Anant Sahai

Shannon meets Tesla: Wireless information and power transfer

The problem considered here is that of wireless information and power transfer across a noisy coupled-inductor circuit, which is a frequency-selective channel with additive white Gaussian noise. The optimal tradeoff between the achievable rate and the power transferred is characterized given the total power available. The practical utility of such systems is also discussed.

What is a Spectrum Hole and What Does it Take to Recognize One

ldquoSpectrum holesrdquo represent the potential opportunities for noninterfering (safe) use of spectrum and can be considered as multidimensional regions within frequency, time, and space. The main challenge for secondary radio systems is to be able to robustly sense when they are within such a spectrum hole. To allow a unified discussion of the core issues in spectrum sensing, the ldquoweighted probability of area recoveredrdquo (WPAR) metric is introduced to measure the performance of a sensing strategy; and the ldquofear of harmful interferencerdquo F HI metric is introduced to measure its safety. These metrics explicitly consider the impact of asymmetric uncertainties (and misaligned incentives) in the system model. Furthermore, they allow a meaningful comparison of diverse approaches to spectrum sensing unlike the traditional triad of sensitivity, probability of false-alarm P FA, and probability of missed-detection P MD. These new metrics are used to show that fading uncertainty forces the WPAR performance of single-radio sensing algorithms to be very low for small values of F HI, even for ideal detectors. Cooperative sensing algorithms enable a much higher WPAR, but only if users are guaranteed to experience independent fading. Lastly, in-the-field calibration for wide-band (but uncertain) environment variables (e.g., interference and shadowing) can robustly guarantee safety (low F HI) even in the face of potentially correlated users without sacrificing WPAR.

Stochastic linear control over a communication channel

We examine linear stochastic control systems when there is a communication channel connecting the sensor to the controller. The problem consists of designing the channel encoder and decoder as well as the controller to satisfy some given control objectives. In particular, we examine the role communication has on the classical linear quadratic Gaussian problem. We give conditions under which the classical separation property between estimation and control holds and the certainty equivalent control law is optimal. We then present the sequential rate distortion framework. We present bounds on the achievable performance and show the inherent tradeoffs between control and communication costs. In particular, we show that optimal quadratic cost decomposes into two terms: A full knowledge cost and a sequential rate distortion cost.

Power scaling for cognitive radio

In this paper we explore the idea of using cognitive radios to reuse locally unused spectrum for their own transmissions. We impose the constraint that they cannot general e unacceptable levels of interference to licensed systems on the same frequency. Using received SNR as a proxy for distance, we prove that a cognitive radio can vary its transmit power while maintaining a guarantee of service to primary users. We consider the aggregate interference caused by multiple cognitive radios and show that aggregation causes a change in the effective decay rate of the interference. We examine the effects of heterogeneous propagation path loss functions and justify the feasibility of multiple secondary users with dynamic transmit powers. Finally, we prove the fundamental constraint on a cognitive radios transmit power is the minimum SNR it can detect and explore the effect of this power cap.

Fundamental design tradeoffs in cognitive radio systems

Under the current system of spectrum allocation, rigid partitioning has resulted in vastly underutilized spectrum bands, even in urban locales. Cognitive radios have been proposed as a way to reuse this underutilized spectrum in an opportunistic manner. To achieve this reuse while guaranteeing non-interference with the primary user, cognitive radios must detect very weak primary signals. However, uncertainties in the noise+interference impose a limit on how low of a primary signal can be robustly detected. In this paper, we show that the presence/absence of possible interference from other opportunistic spectrum users represents a major component of the uncertainty limiting the ability of a cognitive radio network to reclaim a band for its use. Coordination among nearby cognitive radios is required to control this uncertainty. While this coordination can take a form similar to a traditional MAC protocol for data communication, its role is different in that it aims to reduce the uncertainty about interference rather than just reducing the interference itself. We show how the degree of coordination required can vary based on the coherence times and bandwidths involved, as well as the complexity of the detectors themselves. The simplest sensing strategies end up needing the most coordination, while more complex strategies involving adaptive coherent processing and interference prediction can be individually more robust and thereby reduce the need for coordination across different networks. We also show the existence of a coordination radius wall which limits secondary user densities that can be supported irrespective of coordination involved. Furthermore, local cooperation among cognitive radios for collective decision making can reduce the fading margins we need to budget for. This cooperation benefits from increased secondary user densities and hence induces a minima in the power-coordination tradeoff.

