Robert Calderbank

Adaptive Waveform Design for Improved Detection of Low-RCS Targets in Heavy Sea Clutter

The dynamic adaptation of waveforms for transmission by active radar has been facilitated by the availability of waveform-agile sensors. In this paper, we propose a method to employ waveform agility to improve the detection of low radar-cross section (RCS) targets on the ocean surface that present low signal-to-clutter ratios due to high sea states and low grazing angles. Employing the expectation-maximization algorithm to estimate the time-varying parameters for compound-Gaussian sea clutter, we develop a generalized likelihood ratio test (GLRT) detector and identify a range bin of interest. The clutter estimates are then used to dynamically design a phase-modulated waveform that minimizes the out-of-bin clutter contributions to this range bin. A simulation based on parameters derived from real sea clutter data demonstrates that our approach provides around 10 dB improvement in detection performance over a nonadaptive system

Waveform Diversity in Radar Signal Processing

This article shows that suitably transmitted and processed, radar waveforms based on Golay sequences provide new primitives for adaptive transmission that enable better detection and finer resolution, while managing computational complexity at the receiver. The ability to exploit space-time adaptive processing is limited by the computational power available at the receiver, and increased flexibility on transmission only exacerbates this problem unless the waveforms are properly designed to simplify processing at the receiver.

Two are better than one: Fundamental parameters of frame coherence

This paper investigates two parameters that measure the coherence of a frame: worst-case and average coherence. We first use worst-case and average coherence to derive near-optimal probabilistic guarantees on both sparse signal detection and reconstruction in the presence of noise. Next, we provide a catalog of nearly tight frames with small worst-case and average coherence. Later, we find a new lower bound on worst-case coherence; we compare it to the Welch bound and use it to interpret recently reported signal reconstruction results. Finally, we give an algorithm that transforms frames in a way that decreases average coherence without changing the spectral norm or worst-case coherence.

Space-time processing for broadband wireless access

We present an overview of research activities on space-time coding for broadband wireless transmission performed at AT&T Shannon Laboratory over the past two years. The emphasis is on physical layer modem algorithms such as channel estimation, equalization, and interference cancellation. However, we also discuss the impact of space-time coding gains at the physical layer on throughput at or above the networking layer. Furthermore, we describe a flexible graphical user interface attached to our physical layer simulation engine in order to explore the performance of space-time codes under a variety of practical transmission scenarios. Simulation results for the EDGE cellular system and the 802.11 wireless LAN environment are presented.

Rate-achievability strategies for two-hop interference flows

We consider a basic model for two-hop transmissions of two information flows which interfere with each other. In this model, two sources simultaneously transmit to two relays (in the first hop), which then simultaneously transmit to two destinations (in the second hop). While the transmission during the first hop is essentially the transmission over a classical interference channel, the transmission in the second hop enjoys an interesting advantage. Specifically, as a byproduct of the Han-Kobayashi transmission scheme applied to the first hop, each of the relays (in the second hop) has access to some of the data that is intended to the other destination, in addition to its own data. As recently observed by Simeone et al., this opens the door to cooperation between the relays. In this paper, we observe that the cooperation can take the form of distributed MIMO broadcast, thus greatly enhancing its effectiveness at high SNR. However, since each relay is only aware of part of the data beyond its own, full cooperation is not possible. We propose several approaches that combine MIMO broadcast strategies (including ldquodirty paperrdquo) with standard non-cooperative strategies for the interference channel. Numerical results are provided, which indicate that our approaches provide substantial benefits at high SNR.

Unitary design of radar waveform diversity sets

In this work, multiple radar waveforms are simultaneously transmitted, emitted from different ldquovirtualrdquo antennas. The goal is to process the returns in such a way that the overall ambiguity function is a sum of ambiguity functions better approximating the desired thumbtack shape. A 4times4 example involves two spatially separated antennas with each able to transmit and receive simultaneously on two different polarizations. The 4times4 unitary design dictates the scheduling of the waveforms over the four virtual antennas over four PRIs (pulse repetition intervals), and how the matched filtering of the returns over four PRIs is combined in to achieve both perfect separation (of the superimposed returns) and perfect reconstruction. Perfect reconstruction means the sum of the time-autocorrelations associated with each of the four waveforms is a delta function. Conditions for both perfect separation and perfect reconstruction are developed, and a variety of waveform sets satisfying both are presented.

