In MIMO communications, it is expensive and some-times impossible to obtain timely channel state information at transmitter (CSIT) when the number of antennas is large. Furthermore, if the carrier frequency is high, the variation of the phases of the channel state information is significant with small movement in the channels. On the other hand, spatial signal path directions and the amplitudes of path gains vary slowly. We propose a beam network methodology for multi-antenna communication using such partial CSIT as directions and amplitudes instead of the conventional approach that employs full CSIT. Three representative problems are presented to demonstrate the simplicity and performance of the methodology. These include the single-user MIMO channel, a MIMO interference channel, and a multicast network via a reconfigurable intelligent surface (RIS). In particular, we see that the usual high complexity of RIS state design can be simplified to choosing states to connect an incoming beam to outgoing beams.1

Churn prediction is an important topic in the free online game industry. Reducing the churn rate of a game significantly helps with the success of the game. Churn prediction helps a game operator identify possible churning players and keep them engaged in the game via appropriate operational strategies, marketing strategies, and/or incentives. Playtime-related features are some of the widely used universal features for most churn prediction models. In this article, we consider developing new universal features for churn predictions for long-term players based on playtime. In particular, we measure playtime regularity using the notion ofentropyandcross-entropyfrom information theory. After computing playtime regularity of players from the datasets of six free online games of different types, we leverage information from the playtime regularity in the form of universal features for churn prediction. Experiments show that the proposed features are better at predicting churners compared to the baseline features, implying that the proposed features could utilize the information extracted from playtime more effectively than the related baseline playtime features.

Personality inference could create useful information, especially for the game industry. In this paper, we investigate whether and how the player personality is revealed in the player social interactions in a massively multiplayer online strategy game. We conduct an online survey with 50,319 participants to collect the player personality traits. We then develop proper features to capture the player in-game social interactions, and analyze correlations between personality and social interactions using these features. Our results show that the in-game social interactions are correlated with personality, and reveal how personality can affect social interactions in massively multiplayer online strategy games. Then we further discuss the implication of our results.

In the free online game industry, in-game purchase prediction is an important research topic. On the one hand, knowing the players who are likely or unlikely to pay for the game can help the development of corresponding marketing strategies and incentives. On the other hand, the result of purchase prediction indicates the status of the game operation status and helps the game company allocate a reasonable amount of resources for the game. In this paper, we focus on predicting the purchase probability of paying players and finding important features. We consider two types of features related to players’ playing and purchase behaviors. Then, based on these features we proposed, we use two different models to predict the survival probability for players and analyze the feature importance.

In the free online game industry, churn prediction is an important research topic. Reducing churn rate of a game significantly helps with the success of the game. Churn prediction helps a game operator identify possible churning players and keep them engaged in the game via appropriate operational strategies, marketing strategies, and/or incentives. Most churn prediction models are based on game-specific features, which limits their applicability to other games that do not share those features. In this paper, we consider developing universal features for churn predictions for long-term players. In particular, we mine player time spending regularity from data sets of two free online games. We leverage information from players’ in-game time spending regularity in the form of universal features for churn prediction. Experiments show that our developed features are better at predicting churners, compared to the baseline features. The performance of our developed features is satisfactory even without game-specific features.

Carrier frequency offset (CFO) and channel estimation is a classic topic with a large body of prior work using the maximum likelihood (ML) approach together with the CramérRao lower bound (CRLB) analysis. We give the maximum a posteriori probability (MAP) estimation solution which is particularly useful for tracking. Unlike the ML cases, the corresponding Bayesian CRLB (BCRLB) shows a clear relation with parameters and a low complexity algorithm achieves the BCRLB in almost all SNR range. We allow the time invariant MIMO channel within a packet to have arbitrary spatial correlation and mean. The estimation is based on pilot signals. An unexpected result is that the joint MAP estimation is equivalent to an individual MAP estimation of the frequency offset first, again different from the ML results. We provide insight on the pilot/training signal design based on the BCRLB. Unlike past algorithms that trade performance and/or complexity for the accommodation of time varying channels, the MAP solution provides a different route for dealing with time variation.

The free online game market is one of the fastest growing and most profitable markets in the electronic game industry. In order to improve players’ gaming experience and increase revenue, game data analytics is usually applied to support game development, in-game event design, and game operation. In particular, the game companies strive to understand and characterize the players’ buying power and design marketing strategies or incentives accordingly to increase their revenues. In this paper, we propose a novel algorithm to perform player clustering into the groups of high spenders (whales), moderate spenders (dolphins), and low spenders (minnows) based on the players’ purchase records via data mining technique. Evaluations including an A/B test with a typical popular free online game show that our proposed algorithm can effectively cluster the players in terms of their purchasing behavior and the game companies can benefit from our algorithm.

This paper presents an FPGA-based prototype of the dual link algorithm that maximize the achievable weighted sum rate for MIMO interference network. The iterative algorithm is fast monotone convergent but it must be completed quickly through pilot signaling. Therefore we propose an FPGA-based implementation, targeting software defined radio (SDR) platforms, that is designed to rapidly process the received pilot signals, estimate local channel information, and compute the transmit signal covariance matrices. Compared to its implementation on a CPU, the FPGA implementation is 2 to 4 times faster using fixed-point or floating-point designs.

