Raghu Mudumbai

A distributed consensus approach to synchronization of RF signals

We propose a consensus-based algorithm for the synchronization of carrier signals in a wireless network. This work is motivated by recent progress on distributed beamforming and other cooperative MIMO techniques that require synchronized RF signals among all the cooperating nodes in a network and is aimed at addressing the limitations of the centralized master-slave approach used in previous work in this area. Our proposed algorithm is based on a variation of the classic Kuramoto model for the synchronization of coupled oscillators and is well-suited for a digital baseband implementation. We describe our proposed algorithm in detail and present initial results that show that this algorithm achieves global frequency lock given only that the network is connected i.e. there exists (possibly multi-hop) paths for every node to transmit and receive a signal from every other node.

Initial over-the-air performance assessment of ranging and clock synchronization using radio frequency signal exchange

In this paper we demonstrate results of a technique for synchronizing clocks and estimating ranges between a pair of RF transceivers. The technique uses a periodic exchange of ranging waveforms between two transceivers along with sophisticated delay estimation and tracking. The technique was implemented on wireless testbed transceivers with independent clocks and tested over-the-air in stationary and moving configurations. The technique achieved ~10ps synchronization accuracy and 2.1mm range deviation, using A two-channel oscilloscope and tape measure as truth sources. The timing resolution attained is three orders of magnitude better than the inverse signal bandwidth of the ranging waveform (50MHz⇒ 6m resolution), and is within a small fraction of the carrier wavelength (915MHz⇒ 327mm wavelength). We discuss how this result is consistent with the Weiss-Weinstein bound and cite new applications enabled by this technique.

Experimental demonstration of a distributed antenna array pre-synchronized for retrodirective transmission

We describe the key ideas behind our implementation of a distributed antenna array fully pre-synchronized for retrodirective transmission to an external receiver. In our implementation, a number of wireless transceivers in a network use a sequence of simple in-band wireless message exchanges to calibrate themselves so that these transceivers can obtain their channel gains to an external receiver using reciprocity simply by observing a single incoming transmission from that receiver without any channel feedback or other cooperation from the receiver. Some notable features of our implementation are as follows: (a) it automatically calibrates and corrects for unknown channel gains, oscillator offsets and drifts between the array nodes as well as the effect of non-reciprocal RF hardware; (b) it is fully wireless and endogenous i.e., does not use any wired backhaul connections or side channels including GPS; and (c) it uses simple signal processing on a standard and widely available software-defined radio platform based on off-the-shelf hardware and open-source software. Also, to the best of our knowledge, this is the first ever demonstration of a pre-synchronized distributed array, and thus our implementation serves as a proof-of-concept and allows for the development of more advanced distributed array techniques building on this capability.

Scalable algorithms for joint beam and null-forming using distributed antenna arrays

We consider the problem of multicasting a common message signal to a set of designated receivers from a distributed antenna array, while simultaneously forming nulls to another set of null targets. We propose an algorithm under which each transmitter in the distributed array iteratively makes an incremental adjustment to its complex gain (which controls the amplitude and phase of its transmitted RF signal). The cumulative effect of these incremental adjustments is that the individual transmitted RF signals from the transmitters add up at the intended receivers to a desired SNR level, while simultaneously canceling each other perfectly at the null targets. A crucial feature of this algorithm is that it can be implemented in a purely distributed fashion at each transmitter using only an estimate of its own channel gain to each receiver, and an aggregate feedback signal from each of the receivers that is broadcast to all the transmitters. This is an important advantage of our approach and assures its scalability; in contrast any non-iterative approach to the beam/nullforming problem requires knowledge of all channel gains - from all transmitters to all receivers - to be available at every transmitter.

Frequency estimation in the presence of cycle slips: Filter banks and error bounds for phase unwrapping

We consider a setting in which a receiver uses a sequence of short, narrowband training burst signals from a transmitter to jointly estimate the time delay and frequency offset of its local clock with respect to the transmitter. A key challenge in this estimation problem is in handling cycle-slips arising from ambiguities in phase unwrapping when (a) the repetition rate of the training signal is small compared to the frequency offset, and (b) the bandwidth of the training signal is small relative to the carrier frequency. We propose a novel Bayesian filter-bank approach to handling these ambiguities. We present numerical simulations to show the effectiveness of this approach and compare our results with the fundamental posterior Cramer-Rao lower bound. The filter achieves the bound for signals between about 5 and 35 dB SNR, showing that it is optimal in this regime.