Range sidelobe suppression in a desired Doppler interval

We present a novel method of constructing a Doppler resilient pulse train of Golay complementary waveforms, for which the range sidelobes of the pulse train ambiguity function vanish inside a desired Doppler interval. This is accomplished by coordinating the transmission of a Golay pair of phase coded waveforms in time according to the 1s and -1s in a biphase sequence. The magnitude of the range sidelobes of the pulse train ambiguity function is shown to be proportional to the magnitude spectrum of the biphase sequence. Range sidelobes inside a desired Doppler interval are suppressed by selecting a sequence whose spectrum has a high-order null at a Doppler frequency inside the desired interval. We show that the spectrum of the biphase sequence obtained by oversampling the length-2M Prouhet-Thue-Morse (PTM) sequence by a factor m has an Mthorder null at all rational Doppler shifts θ0 = 2πl/m, where l ≠ 0 and m ≠ 1 are co-prime integers. This spectrum also has an (M - 1)th-order null at zero Doppler and (M - h - 1)thorder nulls at all Doppler shifts θ0 = 2πl/(2hm), where l ≠ 0 and m ≠ 1 are again co-prime and 1 ≤ h ≤ M - 1.

Multiuser detection in asynchronous on-off random access channels using lasso

This paper considers on-off random access channels where users transmit either a one or a zero to a base station. Such channels represent an abstraction of control channels used for scheduling requests in third-generation cellular systems and uplinks in wireless sensor networks deployed for target detection. This paper introduces a novel convex-optimization-based scheme for multiuser detection (MUD) in asynchronous on-off random access channels that does not require knowledge of the delays or the instantaneous received signal-to-noise ratios of the individual users at the base station. For any fixed number of temporal signal space dimensions N and maximum delay τ in the system, the proposed scheme can accommodate M ≲ exp(O(N1/3)) total users and k ≲ N/ logM active users in the system—a significant improvement over the k ≤ M ≲ N scaling suggested by the use of classical matched-filtering-based approaches to MUD employing orthogonal signaling. Furthermore, the computational complexity of the proposed scheme differs from that of a similar oracle-based scheme with perfect knowledge of the user delays by at most a factor of log(N+τ). Finally, the results presented in here are non-asymptotic, in contrast to related previous work for synchronous channels that only guarantees that the probability of MUD error at the base station goes to zero asymptotically in M.

A sublinear algorithm for sparse reconstruction with ℓ 2 /ℓ 2 recovery guarantees

Compressed Sensing aims to capture attributes of a sparse signal using very few measurements. Candès and Tao showed that sparse reconstruction is possible if the sensing matrix acts as a near isometry on all k-sparse signals. This property holds with overwhelming probability if the entries of the matrix are generated by an iid Gaussian or Bernoulli process. There has been significant recent interest in an alternative signal processing framework; exploiting deterministic sensing matrices that with overwhelming probability act as a near isometry on k-sparse vectors with uniformly random support, a geometric condition that is called the Statistical Restricted Isometry Property or StRIP. This paper considers a family of deterministic sensing matrices satisfying the StRIP that are based on Delsarte-Goethals Codes codes (binary chirps) and a k-sparse reconstruction algorithm with sublinear complexity. In the presence of stochastic noise in the data domain, this paper derives bounds on the ℓ<inf>2</inf> accuracy of approximation in terms of the ℓ<inf>2</inf> norm of the measurement noise and the accuracy of the best k-sparse approximation, also measured in the ℓ<inf>2</inf> norm. This type of ℓ<inf>2</inf>/ℓ<inf>2</inf> bound is tighter than the standard ℓ<inf>2</inf>/ℓ<inf>1</inf> or ℓ<inf>1</inf>/ℓ<inf>1</inf> bounds.

Complementary codes based channel estimation for MIMO-OFDM systems

We present a pilot-assisted method for estimating the frequency selective channel in a MIMO-OFDM (multiple input multiple output -orthogonal frequency division multiplexing) system. The pilot sequence is designed using the DFT (discrete Fourier transform) of the Golay complementary sequences. Novel exploitation of the perfect autocorrelation property of the Golay codes, in conjunction with OSTBC (orthogonal space-time block code) based pilot waveform scheduling across multiple OFDM frames, facilitates simple separation of the channel mixtures at the receive antennas. The DFT length used to transform the complementary sequence into the frequency domain is shown to be a key critical parameter for correctly estimating the channel. NMSE (normalized mean squared error) between the actual and the estimated channel is used to characterize the estimation performance.