Showing papers by "David Gesbert published in 2007"

Shifting the MIMO Paradigm

Abstract: Multi-user MIMO (MU-MIMO) networks reveal the unique opportunities arising from a joint optimization of antenna combining techniques with resource allocation protocols. Furthermore, it brings robustness with respect to multipath richness, allowing for compact antenna spacing at the BS and, crucially, yielding the diversity and multiplexing gains without the need for multiple antenna user terminals. To realize these gains, however, the BS should be informed with the user's channel coefficients, which may limit practical application to TDD or low-mobility settings. To circumvent this problem and reduce feedback load, combining MU-MIMO with opportunistic scheduling seems a promising direction. The success for this type of scheduler is strongly traffic and QoS-dependent, however.

Complex-Valued Matrix Differentiation: Techniques and Key Results

Abstract: A systematic theory is introduced for finding the derivatives of complex-valued matrix functions with respect to a complex-valued matrix variable and the complex conjugate of this variable. In the framework introduced, the differential of the complex-valued matrix function is used to identify the derivatives of this function. Matrix differentiation results are derived and summarized in tables which can be exploited in a wide range of signal processing related situations

Adaptation, Coordination, and Distributed Resource Allocation in Interference-Limited Wireless Networks

Abstract: A sensible design of wireless networks involves striking a good balance between an aggressive reuse of the spectral resource throughout the network and managing the resulting co-channel interference. Traditionally, this problem has been tackled using a ldquodivide and conquerrdquo approach. The latter consists in deploying the network with a static or semidynamic pattern of resource reutilization. The chosen reuse factor, while sacrificing a substantial amount of efficiency, brings the interference to a tolerable level. The resource can then be managed in each cell so as to optimize the per cell capacity using an advanced air interface design. In this paper, we focus our attention on the overall network capacity as a measure of system performance. We consider the problem of resource allocation and adaptive transmission in multicell scenarios. As a key instance, the problem of joint scheduling and power control simultaneously in multiple transmit-receive links, which employ capacity-achieving adaptive codes, is studied. In principle, the solution of such an optimization hinges on tough issues such as the computational complexity and the requirement for heavy receiver-to-transmitter feedback and, for cellular networks, cell-to-cell channel state information (CSI) signaling. We give asymptotic properties pertaining to rate-maximizing power control and scheduling in multicell networks. We then present some promising leads for substantial complexity and signaling reduction via the use of newly developed distributed and game theoretic techniques.

Adaptation, Coordination, and Distributed Resource Allocation in Interference-Limited Wireless Networks Joint multicell resource allocation offers an enormous number of degrees of freedom that can be exploited to optimize the network performance.

Abstract: A sensible design of wireless networks involves striking a good balance between an aggressive reuse of the spectral resource throughout the network and managing the resulting co-channel interference. Traditionally, this problem has been tackled using a Bdivide and conquer( approach. The latter consists in deploying the network with a static or semidynamic pattern of resource reutilization. The chosen reuse factor, while sacrificing a substantial amount of efficien- cy, brings the interference to a tolerable level. The resource can then be managed in each cell so as to optimize the per cell capacity using an advanced air interface design. In this paper, we focus our attention on the overall network capacity as a measure of system performance. We consider the problem of resource allocation and adaptive transmission in multicell scenarios. As a key instance, the problem of joint scheduling and power control simultaneously in multiple transmit-receive links, which employ capacity-achieving adap- tive codes, is studied. In principle, the solution of such an optimization hinges on tough issues such as the computational complexity and the requirement for heavy receiver-to- transmitter feedback and, for cellular networks, cell-to-cell channel state information (CSI) signaling. We give asymptotic properties pertaining to rate-maximizing power control and scheduling in multicell networks. We then present some promising leads for substantial complexity and signaling reduction via the use of newly developed distributed and game theoretic techniques.

Maximizing Multicell Capacity Using Distributed Power Allocation and Scheduling

Abstract: Joint optimization of transmit power and scheduling in wireless data networks promises significant system-wide capacity gains. However, this problem is known to be NP-hard and thus difficult to tackle in practice. We analyze this problem for the downlink of a multicell full reuse network with the goal of maximizing the overall network capacity. We propose a distributed power allocation and scheduling algorithm which provides significant capacity gain for any finite number of users. This distributed cell coordination scheme, in effect, achieves a form of dynamic spectral reuse, whereby the amount of reuse varies as a function of the underlying channel conditions and only limited inter-cell signaling is required.

