secondary source may not operate at its maximum allowable power. The tradeoff between the secondary rate and the interference on the primary is also characterized, showing that the primary interference can be reduced asymptotically to zero as n increases, while still maintaining a secondary rate that grows proportionally to log n. Finally, to address the rate loss due to half-duplex relaying in the secondary, we propose an alternating relay protocol and investigate its performance., Comment: accepted by IEEE Trans. Commun., 11 pages, 8 figures

Linear precoding is a relatively simple method of MIMO signaling that can also be optimal in certain special cases. This paper is dedicated to high-SNR analysis of MIMO linear precoding. The Diversity-Multiplexing Tradeoff (DMT) of a number of linear precoders is analyzed. Furthermore, since the diversity at finite rate (also known as the fixed-rate regime, corresponding to multiplexing gain of zero) does not always follow from the DMT, linear precoders are also analyzed for their diversity at fixed rates. In several cases, the diversity at multiplexing gain of zero is found not to be unique, but rather to depend on spectral efficiency. The analysis includes the zero-forcing (ZF), regularized ZF, matched filtering and Wiener filtering precoders. We calculate the DMT of ZF precoding under two common design approaches, namely maximizing the throughput and minimizing the transmit power. It is shown that regularized ZF (RZF) or Matched filter (MF) suffer from error floors for all positive multiplexing gains. However, in the fixed rate regime, RZF and MF precoding achieve full diversity up to a certain spectral efficiency and zero diversity at rates above it. When the regularization parameter in the RZF is optimized in the MMSE sense, the structure is known as the Wiener precoder which in the fixed-rate regime is shown to have diversity that depends not only on the number of antennas, but also on the spectral efficiency. The diversity in the presence of both precoding and equalization is also analyzed., Comment: 46 pages, 10 figures

This paper investigates the degrees of freedom of the interference channel in the presence of a dedicated MIMO relay. The relay is used to manage the interference at the receivers. It is assumed that all nodes including the relay have channel state information only for their own links and that the relay has M (greater than or equal to K) antennas in a K-user network. We pose the question: What is the benefit of exploiting the direct links from the source to destinations compared to a simpler two-hop strategy. To answer this question, we first establish the degrees of freedom of the interference channel with a MIMO relay, showing that a K-pair network with a MIMO relay has K/2 degrees of freedom. Thus, appropriate signaling in a two-hop scenario captures the degrees of freedom without the need for the direct links. We then consider more sophisticated encoding strategies in search of other ways to exploit the direct links. Using a number of hybrid encoding strategies, we obtain non-asymptotic achievable sum-rates. We investigate the case where the relay (unlike other nodes) has access to abundant power, showing that when sources have power P and the relay is allowed power proportional to O(P^2), the full degrees of freedom K are available to the network., Comment: 7 double-column pages, 3 figures, accepted in IEEE Transactions on Information Theory

Opportunistic analysis has traditionally relied on independence assumptions that break down in many interesting and useful network topologies. This paper develops techniques that expand opportunistic analysis to a broader class of networks, proposes new opportunistic methods for several network geometries, and analyzes them in the high-SNR regime. For each of the geometries studied in the paper, we analyze the opportunistic DMT of several relay protocols, including amplify-and-forward, decode-and-forward, compress-and-forward, non-orthogonal amplify-forward, and dynamic decode-forward. Among the highlights of the results: in a variety of multi-user single-relay networks, simple selection strategies are developed and shown to be DMT-optimal. It is shown that compress-forward relaying achieves the DMT upper bound in the opportunistic multiple-access relay channel as well as in the opportunistic nxn user network with relay. Other protocols, e.g. dynamic decode-forward, are shown to be near optimal in several cases. Finite-precision feedback is analyzed for the opportunistic multiple-access relay channel, the opportunistic broadcast relay channel, and the opportunistic gateway channel, and is shown to be almost as good as full channel state information., Comment: To appear in IEEE Trans. Information Theory

In frequency-selective channels linear receivers enjoy significantly-reduced complexity compared with maximum likelihood receivers at the cost of performance degradation which can be in the form of a loss of the inherent frequency diversity order or reduced coding gain. This paper demonstrates that the minimum mean-square error symbol-by-symbol linear equalizer incurs no diversity loss compared to the maximum likelihood receivers. In particular, for a channel with memory $\nu$, it achieves the full diversity order of ($\nu+1$) while the zero-forcing symbol-by-symbol linear equalizer always achieves a diversity order of one.