In this paper, a comprehensive study of the downlink performance in a heterogeneous cellular network (or HetNet) is conducted via stochastic geometry. A general HetNet model is considered consisting of an arbitrary number of open-access and closed-access tiers of base stations (BSs) arranged according to independent homogeneous Poisson point processes. The BSs within each tier have a constant transmission power, random fading factors with an arbitrary distribution and arbitrary path-loss exponent of the power-law path-loss model. For such a system, analytical characterizations for the coverage probability are derived for the max-SINR connectivity and nearest-BS connectivity models. Using stochastic ordering, interesting properties and simplifications for the HetNet downlink performance are derived by relating these two connectivity models to the maximum instantaneous received power (MIRP) connectivity model and the maximum biased received power (MBRP) connectivity models, providing good insights about HetNets and their downlink performance in these complex networks. Furthermore, the results also demonstrate the effectiveness and analytical tractability of the stochastic geometric approach to study the HetNet performance.

This paper presents a simple method of internal channel calibration for MIMO interference networks to maintain TDD channel reciprocity. The method works for algorithms requiring channel reciprocity. In particular, it is shown how the method works for the distributed implementation of the Dual Link algorithm, which is a very fast and provably convergent algorithm for optimal interference management.

MIMO interference network optimization is important for increasingly crowded wireless communication networks. This paper presents a new algorithm, named Dual Link Algorithm, for weighted sum-rate maximization where the interference is efficiently managed. We consider general MIMO interference channels with Gaussian input and a total power constraint. Two of the previous state-of-the-art algorithms are the WMMSE algorithm and the polite water-filling (PWF) algorithm. The WMMSE algorithm is provably convergent, while the PWF algorithm takes the advantage of the optimal transmit signal structure and converges the fastest in most situations but is not guaranteed to converge in all situations. Therefore, it is highly desirable to design an algorithm that has the advantages of both algorithms. The proposed dual link algorithm is such an algorithm. Its fast and guaranteed convergence is important to distributed implementation and time varying channels. In addition, the technique and a scaling invariance property used in the convergence proof may find applications in other non-convex problems in communication networks.

The weighted sum-rate maximization in a general multiple-input multiple-output (MIMO) interference network has known to be a challenging non-convex problem, mainly due to the interference between different links. In this paper, by exploring the special structure of the sum-rate function being a difference of concave functions, we apply the convex-concave procedure to the weighted sum-rate maximization to handle non-convexity. With the introduction of a certain damping term, we establish the monotonie convergence of the proposed algorithm. Numerical examples show that the introduced damping term slows down the convergence of our algorithm but helps with finding a better solution in the network with high interference. Even though our algorithm has a slower convergence than some existing ones, it has the guaranteed convergence and can handle more general constraints and thus provides a general solver that can find broader applications.

In this paper, a comprehensive study of the downlink performance in a heterogeneous cellular network (or hetnet) is conducted. A general hetnet model is considered consisting of an arbitrary number of open-access and closed-access tier of base stations (BSs) arranged according to independent homogeneous Poisson point processes. The BSs of each tier have a constant transmission power, random fading coefficient with an arbitrary distribution and arbitrary path-loss exponent of the power-law path-loss model. For such a system, analytical characterizations for the coverage probability and average rate at an arbitrary mobile-station (MS), and average per-tier load are derived for the max-SINR connectivity model. Using stochastic ordering, interesting properties and simplifications for the hetnet downlink performance are derived by relating this connectivity model to the maximum instantaneous received power (MIRP) connectivity model, providing good insights about the hetnets and the downlink performance in these complex networks. Furthermore, the results also demonstrate the effectiveness and analytical tractability of the stochastic geometric approach to study the hetnet performance.

In a cognitive radio (CR) network, the CR devices opportunistically communicate in the frequency bands occupied by the primary users in order to improve the spectral efficiency in these bands. By sensing the primary users, e.g., the television transmitter-receiver pairs and the wireless microphone systems, each CR device determines whether or not to operate in the band. The CR devices, due to erroneous sensing, either fail to detect the primary user, causing excessive interference at the primary users, or have a false-alarm, causing it to remain silent in a white-space band leading to poor spectrum utility. The impact of these imperfections on the primary user operations in terms of the coverage probability is characterized where the primary users and the CR devices are distributed according to independent homogeneous Poisson point processes on the plane.

In this paper, we analyze the signal-to-interference-plus-noise ratio (SINR) performance at a mobile station (MS) in a random cellular network. The cellular network is formed by base stations (BSs) placed in a one-, two-, or three-dimensional space according to a possibly non-homogeneous Poisson point process, which is a generalization of the so-called shotgun cellular system. We develop a sequence of equivalence relations for the SCSs and use them to derive semi-analytical expressions for the coverage probability at the MS when the transmissions from each BS may be affected by random fading with arbitrary distributions as well as attenuation following arbitrary path-loss models. For homogeneous Poisson point processes in the interference-limited case with power-law path-loss model, we show that the SINR distribution is the same for all fading distributions and is not a function of the base station density. In addition, the influence of random transmission power, power control, and multiple channel reuse groups on the downlink performance is also discussed. The techniques developed for the analysis of SINR have applications beyond cellular networks and can be used in similar studies for cognitive radio networks, femtocell networks, and other heterogeneous and multi-tier networks.