Experimental demonstration of nullforming from a fully wireless distributed array

We consider distributed nullforming using an array of wireless transmitters that coordinate their transmissions to achieve destructive interference at a designated receiver. We describe the first experimental demonstration of distributed nullforming to a target receiver from an array of three distributed transmitters using (mostly) off-the-shelf hardware and simple and standard signal processing techniques. We are motivated by the goal of using distributed arrays to achieve increased spectrum reuse through interference cancellation. Our results show interference suppression in excess of 25dB over uncoordinated transmission. We build on our recent experimental demonstration of beamforming from a distributed antenna array after estimating and compensate for the combined effects of unknown propagation channels, hardware mismatches and clock drifts between the array nodes. The transmitters do not share clocks or have any wired back channels. They coordinate achieve nullforming entirely using in-band wireless message exchanges. Thus these methods can be implemented on portable mobile devices rather than being limited to Base Stations.

Experimental demonstration of retrodirective beamforming from a fully wireless distributed array

We report on recent results from our ongoing work on demonstrating retrodirective transmission from distributed arrays. Specifically, we describe a successful experimental demonstration of retrodirective beamforming to a non-cooperating receiver from an array of three distributed transceivers using (mostly) off-the-shelf hardware and simple and standard signal processing techniques. We build on our recently reported work that describes a synchronization procedure that allows the array nodes to estimate and compensate for the combined effects of frequency offsets and drifts in the oscillators as well as nonreciprocal elements in the transceiver hardware. We show how the array nodes that have performed the above synchronization process can then use an opportunistic incoming transmission from an external target to perform retrodirective beamforming back to that target without any coordination with that target. Our experimental results show beamforming gains greater than 90%. A key distinguishing feature of our work is that our procedure requires no wired links between the array nodes, no GPS, nor any other shared signal. To the best of our knowledge, this is the first ever demonstration of retrodirective beamforming from a fully wireless distributed array.

Source location estimation for possibly unknown propagation models

In this paper the source localization problem is considered without any knowledge of the signal propagation model, beyond the fact that the measured signal, e.g. received signal strength, strictly decreases with distance. Three algorithms dedicated to various scenarios are developed. Their convergence and other properties are established.

Optimizing wireless power transfer with multiple transmitters

We present a simple theoretical model and supporting experimental evidence for a new approach to maximizing the efficiency of wireless power transfer (WPT) to a receiver from multiple transmitters. Specifically, we consider a multiple-input single-output (MISO) WPT system using near-field inductive coupling to transfer power from multiple transmitting coils to a single receiver; the use of multiple transmitters can potentially allow the system to efficiently focus the transmitted power in the direction of the receiver similar to beamforming from a phased array. This idea is not new and such systems have been extensively studied in previous work using lumped RLMC circuit models to analyze their behavior. However, the difficulty of constructing tractable and realistic circuit models has limited our ability to accurately predicting and optimizing the performance of these systems. Our key novelty is to take the more abstract approach of modeling the WPT system as a linear circuit whose input-output relationship is expressed in terms of a small number of unknown parameters that can be thought of equivalent impedances and transconductances. The crucial advantage of this approach is the economy of the representation: the number of unknown parameters can be much smaller than the number of lumped circuit elements required for a complete and accurate RLMC circuit representation. We present a simple derivation of the optimal voltage excitations to be applied at the transmitters to maximize power transfer efficiency, and also some general properties of the optimal solution. This optimal excitation is, of course, a function of the unknown parameters in our abstract circuit model. We describe a simple procedure for estimating these parameters using a small set of direct measurements. We describe a simple experimental setup with two transmitter coils and a receiver designed to illustrate our approach and present results to demonstrate the efficiency increase achieved using the calculated optimal solution from our model.

Maximizing wireless power transfer using distributed beamforming

We consider the problem of maximizing the total wireless signal power delivered by a distributed antenna array to a receiver where the transmitting nodes each have known frequency-selective channel responses to the receiver and are subject to individual total transmit power constraints. This optimization problem is mathematically quite different from the power maximization problems involving single transmitters or for narrowband systems. We show that the power maximizing solution involves the array nodes performing distributed beam-forming while concentrating their power in a small, finite set of frequencies resulting in an overall received signal consisting of a small number of sinusoidal tones. We derive some properties of the power maximizing solution and describe an iterative algorithm that efficiently computes the solution. We show using numerical simulations that the power maximization problem can yield substantially larger received power compared to alternatives such as a matched filter for frequency-selective channels.