Estimation bounds for localization

The localization problem is fundamentally important for sensor networks. We study the Cramer-Rao lower bound (CRB) for two kinds of localization based on noisy range measurements. The first is anchored localization in which we know true positions of at least 3 nodes. We show some basic invariances of the CRB in this case and derive lower and upper bounds on the CRB which can be computed using only local information. The second is anchor-free localization where no absolute positions are known. Although the Fisher information matrix is singular, we derive a CRB-like bound on the total estimation variance. Finally, for both cases we discuss how the bounds scale to large networks under different models of wireless signal propagation.

Why Do Block Length and Delay Behave Differently if Feedback Is Present

For output-symmetric discrete memoryless channels (DMCs) at even moderately high rates, fixed-block-length communication systems show no improvements in their error exponents with feedback. This paper studies systems with fixed end-to-end delay and shows that feedback generally provides dramatic gains in the error exponents. A new upper bound (the uncertainty-focusing bound) is given on the probability of symbol error in a fixed-delay communication system with feedback. This bound turns out to have a form similar to Viterbis bound used for the block error probability of convolutional codes as a function of the fixed constraint length. The uncertainty-focusing bound is shown to be asymptotically achievable with noiseless feedback for erasure channels as well as for any output-symmetric DMC that has strictly positive zero-error capacity. Furthermore, it can be achieved in a delay-universal (anytime) fashion even if the feedback itself is delayed by a small amount. Finally, it is shown that for end-to-end delay, it is generally possible at high rates to beat the sphere-packing bound for general DMCs - thereby providing a counterexample to a conjecture of Pinsker.

Object tracking in a 2D UWB sensor network

We consider object tracking by a UWB sensor network using multipath measurements in different scenarios: single Tx with single Rx, multiple Tx with single Rx and multiple Tx with multiple Rx. For each scenario, we examine the Cramer-Rao lower bound (CRLB) for the high-SNR case where multipath measurements are corrupted by iid Gaussians. We focus on the dense network asymptotics and show how the CRLB is inversely proportional to the number of measurements available to the network as a whole, even when the individual measurements are taken from different locations. An order-optimal semilinear algorithm is given.

Design of a low-latency, high-reliability wireless communication system for control applications

High-performance industrial control systems with tens to hundreds of sensors and actuators use wired connections between all of their components because they require low-latency, high-reliability links to maintain stability; however, the wires cause many mechanical problems that moving to wireless links would solve. No existing or proposed wireless system can achieve the latency and reliability required by the control algorithms because they are designed for either high-throughput or low-power communication between a pair or a small number of terminals. A preliminary wireless system architecture is proposed that focuses on low-latency operation through the use of reliable broadcasting, semi-fixed resource allocation, and low-rate coding. For an industrial printer application with 30 nodes in the control loop and a moderate information throughput of 4.8Mb/s, the system can achieve latencies under 2ms for SNRs above 7dB.

Zero-Rate Feedback Can Achieve the Empirical Capacity

The utility of limited feedback for coding over an individual sequence of discrete memoryless channels is investigated. This study complements recent results showing how limited or noisy feedback can boost the reliability of communication. A strategy with fixed input distribution P is given that asymptotically achieves rates arbitrarily close to the mutual information induced by P and the state-averaged channel. When the capacity-achieving input distribution is the same over all channel states, this achieves rates at least as large as the capacity of the state-averaged channel, sometimes called the empirical capacity.