It is often impractical to obtain global channel knowledge and conduct centralized optimization for wireless networks. We study distributed weighted sum-rate maximization (WSRM) in general MIMO interference networks, named B-MAC interference networks. It is desirable to exploit the structure of the problem to design distributed algorithms with high performance and low signaling overhead. We recently unveiled a polite water-filling (PWF) structure satisfied by all Pareto optimal inputs of important achievable regions of the B-MAC interference networks. The PWF offers an elegant method to decompose a network into multiple equivalent single user channels and thus, facilitates the design of distributed algorithms. Based on the PWF, we design efficient distributed algorithms which only need local channel knowledge and converge to a stationary point of the WSRM problem. For TDD networks, the duality inherited in PWF and the channel reciprocity are further exploited to reduce the signaling overhead. The proposed algorithms are shown by simulations to outperform the state-of-the-art.

The motivation of this work is to examine how well methods, such as successive interference cancellation and interference alignment from information theoretic solution, work in real-world where the received signal is quantized for digital processing. As a first step, we consider Gaussian Multiple Access Channels with the quantization noise modeled as Gaussian noise, whose variance depends on the received signal power at the receiver. We call this model Gaussian Multiple Access Channel with Signal Dependent Noise. The achievable rate region of this model is given under finite transmitted signal power constraint, where the achievable scheme could be successive interference cancellation (SIC). This region is outer bounded by a finite region with unlimited received signal power, where the achievable scheme is time division multiple access (TDMA). Thus, one way to measure the usefulness of successive interference cancellation is to study the gap between the SIC region and the TDMA region under finite power constraints. For the symmetric maximum signal to channel noise ratio (SCNR) case, where the maximum SCNR of all users are the same, we show that the gap between the SIC region and the TDMA region is within 0.5 bits for any number of users. Furthermore, for this case, if the maximum quantization noise power due to one user is stronger than the channel noise power, then the sum rate difference between the SIC region and the TDMA region is within 0.5 bits. For the asymmetric maximum SCNR case, the gap can be small when all users have high SCNR (e.g., 30dB), where the receiver is equipped with a low precision ADC (e.g., 2–3 bits).

In this paper, we consider the downlink signal-to-interference-plus-noise ratio (SINR) analysis in a heterogeneous cellular network with K tiers. Each tier is characterized by a base-station (BS) arrangement according to a homogeneous Poisson point process with certain BS density, transmission power, random shadow fading factors with arbitrary distribution, arbitrary path-loss exponent and a certain bias towards admitting the mobile-station (MS). The MS associates with the BS that has the maximum instantaneous biased received power under the open access cell association scheme. For such a general setting, we provide an analytical characterization of the coverage probability at the MS.

Due to the large size of wireless networks, it is often impractical for nodes to track changes in the complete network state. As a result, nodes have to make distributed decisions about their transmission and reception parameters based on their local view of the network. In this paper, we characterize the impact of distributed decisions on the global network performance in terms of achievable sum rates. We first formalize the concept of local view by proposing a protocol abstraction using the concept of local message passing. In the proposed protocol, nodes forward information about the network state to other neighboring nodes, thereby allowing network-state information to trickle to all the nodes. The protocol proceeds in rounds, where all transmitters send a message followed by a message by all receivers. The number of rounds then provides a natural metric to quantify the extent of local information at each node. We next study two network connectivities, Z-channel, and a three-user double Z-channel. In each case, we characterize achievable sum rate with partial message passing leading to two main results. First, in many cases, nodes can make distributed decisions with only local information about the network and can still achieve the same sum capacity as can be attained with global information irrespective of the actual channel gains. We label such schemes as universally optimal. Second, for the case of three-user double Z-channel, we show that universal optimality is not achievable if the per node information is below a threshold. In fact, distributed decisions can lead to unbounded losses compared to full information case for some channel gains.

This paper studies the carrier-to-interference ratio (CIR) and carrier-to-interference-plus-noise ratio (CINR) performance at the mobile station (MS) within a multi-tier network composed of M tiers of wireless networks, with each tier modeled as the homogeneous n-dimensional (n-D, n=1,2, and 3) shotgun cellular system, where the base station (BS) distribution is given by the homogeneous Poisson point process in n-D. The CIR and CINR at the MS in a single tier network are thoroughly analyzed to simplify the analysis of the multi-tier network. For the multi-tier network with given system parameters, the following are the main results of this paper: (1) semi-analytical expressions for the tail probabilities of CIR and CINR; (2) a closed form expression for the tail probability of CIR in the range [1,infinity); (3) a closed form expression for the tail probability of an approximation to CINR in the entire range [0,infinity); (4) a lookup table based approach for obtaining the tail probability of CINR, and (5) the study of the effect of shadow fading and BSs with ideal sectorized antennas on the CIR and CINR. Based on these results, it is shown that, in a practical cellular system, the installation of additional wireless networks (microcells, picocells and femtocells) with low power BSs over the already existing macrocell network will always improve the CINR performance at the MS.

The algorithms in this paper exploit optimal input structure in interference networks and is a major advance from the state-of-the-art. Optimization under multiple linear constraints is important for interference networks with individual power constraints, per-antenna power constraints, and/or interference constraints as in cognitive radios. While for single-user MIMO channel transmitter optimization, no one uses general purpose optimization algorithms such as steepest ascent because water-filling is optimal and much simpler, this is not true for MIMO multiaccess channels (MAC), broadcast channels (BC), and the non-convex optimization of interference networks because the traditional water-filling is far from optimal for networks. We recently found the right form of water-filling, polite water-filling, for some capacity/achievable regions of the general MIMO interference networks, named B-MAC networks, which include BC, MAC, interference channels, X networks, and most practical wireless networks as special cases. In this paper, we use weighted sum-rate maximization under multiple linear constraints in interference tree networks, a natural extension of MAC and BC, as an example to show how to design highly efficiency and low complexity algorithms. Several times faster convergence speed and orders of magnitude higher accuracy than the state-of-the-art are demonstrated by numerical examples.