A Threshold-Based Channel State Feedback Algorithm for Modern Cellular Systems

Abstract: In this paper we propose a channel state feedback algorithm that uses multiple feedback thresholds to reduce the number of users transmitting feedback to a minimum. The users are polled with lower and lower threshold values and only the users that are above a threshold value transmit feedback to the base station. We show how this feedback algorithm can be used for any scheduling algorithm and show how closed-form expressions for the optimal threshold values can be obtained for two well-known scheduling algorithms. Finally, we propose a two-step optimization procedure for optimizing the feedback algorithm for real-life cellular standards.

Precoding of Orthogonal Space-Time Block Codes in Arbitrarily Correlated MIMO Channels: Iterative and Closed-Form Solutions

Abstract: A memoryless precoder is designed for orthogonal space-time block codes (OSTBCs) for multiple-input multiple-output (MIMO) channels exhibiting joint transmit-receive correlation. Unlike most previous similar works which concentrate on transmit correlation only and pair-wise error probability (PEP) metrics. 1) The precoder is designed to minimize the exact symbol error rate (SER) as function of the channel correlation coefficients, which are fed back to the transmitter. 2) The correlation is arbitrary as it may or may not follow the so-called Kronecker structure. 3) The proposed method can handle general propagation settings including those arising from a cooperative macro-diversity (multi-base) scenario. We present two algorithms. The first is suboptimal, but provides a simple closed-form precoder that handles the case of uncorrelated transmitters, correlated receivers. The second is a fast-converging numerical optimization of the exact SEE which covers the general case. Finally, a number of novel properties of the minimum SER precoder are derived

A Two-Stage Approach to Feedback Design in Multi-User MIMO Channels with Limited Channel State Information

Abstract: We consider the downlink of a multiuser MIMO channel, corresponding to a single cell with an Nt-antenna base station and K single-antenna mobile terminals (MTs). It is known that when full channel state information (CSI) is available at the transmitter (full CSIT) the capacity of the system scales as Nt log(P/Nt- log K), under a total power constraint P [1], While, when the transmitter has no CSI, scaling reduces to that of a TDMA system. This paper examines the more realistic case of having an intermediate state of CSI. The key idea is based on a split of the allotted feedback between two stages: A first stage devoted to scheduling followed by a second stage for precoder design for the selected users. Based on an approximation of the achievable sum rate, we introduce a method for determining the splitting of the feedback rate so as to maximize performance and provide intuitions. We illustrate the gains of the 2-stage approach via Monte Carlo simulations.

Efficient Metrics for Scheduling in MIMO Broadcast Channels with Limited Feedback

Abstract: We consider a downlink channel where a base station equipped with M transmit antennas communicates with K ≥ M single-antenna receivers and has partial channel knowledge obtained via a limited rate feedback channel. We propose scalar feedback metrics that provide an estimate of the received signal-to-noise plus interference ratio (SINR), which are combined with efficient user selection algorithms and zero-forcing beamforming. The asymptotic system sum rate for large K is analyzed and numerical results are provided, showing the performance of each metric in different scenarios.

Orthogonal Linear Beamforming in MIMO Broadcast Channels

Abstract: The problem of joint linear beamforming and scheduling in a MIMO broadcast channel is considered. We show how orthogonal linear beamforming (OLBF) can be efficiently combined with a low-complexity user selection algorithm to achieve a large portion of the multiuser capacity. The use of orthogonal transmission enables the transmitter to calculate exact signal-to-interference plus noise ratio (SINR) values during the user selection process. The knowledge of multiuser interference proves to be of particular importance for user scheduling as both the number of users in the cell and the average signal-to-noise ratio (SNR) decrease. The sum capacity of our scheme is characterized in the low-SNR regime, providing analytical results on the performance gain over zero-forcing beamforming (ZFBF). Numerical results show gains over both suboptimal and optimal ZFBF techniques in different scenarios.

