Reduced-Dimension Linear Transform Coding of Correlated Signals in Networks

A model, called the linear transform network (LTN), is proposed to analyze the compression and estimation of correlated signals transmitted over directed acyclic graphs (DAGs). An LTN is a DAG network with multiple source and receiver nodes. Source nodes transmit subspace projections of random correlated signals by applying reduced-dimension linear transforms. The subspace projections are linearly processed by multiple relays and routed to intended receivers. Each receiver applies a linear estimator to approximate a subset of the sources with minimum mean squared error (MSE) distortion. The model is extended to include noisy networks with power constraints on transmitters. A key task is to compute all local compression matrices and linear estimators in the network to minimize end-to-end distortion. The non-convex problem is solved iteratively within an optimization framework using constrained quadratic programs (QPs). The proposed algorithm recovers as special cases the regular and distributed Karhunen-Loeve transforms (KLTs). Cut-set lower bounds on the distortion region of multi-source, multi-receiver networks are given for linear coding based on convex relaxations. Cut-set lower bounds are also given for any coding strategy based on information theory. The distortion region and compression-estimation tradeoffs are illustrated for different communication demands (e.g. multiple unicast), and graph structures.Comment: 33 pages, 7 figures, To appear in IEEE Transactions on Signal Processin

Power-Constrained Sparse Gaussian Linear Dimensionality Reduction over Noisy Channels

In this paper, we investigate power-constrained sensing matrix design in a sparse Gaussian linear dimensionality reduction framework. Our study is carried out in a single--terminal setup as well as in a multi--terminal setup consisting of orthogonal or coherent multiple access channels (MAC). We adopt the mean square error (MSE) performance criterion for sparse source reconstruction in a system where source-to-sensor channel(s) and sensor-to-decoder communication channel(s) are noisy. Our proposed sensing matrix design procedure relies upon minimizing a lower-bound on the MSE in single-- and multiple--terminal setups. We propose a three-stage sensing matrix optimization scheme that combines semi-definite relaxation (SDR) programming, a low-rank approximation problem and power-rescaling. Under certain conditions, we derive closed-form solutions to the proposed optimization procedure. Through numerical experiments, by applying practical sparse reconstruction algorithms, we show the superiority of the proposed scheme by comparing it with other relevant methods. This performance improvement is achieved at the price of higher computational complexity. Hence, in order to address the complexity burden, we present an equivalent stochastic optimization method to the problem of interest that can be solved approximately, while still providing a superior performance over the popular methods.Comment: Accepted for publication in IEEE Transactions on Signal Processing (16 pages

Random Projections For Large-Scale Regression

Fitting linear regression models can be computationally very expensive in large-scale data analysis tasks if the sample size and the number of variables are very large. Random projections are extensively used as a dimension reduction tool in machine learning and statistics. We discuss the applications of random projections in linear regression problems, developed to decrease computational costs, and give an overview of the theoretical guarantees of the generalization error. It can be shown that the combination of random projections with least squares regression leads to similar recovery as ridge regression and principal component regression. We also discuss possible improvements when averaging over multiple random projections, an approach that lends itself easily to parallel implementation.Comment: 13 pages, 3 Figure

Optimized Compressed Sensing Matrix Design for Noisy Communication Channels

We investigate a power-constrained sensing matrix design problem for a compressed sensing framework. We adopt a mean square error (MSE) performance criterion for sparse source reconstruction in a system where the source-to-sensor channel and the sensor-to-decoder communication channel are noisy. Our proposed sensing matrix design procedure relies upon minimizing a lower-bound on the MSE. Under certain conditions, we derive closed-form solutions to the optimization problem. Through numerical experiments, by applying practical sparse reconstruction algorithms, we show the strength of the proposed scheme by comparing it with other relevant methods. We discuss the computational complexity of our design method, and develop an equivalent stochastic optimization method to the problem of interest that can be solved approximately with a significantly less computational burden. We illustrate that the low-complexity method still outperforms the popular competing methods.Comment: Submitted to IEEE ICC 2015 (EXTENDED VERSION