We found a network version of water-filling, named polite water-filling, that is optimal for all boundary points of the capacity regions of MAC and BC and for all boundary points of a set of achievable regions of a general class of interference networks, named MIMO B-MAC networks that include BC, MAC, interference channels, X networks, and most practical networks as special cases. It is polite because it strikes an optimal balance between reducing interference to others and maximizing a link's own rate. Unlike in single-user MIMO channels, where the optimal input covariance can be solved by the water-filling, the traditional water-filling is far from optimal in networks. Thus, general purpose optimization algorithms have been used for networks but have high complexity and do not work well for non-convex cases. Together with our duality result, the polite water-filling can be used to design highly efficient low-complexity iterative centralized/distributed algorithms for the optimization of input covariance matrices, including both power and beamforming matrices, because it takes the advantage of the structure of the problems. References to the resulting algorithms that outperform the state-of-the-art by a wide margin are provided.

This paper proposes a three dimensional channel model for the study of distributed MIMO communication systems, where the transmit antennas may be at different directions when viewed from the receiver. Examples of such systems include cooperative satellites and air based base stations. Both line of sight and multipath signal components are considered. A common difficulty of such channel models is that there are too many geometric parameters to produce analytical correlation functions of the antennas in order to gain insight on how the channel depends on those parameters. The difficulty is solved here by identifying a single key parameter, the projected distance, to summarize the effect of all the geometric parameters, and thus, the model is simple enough to be useful for system designers. Analytical correlation functions are provided, which is used to compare the rate of the MIMO and SIMO systems in order to demonstrate that with high probability, significant rate gain can be obtained by the distributed MIMO systems.

It is well known that in general, the traditional water-filling is far from optimal in networks. We recently found the long-sought network version of water-filling named polite water-filling that is optimal for a large class of MIMO networks called B-MAC networks, of which interference Tree (iTree) networks is a subset whose interference graphs have no directional loop. iTree networks is a natural extension of both broadcast channel (BC) and multiaccess channel (MAC) and possesses many desirable properties for further information theoretic study. Given the optimality of the polite water-filling, general purpose optimization algorithms for networks are no longer needed because they do not exploit the structure of the problems. Here, we demonstrate it through the weighted sum-rate maximization. The significance of the results is that the algorithm can be easily modified for general B-MAC networks with interference loops. It illustrates the properties of iTree networks and for the special cases of MAC and BC, replaces the current steepest ascent algorithms for finding the capacity regions. The fast convergence and high accuracy of the proposed algorithms are verified by simulation.

Cognitive radios (CR) must ensure that their transmissions do not cause harmful interference to the primary users that operate in the same band. Primary users with short communication range transmitters, such as wireless microphone systems, are considered. The CR network is distributed according to a Poisson process. The CRs detect the primary user either through primary transmitter signals or through beacons collocated with the primary receiver. Three levels of cooperative sensing by CRs are analyzed, namely, no cooperation, full cooperation and partial cooperation. The characteristic function of the interference at the primary receiver for all combinations of primary user detection and cooperative sensing schemes are derived for the system modeled along a line (1-D) and about a plane (2-D). The analysis in 1-D corresponds to a highway scenario and 2-D corresponds to a planar system. The carrier-to-interference ratio (C/I) at the primary receiver is evaluated using the characteristic function. The analysis clearly shows the need for cooperative spectrum sensing when the density of the CRs is high. It is shown that the effect of shadowing, small scale fading, and power control at the CRs can be captured into the density of the CR network. The results hold for the CRs that are wide-band devices as well as narrow-band devices.

Abstract This paper investigates the disaster area communication system using relay‐assisted wireless network for first responders as mobile nodes (MNs). Firstly, a novel mobility model is proposed to describe the movement pattern of MNs within a large disaster area. Secondly, we study the relay management problem of finding a minimum number of relay nodes (RNs) and their dynamic locations to cover all the MNs within the disaster area. A square disk cover (SDC) problem is formulated and three different algorithms, including the two‐vertex square covering (TVSC) algorithm, the circle covering algorithm and the binary integer programming (BIP) algorithm, are proposed to solve the SDC problem. Simulation results are presented to validate the mobility model and compare the algorithms with respect to computational complexity and worst case performance ratio. Copyright © 2008 John Wiley & Sons, Ltd.

In this paper, we establish a rate duality between the forward and reverse links of MIMO interference channel, where the reverse links are obtained by exchanging the roles of transmitters and receivers in the forward links, and the corresponding channel matrices are conjugate transpose of the forward channel matrices. Since the capacity region for general interference channel is unknown, we show that the forward and reverse links have the same achievable rate region by treating interference as noise under some sum power constraint. The explicit expression of the corresponding input covariance matrix transformation is provided. We discuss the connection between the proposed transformation and the MAC-BC transformations in the previous works. As an application, a duality based iterative algorithm is proposed to maximize the sum rate of MIMO interference channel under sum power constraint. We also extend the algorithm to individual power constraint. The proposed algorithms are shown to be effective by simulation.