Binary power control for multi-cell capacity maximization

Abstract: We consider the problem of optimally allocating the base station transmit powers for a wireless multi-cellular (W-cell) system in order to maximize the total system throughput under interference and noise impairments, and short term (minimum and peak) power constraints. Employing dynamic reuse of spectral resources, we impose the power constraints at each base station and allow for coordination between the base stations. For the two-cell case, the capacity-optimal power allocation has been previously shown to be binary [1]. We now propose to perform binary power allocation, (by simply checking the corners of the domain resulting from the power constraints), also when N > 2, and we identify two scenarios in which the optimality of binary power control can be proven also for arbitrary N. Furthermore, in the general setting for N > 2, we demonstrate by simulations that a network performance with negligible loss, compared to the best non-binary scheme found by geometric programming, can be obtained.

Transmit Diversity Versus Opportunistic Beamforming in Data Packet Mobile Downlink Transmission

Abstract: We compare space-time coding (transmit diversity) and random "opportunistic" beamforming in a space-division multiple access/time-division multiple access single-cell downlink system with random packet arrivals, correlated block-fading channels, and non-perfect channel state information at the transmitter due to a feedback delay. Our comparison is based on system stability. The ability of accurately predicting the channel signal-to-noise ratio dominates the performance of opportunistic beamforming, even under the optimistic assumption that the sequence of beamforming matrices is perfectly known a priori by the receivers. Our results show that the relative merit of opportunistic beamforming versus space-time coding strongly depends on the channel Doppler bandwidth. Therefore, previous naive conclusions on the fact that transmit diversity always hurts the system performance under multiuser-diversity scheduling should be taken with great care

Joint power control and user scheduling in multicell wireless networks: Capacity scaling laws

Abstract: We address the optimization of the sum rate performance in multicell interference-limited singlehop networks where access points are allowed to cooperate in terms of joint resource allocation. The resource allocation policies considered here combine power control and user scheduling. Although very promising from a conceptual point of view, the optimization of the sum of per-link rates hinges, in principle, on tough issues such as computational complexity and the requirement for heavy receiver-to-transmitter channel information feedback across all network cells. In this paper, we show that, in fact, distributed algorithms are actually obtainable in the asymptotic regime where the numbers of users per cell is allowed to grow large. Additionally, using extreme value theory, we provide scaling laws for upper and lower bounds for the network capacity (sum of single user rates over all cells), corresponding to zero-interference and worst-case interference scenarios. We show that the scaling is either dominated by path loss statistics or by small-scale fading, depending on the regime and user location scenario. We show that upper and lower rate bounds behave in fact identically, asymptotically. This remarkable result suggests not only that distributed resource allocation is practically possible but also that the impact of multicell interference on the capacity (in terms of scaling) actually vanishes asymptotically.

Optimal Matching in Wireless Sensor Networks

Abstract: We design a wireless sensor network (WSN) in terms of rate and power allocation in order to send without loss the data gathered by the nodes to a common sink. Correlation between the data and channel impairments dictate the constraints of the optimization problem. We further assume that the WSN uses off-the-shelf compression and channel coding algorithms. More precisely source and channel coding are separated and distributed source coding is performed by pairs of nodes. This raises the problem of optimally matching the nodes. We show that under all these constraints the optimal design (including rate/power allocation and matching) has polynomial complexity (in the number of nodes in the network). A closed form solution is given for the rate/power allocation, and the matching solution is readily interpreted. For noiseless channels, the optimization matches close nodes whereas, for noisy channels, there is a tradeoff between matching close nodes and matching nodes with different distances to the sink. This fact is illustrated by simulations based on empirical measures. We also show that the matching technique provides substantial gains in either storage capacity or power consumption for the WSN with regard to the case where the correlation between the nodes is not used.

Unified Theory of Complex-Valued Matrix Differentiation

Abstract: A systematic theory is introduced for finding the derivatives of complex-valued matrix functions with respect to a complex-valued matrix variable and the complex conjugate of this variable. In the framework introduced, the differential of the complex-valued matrix function is used to identify the derivatives of this function. Matrix differentiation results are developed for use in signal processing and communications applications. Several other examples are given.

Resource allocation in multicell wireless networks: Some capacity scaling laws

Abstract: We address the optimization of the sum rate performance in multicell interference-limited wireless networks where access points are allowed to cooperate in terms of joint resource allocation. The resource allocation policies considered here combine power control and user scheduling. Although very promising from a conceptual point of view, the optimization of the sum rate (network capacity) hinges, in principle, on tough issues such as computational complexity and the requirement for heavy receiver-to-transmitter channel information feedback across all network cells. However, we show that, in fact, distributed algorithms are actually obtainable in the asymptotic regime where the numbers of users per cell is allowed to grow to infinity. Additionally, using extreme value theory, we provide scaling laws for upper and lower bounds for the network capacity (as the number of users grows large), corresponding to two forms of distributed resource allocation schemes. We show these bounds are in fact identical asymptotically. This remarkable result suggests that distributed resource allocation is practically possible, with vanishing loss of network capacity if enough users exist.