Computation-Communication Trade-offs and Sensor Selection in Real-time Estimation for Processing Networks

Recent advances in electronics are enabling substantial processing to be performed at each node (robots, sensors) of a networked system. Local processing enables data compression and may mitigate measurement noise, but it is still slower compared to a central computer (it entails a larger computational delay). However, while nodes can process the data in parallel, the centralized computational is sequential in nature. On the other hand, if a node sends raw data to a central computer for processing, it incurs communication delay. This leads to a fundamental communication-computation trade-off, where each node has to decide on the optimal amount of preprocessing in order to maximize the network performance. We consider a network in charge of estimating the state of a dynamical system and provide three contributions. First, we provide a rigorous problem formulation for optimal real-time estimation in processing networks in the presence of delays. Second, we show that, in the case of a homogeneous network (where all sensors have the same computation) that monitors a continuous-time scalar linear system, the optimal amount of local preprocessing maximizing the network estimation performance can be computed analytically. Third, we consider the realistic case of a heterogeneous network monitoring a discrete-time multi-variate linear system and provide algorithms to decide on suitable preprocessing at each node, and to select a sensor subset when computational constraints make using all sensors suboptimal. Numerical simulations show that selecting the sensors is crucial. Moreover, we show that if the nodes apply the preprocessing policy suggested by our algorithms, they can largely improve the network estimation performance.Comment: 15 pages, 16 figures. Accepted journal versio

Optimal Channel Training in Uplink Network MIMO Systems

We consider a multi-cell frequency-selective fading uplink channel (network MIMO) from K single-antenna user terminals (UTs) to B cooperative base stations (BSs) with M antennas each. The BSs, assumed to be oblivious of the applied codebooks, forward compressed versions of their observations to a central station (CS) via capacity limited backhaul links. The CS jointly decodes the messages from all UTs. Since the BSs and the CS are assumed to have no prior channel state information (CSI), the channel needs to be estimated during its coherence time. Based on a lower bound of the ergodic mutual information, we determine the optimal fraction of the coherence time used for channel training, taking different path losses between the UTs and the BSs into account. We then study how the optimal training length is impacted by the backhaul capacity. Although our analytical results are based on a large system limit, we show by simulations that they provide very accurate approximations for even small system dimensions.Comment: 15 pages, 7 figures. To appear in the IEEE Transactions on Signal Processin

Boosting Fronthaul Capacity: Global Optimization of Power Sharing for Centralized Radio Access Network

The limited fronthaul capacity imposes a challenge on the uplink of centralized radio access network (C-RAN). We propose to boost the fronthaul capacity of massive multiple-input multiple-output (MIMO) aided C-RAN by globally optimizing the power sharing between channel estimation and data transmission both for the user devices (UDs) and the remote radio units (RRUs). Intuitively, allocating more power to the channel estimation will result in more accurate channel estimates, which increases the achievable throughput. However, increasing the power allocated to the pilot training will reduce the power assigned to data transmission, which reduces the achievable throughput. In order to optimize the powers allocated to the pilot training and to the data transmission of both the UDs and the RRUs, we assign an individual power sharing factor to each of them and derive an asymptotic closed-form expression of the signal-to-interference-plus-noise for the massive MIMO aided C-RAN consisting of both the UD-to-RRU links and the RRU-to-baseband unit (BBU) links. We then exploit the C-RAN architecture's central computing and control capability for jointly optimizing the UDs' power sharing factors and the RRUs' power sharing factors aiming for maximizing the fronthaul capacity. Our simulation results show that the fronthaul capacity is significantly boosted by the proposed global optimization of the power allocation between channel estimation and data transmission both for the UDs and for their host RRUs. As a specific example of 32 receive antennas (RAs) deployed by RRU and 128 RAs deployed by BBU, the sum-rate of 10 UDs achieved with the optimal power sharing factors improves 33\% compared with the one attained without optimizing power sharing factors