This paper analyzes the carrier-to-interference ratio of the so-called shotgun cellular system (SCS). In the SCS, base-stations are placed randomly according to a two-dimensional Poisson point process. Such a system can model a dense cellular or wireless data network deployment, where the base station locations end up being close to random due to constraints other than optimal coverage. The SCS is a simple cellular system where we can introduce several variations and design scenarios such as shadow fading, power control features, and multiple channel reuse groups, and assess their impact on the performance. We first derive an analytical expression for the characteristic function of the inverse of the carrier-to-interference ratio. Using this result, we show that the carrier-to-interference ratio is independent of the base station density and further, we derive a semi-analytical expression for the tail-probability. These results enable a complete characterization of the cellular performance of the SCS. Next, we incorporate shadow fading into the SCS and demonstrate that it merely scales the base station density by a constant. Hence, the cellular performance of the SCS is independent of shadow fading. These results are further used to analyze dense cellular scenarios.

In distributed wireless networks, nodes often do not know the topology (network size, connectivity and the channel gains) of the network. Thus, they cannot compute their own maximum transmission rate and appropriate transmission scheme. In this paper, we address the inter-related problems of learning the network and the associated best achievable rates. To make progress, we will focus on K-user deterministic interference networks. First, we propose a message passing algorithm which allows nodes to incrementally learn the network topology. In each round of message passing, nodes forward what they believe is the new information to their neighbors and thus the network topology information trickles via broadcasts. Next, we consider two special examples of Z-channel and double-Z interference network and determine the sum-rate points with incomplete network information at different nodes. We show that the sum-rate point can in fact be achieved with less than full information at all the nodes but in general, less network information implies reduced set of achievable rates. In order to analyze the performance of a double-Z interference network with limited information, we find the capacity region of a deterministic double-Z interference network with full information, which is of independent interest.

We analyze the effect of finite rate feedback on code-division multiple-access (CDMA) signature optimization and multiple-input multiple-output (MIMO) beamforming vector selection. In CDMA signature optimization, for a particular user, the receiver selects a signature vector from a codebook to best avoid interference from other users, and then feeds the corresponding index back to the specified user. For MIMO beamforming vector selection, the receiver chooses a beamforming vector from a given codebook to maximize the instantaneous information rate, and feeds back the corresponding index to the transmitter. These two problems are dual: both can be modeled as selecting a unit norm vector from a finite size codebook to ldquomatchrdquo a randomly generated Gaussian matrix. Assuming that the feedback link is rate limited, our main result is an exact asymptotic performance formula where the length of the signature/beamforming vector, the dimensions of interference/channel matrix, and the feedback rate approach infinity with constant ratios. The proof rests on the large deviations of the underlying random matrix ensemble. Further, we show that random codebooks generated from the isotropic distribution are asymptotically optimal not only on average, but also in probability.

It is well known that multiple-input multiple-output (MIMO) systems have high spectral efficiency, especially when channel state information at the transmitter (CSIT) is available. In many practical systems, it is reasonable to assume that the CSIT is obtained by a limited (i.e., finite rate) feedback and is therefore imperfect. We consider the design problem of how to use the limited feedback resource to maximize the achievable information rate. In particular, we develop a low complexity power on/off strategy with beamforming (or Grassmann precoding), and analytically characterize its performance. Given the eigenvalue decomposition of the covariance matrix of the transmitted signal, refer to the eigenvectors as beams, and to the corresponding eigenvalues as the beam's power. A power on/off strategy means that a beam is either turned on with a constant power, or turned off. We will first assume that the beams match the channel perfectly and show that the ratio between the optimal number of beams turned on and the number of antennas converges to a constant when the numbers of transmit and receive antennas approach infinity proportionally. This motivates our power on/off strategy where the number of beams turned on is independent of channel realizations but is a function of the signal-to-noise ratio (SNR). When the feedback rate is finite, beamforming cannot be perfect, and we characterize the effect of imperfect beamforming by quantization bounds on the Grassmann manifold. By combining the results for power on/off and beamforming, a good approximation to the achievable information rate is derived. Simulations show that the proposed strategy is near optimal and the performance approximation is accurate for all experimented SNRs.

This paper presents a high-throughput decoder architecture for generic quasi-cyclic low-density parity-check (QC-LDPC) codes. Various optimizations are employed to increase the clock speed. A row permutation scheme is proposed to significantly simplify the implementation of the shuffle network in LDPC decoder. An approximate layered decoding approach is explored to reduce the critical path of the layered LDPC decoder. The computation core is further optimized to reduce the computation delay. It is estimated that 4.7 Gb/s decoding throughput can be achieved at 15 iterations using the current technology.

We consider multiaccess multiple-input multiple-output (MIMO) systems with finite rate feedback with the aim of understanding how to efficiently employ the given feedback resource to maximize the sum rate. A joint quantization and feedback strategy is proposed: the base station selects the strongest users, jointly quantizes their strongest eigen-channel vectors and broadcasts a common feedback to all the users. This joint strategy differs from an individual strategy in which quantization and feedback are performed independently across users, and it improves upon the individual strategy in the same way that vector quantization improves upon scalar quantization. To analyze the proposed strategy, the effect of user selection is described by extreme order statistics, while the effect of joint quantization is quantified through what we term "the composite Grassmann manifold". The achievable sum rate is then estimated using random matrix theory providing an analytic benchmark for the performance.