Throughput guarantees for wireless networks with opportunistic scheduling: a comparative study

Abstract: In this letter we develop an expression for the approximate throughput guarantee violation probability (TGVP) for users in time-slotted networks for any scheduling algorithm with a given mean and variance of the bit-rate in a time-slot, and a given distribution for the number of time-slots allocated within a time-window. Based on this general result, we evaluate closed-form expressions for the TGVPs for four well-known scheduling algorithms. Through simulations we also show that our TGVP approximation is tight for a realistic network with moving users with correlated channels and realistic throughput guarantees.

EMOS Platform: Real-Time Capacity Estimation of MIMO Channels in the UMTS-TDD Band

Abstract: This work presents some initial results concerning the MIMO channel capacity of real wireless channels in the UMTS-TDD band using the Eurecom MIMO Openair Sounder (EMOS). This paper describes the necessary steps to estimate in real-time the wireless MIMO environment, offering the possibility to identify reliable MIMO channels as well as instantaneous channel capacity. In particular, the problems related to additive and phase-shift noise are solved by employing OFDMA technology. Finally, based on measurements, we analyze the impact of polarization on the capacity performance.

Precoded distributed space-time block codes in cooperative diversity-based downlink

Abstract: Cooperative diversity is a rapidly emerging topic for wireless communications, with ad hoc and hybrid/relay networks as two main applications so far. In this paper, we investigate the cooperative diversity concept for MIMO multicell networks, where the processing must be optimized to account for the variability of the channel conditions across the cooperative devices. This can be done via distributed preceding and is realistically based on channel statistics (average gains, correlations, etc.). We give a new approach to the previously coined equal diversity spread principle, through minimization of an approximated SER expression. Next, we focus on a low-complexity approach to minimizing a PEP-based performance measure. Gains are evaluated in a multicell scenario with collaborating base stations.

Rate and Power Allocation for Discrete-Rate Link Adaptation

Abstract: Link adaptation, in particular adaptive coded modulation (ACM), is a promising tool for bandwidth-efficient transmission in a fading environment. The main motivation behind employing ACM schemes is to improve the spectral efficiency of wireless communication systems. In this paper, using a finite number of capacity achieving component codes, we propose new transmission schemes employing constant power transmission, as well as discrete and continuous power adaptation, for slowly varying flat-fading channels. We show that the proposed transmission schemes can achieve throughputs close to the Shannon limits of flat-fading channels using only a small number of codes. Specifically, using a fully discrete scheme with just four codes, each associated with four power levels, we achieve a spectral efficiency within 1 dB of the continuous-rate continuous-power Shannon capacity. Furthermore, when restricted to a fixed number of codes, the introduction of power adaptation has significant gains with respect to ASE and probability of no transmission compared to a constant power scheme.

Hessians of scalar functions of complex-valued matrices: A systematic computational approach

Abstract: A systematic theory is introduced for finding the four Hessians of complex-valued scalar functions with respect to a complex-valued matrix variable and the complex conjugate of this variable It is shown how the four Hessian matrices of a scalar complex function can be identified from the second-order complex differential of the scalar function These Hessians are the four parts of a bigger matrix which must be checked in order to identify if a stationary point is a local minimum, maximum, or saddle point The method introduced is general such that many results can be derived using the framework introduced Hessians are derived for some useful examples taken from signal processing related functions

Optimal matching in wireless sensor networks

Abstract: We investigate the design of a wireless sensor network (WSN), where distributed source coding (DSC) for pairs of nodes is used. More precisely, we minimize the compression sum rate for noiseless channels and the sum power for noisy orthogonal channels in a context of pairwise DSC. In both cases, the minimization can be separated into a matching problem and a pairwise rate-power control problem (that admits a simple closed-form solution). Using this separation, we obtain an optimization procedure of polynomial (in the number of nodes in the network) complexity. Finally, we show that the overall optimization can be readily interpreted. For noiseless channels, the optimization matches close nodes whereas, for noisy channels, there is a tradeoff between matching close nodes and matching nodes with different distances to the sink. We provide examples of the proposed optimization method based on empirical measures. We show that the matching technique provides substantial gains in either storage capacity or power consumption for the WSN.