In most MIMO systems, the family of waterfall error curves, calculated at different spectral efficiencies, are asymptotically parallel at high SNR. In other words, most MIMO systems exhibit a single diversity value for all fixed rates. The MIMO MMSE receiver does not follow this pattern and exhibits a varying diversity in its family of error curves. This work analyzes this interesting behavior of the MMSE MIMO receiver and produces the MMSE MIMO diversity at all rates. The diversity of the quasi-static flat-fading MIMO channel consisting of any arbitrary number of transmit and receive antennas is fully characterized, showing that full spatial diversity is possible if and only if the rate is within a certain bound which is a function of the number of antennas. For other rates, the available diversity is fully characterized. At sufficiently low rates, the MMSE receiver has a diversity similar to the maximum likelihood receiver (maximal diversity), while at high rates it performs similarly to the zero-forcing receiver (minimal diversity). Linear receivers are also studied in the context of the MIMO multiple access channel (MAC). Then, the quasi-static frequency selective MIMO channel is analyzed under zero-padding (ZP) and cyclic-prefix (CP) block transmissions and MMSE reception, and lower and upper bounds on diversity are derived. For the special case of SIMO under CP, it is shown that the above-mentioned bounds are tight., Comment: To appear in IEEE Transactions on Information Theory

Unlike point-to-point cognitive radio, where the constraint imposed by the primary rigidly curbs the secondary throughput, multiple secondary users have the potential to more efficiently harvest the spectrum and share it among themselves. This paper analyzes the sum throughput of a multiuser cognitive radio system with multi-antenna base stations, either in the uplink or downlink mode. The primary and secondary have $N$ and $n$ users, respectively, and their base stations have $M$ and $m$ antennas, respectively. We show that an uplink secondary throughput grows with $\frac{m}{N +1}\log n$ if the primary is a downlink system, and grows with $\frac{m}{M +1}\log n$ if the primary is an uplink system. These growth rates are shown to be optimal and can be obtained with a simple threshold-based user selection rule. Furthermore, we show that the secondary throughput can grow proportional to $\log n$ while simultaneously pushing the interference on the primary down to zero, asymptotically. Furthermore, we show that a downlink secondary throughput grows with $m\log \log n$ in the presence of either an uplink or downlink primary system. In addition, the interference on the primary can be made to go to zero asymptotically while the secondary throughput increases proportionally to $\log \log n$. Thus, unlike the point-to-point case, multiuser cognitive radios can achieve non-trivial sum throughput despite stringent primary interference constraints., Comment: 32 pages, 6 figures

This paper analyzes the diversity gain achieved by single-carrier frequency-domain equalizer (SC-FDE) in frequency selective channels, and uncovers the interplay between diversity gain $d$, channel memory length $\nu$, transmission block length $L$, and the spectral efficiency $R$. We specifically show that for the class of minimum means-square error (MMSE) SC-FDE receivers, for rates $R\leq\log\frac{L}{\nu}$ full diversity of $d=\nu+1$ is achievable, while for higher rates the diversity is given by $d=\lfloor2^{-R}L\rfloor+1$. In other words, the achievable diversity gain depends not only on the channel memory length, but also on the desired spectral efficiency and the transmission block length. A similar analysis reveals that for zero forcing SC-FDE, the diversity order is always one irrespective of channel memory length and spectral efficiency. These results are supported by simulations., Comment: 30 pages, 6 figures, to appear in the IEEE Transactions on Wireless Communications