We propose a simple power scheduling algorithm for relay channels with multiple antennas. The algorithm combines seamlessly with a low complexity communication protocol that employs rateless coding for the relay channel. The goal of the algorithm is to achieve a target average total transmission power. It requires little signaling and can be used whenever the destination node can predict future channel states. The scheduling works by a power on/off control of the source and relay nodes. It has about 1 dB gain in low SNR. It has little gain in moderate to high SNR due to the very small amount of signaling, but can be used to achieve a range of target average total transmission power without adjusting the on-power.

This paper considers broadcast channels with L antennas at the base station and m single-antenna users, where L and m are typically of the same order. We assume that only partial channel state information is available at the base station through a finite rate feedback. Our key observation is that the optimal number of on-users (users turned on), say s, is a function of signal-to-noise ratio (SNR) and feedback rate. In support of this, an asymptotic analysis is employed where L, m and the feedback rate approach infinity linearly. We derive the asymptotic optimal feedback strategy as well as a realistic criterion to decide which users should be turned on. The corresponding asymptotic throughput per antenna, which we define as the spatial efficiency, turns out to be a function of the number of on-users s, and therefore s must be chosen appropriately. Based on the asymptotics, a scheme is developed for systems with finite many antennas and users. Compared with other studies in which s is presumed constant, our scheme achieves a significant gain. Furthermore, our analysis and scheme are valid for heterogeneous systems where different users may have different path loss coefficients and feedback rates.

The Grassmann manifold Gn,p(L) is the set of all p-dimensional planes (through the origin) in the n-dimensional Euclidean space Ln, where L is either R or C. This paper considers the quantization problem in which a source in Gn,p(L) is quantized through a code in Gn,q(L), with p and q not necessarily the same. The analysis is based on the volume of a metric ball in Gn,p(L) with center in Gn,q(L), and our chief result is a closed-form expression for the volume of a metric ball of radius at most one. This volume formula holds for arbitrary n, p, q, and L, while previous results pertained only to some special cases. Based on this volume formula, several bounds are derived for the rate-distortion tradeoff assuming that the quantization rate is sufficiently high. The lower and upper bounds on the distortion rate function are asymptotically identical, and therefore precisely quantify the asymptotic rate-distortion tradeoff. We also show that random codes are asymptotically optimal in the sense that they achieve the minimum possible distortion in probability as n and the code rate approach infinity linearly. Finally, as an application of the derived results to communication theory, we quantify the effect of beamforming matrix selection in multiple-antenna communication systems with finite rate channel state feedback.

The Grassmann manifold Gn,p (L) is the set of all p-dimensional planes (through the origin) in the n-dimensional Euclidean space Ln, where L is either R or C. This paper considers an unequal dimensional quantization in which a source in Gn,q (L) is quantized through a code in Gn,p (L), where p and q are not necessarily the same. The analysis for unequal dimensional quantization is based on the volume of a metric ball in Gn,q (L) whose center is in Gn,p (L). Our chief result is to show that as n, p, q and the square radius approach infinity with constant ratios, the volume of a metric ball "grows" as exp (-n2V (1 + o (1))) for a computable constant V ges 0. This result is stronger than our previous volume formula which is only valid when the radius is at most one. The tools behind the present result include large deviation techniques and equilibrium measure ideas from potential theory. Based on the volume growth formula, the rate distortion tradeoff is precisely quantified in our asymptotic region. Finally, we prove that random codes are asymptotically optimal in probability.

The Grassmann manifold Gn,p(L) is the set of all p-dimensional planes (through the origin) in the n-dimensional Euclidean space Ln, where L is either R or C. This paper considers an unequal dimensional quantization in which a source in Gn,p(L) is quantized through a code in Gn,q(L), where p and q are not necessarily the same. It is different from most works in literature where p ≡ q. The analysis for unequal dimensional quantization is based on the volume of a metric ball in Gn,p(L) whose center is in Gn,q. Our chief result is a closed-form formula for the volume of a metric ball when the radius is sufficiently small. This volume formula holds for Grassmann manifolds with arbitrary n, p, q and L, while previous results pertained only to some special cases. Based on this volume formula, several bounds are derived for the rate distortion tradeoff assuming the quantization rate is sufficiently high. The lower and upper bounds on the distortion rate function are asymptotically identical, and so precisely quantify the asymptotic rate distortion tradeoff. We also show that random codes are asymptotically optimal in the sense that they achieve the minimum achievable distortion with probability one as n and the code rate approach infinity linearly. Finally, we discuss some applications of the derived results to communication theory. A geometric interpretation in the Grassmann manifold is developed for capacity calculation of additive white Gaussian noise channel.

We provide a low complexity communication protocol for relay channels that can achieve a significant rate reliably even when a code word spans only finite number of fading blocks on average. Both full duplex and half duplex relay are considered. In the past, when a fixed rate code word spans a finite number of fading blocks, the capacity is zero. Therefore, a large amount of research has tried to reduce outage probability and increase throughput, such as the high signal-to-noise ratio (SNR) diversity-and-multiplexing-gain-tradeoff study of relay channels. Differently, the protocol in this paper achieves a significant information rate with asymptotically zero error probability (no outage) when the number of information bits represented by a code word increases to infinity. This performance is achieved by employing rateless codes and acknowledgements so that the destination obtains just enough mutual information to decode. This approach has the advantages that the protocol is not channel statistics dependent, has low complexity, is power efficient, has high performance, and can be easily generalized to other network communication settings