Cooperative diversity using per-user power control in the multiuser MAC channel

Abstract: We consider a multiuser MAC fading channel with two users communicating with a common destination, where each user mutually acts as a relay for the other one as well as transmits his own information. We propose a power control-enhanced cooperative transmission scheme allowing each user to allocate a certain amount of power for his own transmitted data while the rest is devoted to relaying. The underlying protocol is based on a modification of the so-called non-orthogonal amplify and forward (NAF) protocol in Azarian, K. et al, (2005). We develop capacity expressions for our scheme and derive the rate-optimum power allocation, in closed form. Our results indicate that even in a mutual cooperation setting like ours, on any given realization of the channel, one of the users will always allocate zero power to relaying the data of the other one, and thus act selfishly.

Capacity Maximizing Power Allocation for Interfering Wireless Links: A Distributed Approach

Abstract: Recent results show that sum-rate maximizing multicell power allocation promises significant gains in interference- limited data networks. Finding practical, i.e. distributed, versions of this global optimization problem however remains a challenging task. In this work, we establish a general framework for the distributed power allocation problem for N mutually interfering links enabling us to derive a fully distributed power allocation algorithm. Although a gain for N = 2 is observed, a performance gap is still observed compared to a centralized algorithm. As a way to fill that gap, we propose minimal information (in this case 1 bit) message passing between interfering links to improve performance. Numerical results show these algorithms to exploit a substantial amount of the capacity gain offered by centralized optimization.

Intrinsic Subspace Convergence in TDD MIMO Communication

Abstract: In numerical linear algebra, students encounter early the iterative power method, which finds eigenvectors of a matrix from an arbitrary starting point through repeated normalization and multiplications by the matrix itself In practice, more sophisticated methods are used nowadays, threatening to make the power method a historical and pedagogic footnote However, in the context of communication over a time-division duplex (TDD) multiple-input multiple-output (MIMO) channel, the power method takes a special position It can be viewed as an intrinsic part of the uplink and downlink communication switching, enabling estimation of the eigenmodes of the channel without extra overhead Generalizing the method to vector subspaces, communication in the subspaces with the best receive and transmit signal-to-noise ratio (SNR) is made possible In exploring this intrinsic subspace convergence (ISC), we show that several published and new schemes can be cast into a common framework where all members benefit from the ISC

A low complexity distributed multibase transmission scheme for improving the sum capacity of wireless networks

Abstract: This paper addresses the problem of base station coordination in multicell wireless networks. We present a distributed approach to downlink multibase beamforming, as well as a low complexity, near-optimal, scheduling algorithm, allowing the multiplexing of M user terminals randomly located in a network with N base stations. The algorithms rely on the maximization of the sum rate of the network, based on locally available information at each base station. Results show that our approach yields significant gains in the system capacity when compared to schemes not allowing cooperation between cells, without requiring the extensive signaling overhead involved in optimal multicell MIMO processing.

When Network Coding and Dirty Paper Coding meet in a Cooperative Ad Hoc Network

Abstract: We develop and analyze new cooperative strategies for ad hoc networks that are more spectrally efficient than classical DF cooperative protocols. Using analog network coding, our strategies preserve the practical half-duplex assumption but relax the orthogonality constraint. The introduction of interference due to non-orthogonality is mitigated thanks to precoding, in particular Dirty Paper coding. Combined with smart power allocation, our cooperation strategies allow to save time and lead to more efficient use of bandwidth and to improved network throughput with respect to classical RDF/PDF.

Capacity and positioning in dense scattering environments

Abstract: We study the capacity scaling of a system where a source communicates to a destination with the help of several scatterers. Capacity expressions accounting for physical characteristics of the environment (topology, frequency band...) are provided and an asymptotic analysis is performed for an increasing size of the dense scattering environment. The capacity is shown to reach a saturation level in the asymptotic regime, suggesting a capacity-delay trade-off. Moreover the saturation point depends on the positioning of scatterers, in particular in wide band systems where topology impacts capacity in terms of both path-loss and delays. Waiting very long for retransmissions from an infinite number of scatterers is not worth and a few well located scatterers around source and destination lead to better performances than more scatterers uniformly distributed on a square area between source and destination.