This letter studies the performance of uplink cross layer design for multi-antenna systems with outdated channel state information (CSI). We consider a multi-user system with one base station (with n/sub R/ receive antennas) and K mobile users (each with single transmit antenna). The multi-user physical layer is modeled based on information theoretical framework and the cross layer design can be cast as an optimization problem. In view of the high computation complexity in the optimal solution, we propose a low complexity genetic algorithm as suboptimal solution. We found that with outdated CSI, there is significant degradation in the spatial multiplexing and multi-user diversity gain due to potential packet transmission outage as well as misscheduling. To address the poor performance in the presence of outdated CSI, we propose two simple but effective empirical solutions, namely the rate quantization and rate discounting, to tackle the packet outage problem. For instance, it is well-known that rate quantization imposes system capacity loss in systems with perfect CSI. However, we found that rate quantization can enhance the robustness of system capacity with respect to outdated CSI.

This paper considers the quantization problem on the Grassmann manifold with dimension n and p. The unique contribution is the derivation of a closed-form formula for the volume of a metric ball in the Grassmann manifold when the radius is sufficiently small. This volume formula holds for Grassmann manifolds with arbitrary dimension n and p, while previous results are only valid for either p = 1 or a fixed p with asymptotically large n. Based on the volume formula, the Gilbert-Varshamov and Hamming bounds for sphere packings are obtained. Assuming a uniformly distributed source and a distortion metric based on the squared chordal distance, tight lower and upper bounds are established for the distortion rate tradeoff. Simulation results match the derived results. As an application of the derived quantization bounds, the information rate of a multiple-input multiple-output (MIMO) system with finite-rate channel-state feedback is accurately quantified for arbitrary finite number of antennas, while previous results are only valid for either multiple-input single-output (MISO) systems or those with asymptotically large number of transmit antennas but fixed number of receive antennas.

This paper quantifies the information rate of multiple-input multiple-output (MIMO) systems with finite rate channel state feedback and power on/off strategy. In power on/off strategy, a beamforming vector (beam) is either turned on (denoted by on-beam) with a constant power or turned off. We prove that the ratio of the optimal number of on-beams and the number of antennas converges to a constant for a given signal-to-noise ratio (SNR) when the number of transmit and receive antennas approaches infinity simultaneously and when beamforming is perfect. Based on this result, a near optimal strategy, i.e., power on/off strategy with a constant number of on-beams, is discussed. For such a strategy, we propose the power efficiency factor to quantify the effect of imperfect beamforming. A formula is proposed to compute the maximum power efficiency factor achievable given a feedback rate. The information rate of the overall MIMO system can be approximated by combining the asymptotic results and the formula for power efficiency factor. Simulations show that this approximation is accurate for all SNR regimes

This paper provides a simple solution to a long standing problem of applying long block codes to multiple-input multiple-output (MIMO) quasi-static or slowly time-varying fading channels, in which past coding strategy may suffer unnecessary outage if maximum likelihood decoding is too complex to be employed. The solution is to avoid outage by employing a layered coding strategy using a rateless code at a layer. An acknowledgment is sent from the receiver to the transmitter when the receiver has accumulated enough information to decode. In a transmission, a codeword may span one or a few fading blocks. However, the total long term transmission rate can approach the ergodic capacity, and therefore, is lossless compared to outage events in traditional coding strategy. The theoretical tool introduced is a generalization of Feinstein's lemma for channels with acknowledgement. It represents a departure from traditional Shannon channel capacity that characterizes the data rate of one transmission of a code word

For some channels, channel side information at the transmitter (CSIT) may not improve channel capacity. For example, for binary input and symmetric output memoryless channels, uniform input distribution is capacity achieving with or without CSIT. However, we show that CSIT can help reduce the complexity of codes if the code is designed using channel knowledge and provide for lower bounds on complexity. A code optimization problem for minimizing complexity for a given rate loss is also posed.

In this paper, we propose a combined adaptive power control and beamforming framework for optimizing multiple-input/multiple-output (MIMO) link capacity in the presence of feedback-link capacity constraint. The feedback channel is used to carry channel state information only. It is assumed to be noiseless and causal with a feedback capacity constraint in terms of maximum number of feedback bits per fading block. We show that the hybrid design could achieve the optimal MIMO link capacity, and we derive a computationally efficient algorithm to search for the optimal design under a specific average power constraint. Finally, we shall illustrate that a minimum mean-square error spatial processor with a successive interference canceller at the receiver could be used to realize the optimal capacity. We found that feedback effectively enhances the forward channel capacity for all signal-to-noise ratio (SNR) values when the number of transmit antennas (n/sub T/) is larger than the number of receive antennas (n/sub R/). The SNR gain with feedback is contributed by focusing transmission power on active eigenchannel and temporal power waterfilling . The former factor contributed, at most, 10log/sub 10/(n/sub T//n/sub R/) dB SNR gain when n/sub T/>n/sub R/, while the latter factor's SNR gain is significant only for low SNR values.

A coding theorem is proved for memoryless channels when the channel state feedback of finite cardinality can be designed. Channel state information is estimated at the receiver and a function of the estimated channel state is causally fed back to the transmitter. The feedback link is assumed to be noiseless with a finite feedback alphabet, or equivalently, finite feedback rate. It is shown that the capacity can be achieved with a memoryless deterministic feedback and with a memoryless device which select transmitted symbols from a codeword of expanded alphabet according to current feedback. To characterize the capacity, we investigate the optimization of transmission and channel state feedback strategies. The optimization is performed for both channel capacity and error exponents. We show that the design of the optimal feedback scheme is identical to the design of scalar quantizer with modified distortion measures. We illustrate the optimization using Rayleigh block-fading channels. It is shown that the optimal transmission strategy has a general form of temporal water-filling in important cases. Furthermore, while feedback enhances the forward channel capacity more effectively in low-signal-to noise ratio (SNR) region compared with that of high-SNR region, the enhancement in error exponent is significant in both high- and low-SNR regions. This indicates that significant gain due to finite-rate channel state feedback is expected in practical systems in both SNR regions.

In this paper, we focus on investigating the optimal MIMO transmission strategy for forward channel capacity and forward error exponent of the MIMO block fading channels when the feedback link is causal and has a capacity constraint. In this paper, we assume a forward MIMO block fading channel where the channel state information is estimated at the receiver and partially feedback to the transmitter. The feedback link is assumed to be noiseless and causal with a feedback capacity constraint in terms of maximum number of feedback bits per fading block. We show that the design of the optimum feedback scheme is identical to the design of vector quantizer (Lloyd's algorithm [S.P. Lloyd, 1982]) with a modified distortion measure. It is shown that in the general case, the optimal feedback strategy has a general form of power water-filling cascaded with beamforming matrix as well. Furthermore, we show that the SNR gain with feedback is contributed by focusing transmission power on active eigen-channel and temporal power water-filling. The former factor contributed at most log/sub 10/(n/sub T/)n/sub R/ dB SNR gain when n/sub T/ > n/sub R/ in all SNR region while the latter contribution is significant only at low SNR region. Finally, MMSE receiver could be used to achieve the optimal capacity in the general case of partial feedback.

The authors introduced an algebraic design framework for space-time coding in flat-fading channels . We extend this framework to design algebraic codes for multiple-input multiple-output (MIMO) frequency-selective fading channels. The proposed codes strive to optimally exploit both the spatial and frequency diversity available in the channel. We consider two design approaches: The first uses space-time coding and maximum likelihood decoding to exploit the multi-path nature of the channel at the expense of increased receiver complexity. Within this time domain framework, we also propose a serially concatenated coding construction which is shown to offer a performance gain with a reasonable complexity iterative receiver in some scenarios. The second approach utilizes the orthogonal frequency division multiplexing technique to transform the MIMO multipath channel into a MIMO flat block fading channel. The algebraic framework is then used to construct space-frequency codes (SFC) that optimally exploit the diversity available in the resulting flat block fading channel. Finally, the two approaches are compared in terms of decoder complexity, maximum achievable diversity advantage, and simulated frame error rate performance in certain representative scenarios.

Transmit diversity through multiple transmit antennas is generally regarded as beneficial to the link-level performance. In this paper, we shall investigate the role of transmit diversity with respect to the link level and the system-level performance. We focus on the reverse link analysis, where mobile users are assumed to have independent fading, and they are equipped with multiple transmit antennas (n/sub T/). Each mobile station is assumed to have an average power constraint. The base station is assumed to have n/sub R/ receive antennas. We consider two levels of partial feedback, namely, scalar feedback and per-antenna vector feedback. In both cases, the transmitter does not have full knowledge of the channel matrix. Based on the information theoretical analytical model, it is shown that transmit diversity could enhance link-level performance, but is harmful to the multiuser system performance when there is insufficient feedback information.

Space-time coding has been studied extensively as a powerful error correction coding for systems with multiple transmit antennas. An important design goal is to maximize the level of space diversity that a code can achieve. Toward this goal, the only systematic algebraic coding theory so far is binary rank theory by Hammons and El Gamal (see ibid. vol. 46, p.524-42, 2000) for binary phase-shift keying (BPSK) modulated codes defined over binary field and quaternary phase-shift keying (QPSK) modulated codes defined over modulo four finite ring. To design codes with higher bandwidth efficiency, we develop an algebraic rank theory to ensure full space diversity for 2/sup 2k/ quadrature and amplitude modulated (QAM) codes for any positive integer k. The theory provides the most general sufficient condition of full space diversity so far. It includes the BPSK binary rank theory as a special case. Since the condition is over the same domain that a code is defined, the full space diversity code design is greatly simplified. The usefulness of the theory is illustrated in examples, such as analyses of existing codes, constructions of new space-time codes with better performance, including the full diversity space-time turbo codes.

This paper studies the space time code design for single carrier transmission over frequency selective fading channels. The design criteria are derived first and then we apply the algebraic /spl Sigma//sub 0/-rank theory to show how to design codes to take advantage of space and frequency diversity simultaneously. Finally, example codes are shown to achieve desired level of diversity by simulation results.

This paper proposes a class of full space diversity full rate space-time turbo codes. Both parallel concatenated and serially concatenated codes are designed. A rank theory proposed by the authors earlier is employed to check the full space diversity of the codes. The simulations show that the space-time turbo codes can take full advantage of space diversity and time diversity if they are available in the channels. We also study the robustness of performance of both turbo codes and trellis codes in space-time correlated fading channels.

This paper proposes a class of full space diversity QPSK space-time codes based on parallel concatenated convolutional (turbo) codes. A rank criterion of full space diversity is used in the design. Compared with space-time trellis codes, the simulations show it has robust performance at both a quasi-static fading channel and a time varying fading channel.