Large Time-bandwidth Product Research Articles

Phase-Coded Interrupted CW Signals and Processors

High resolution radars require signals with large time-bandwidth product such as CW signal and coherent pulse train (CPT). We discuss a phase-coded interrupted CW (ICW) signal which is the combination of CW signal and CPT. Phase codes used here are with perfect periodic autocorrelation. The periodic ambiguity function of ICW signals is studied including single-carrier signal and multi-carrier signal. It is interesting that the gate function has different effects on two signals and contributes to a multi-carrier ICW signal which yields nearly perfect autocorrelation. Meanwhile we also suggest an efficient receiver approach to ICW signals, which can reduce the computational burden of the processor and utilize the good properties of P3 and P4 codes.

Multimodal Properties and Dynamics of Gradient Echo Quantum Memory

We investigate the properties of a recently proposed gradient echo memory (GEM) scheme for information mapping between optical and atomic systems. We show that GEM can be described by the dynamic formation of polaritons in k space. This picture highlights the flexibility and robustness with regards to the external control of the storage process. Our results also show that, as GEM is a frequency-encoding memory, it can accurately preserve the shape of signals that have large time-bandwidth products, even at moderate optical depths. At higher optical depths, we show that GEM is a high fidelity multimode quantum memory.

Information processing with longitudinal spectral decomposition of ultrafast pulses

We describe what we believe to be novel methods for waveform synthesis and detection relying on longitudinal spectral decomposition of subpicosecond optical pulses. Optical processing is performed in both all-fiber and mixed fiber-free-space systems. Demonstrated applications include ultrafast optical waveform synthesis, microwave spectrum analysis, and high-speed electrical arbitrary waveform generation. The techniques have the potential for time-bandwidth products of > or =10(4) due to exclusive reliance on time-domain processing. We introduce the principles of operation and subsequently support these with results from our experimental systems. Both theory and experiments suggest third-order dispersion as the principle limitation to large time-bandwidth products. Chirped-fiber Bragg gratings offer a route to increasing the number of resolvable spots for use in high-speed signal processing applications.

Sluggish light for radio-frequency true-time-delay applications with a large time-bandwidth product

A new radio-frequency (RF) photonic technique for achieving large RF time delays has been experimentally demonstrated using femtosecond pulses modulated by an acousto-optic tunable filter in a frequency-mapped and Doppler-shifted modulation scheme. A short optical delay line with length of 240 mum produces nearly 3 micros RF time delay after optical heterodyne detection, resulting in an effective slow-light velocity of 86 m/s. A delay-to-pulse-width ratio of 20 based on this technique has been observed, with a larger fractional delay foreseeable.

Dilation dependent matched filtering for SAR signal processing

The relative motion between radar and targets in large time-bandwidth product synthetic aperture radar (SAR) induces serious dilation in the received signal. To process the received signal with serious dilation, a new technique called dilation dependent matched filtering (DDMF) is proposed to combine with the two-dimensional space frequency interpolation wavefront reconstruction (SFIWR) method. The DDMF-SFIWR method can effectively eliminate the impact of dilation when the illuminated area is relatively small, as verified by simulations and acoustic experiments.

Cyclic code shift keying: a low probability of intercept communication technique

A low probability of intercept (LPI), or low probability of detection (LPD) communication technique known as cyclic code shift keying (CCSK) is described. We discuss the basic concepts of CCSK and describe a system based on the use of random or pseudorandom codes for biphase modulation. We use simulation to show that the bit error rate (BER) for CCSK can be closely estimated by using existing equations that apply to M-ary orthogonal signaling (MOS). Also, we show that significantly fewer computations are required for CCSK than for MOS when the number of bits per symbol is the same. We show that using biphase modulation results in waveforms that have a large time-bandwidth product and very low input signal-to-noise ratio (SNR) and thus inherently have an LPI by a radiometer. We evaluate detection by a radiometer and show that LPI can be achieved by using codes of lengths greater than about 2/sup 12/ (i.e., by transmitting more than about 12 bits per symbol). Results illustrate the effect that the CCSK symbol length and error probability, and the radiometer integration time and probability of false alarm (PFA), have on detection by a radiometer. We describe a variation of CCSK called truncated CCSK (TCCSK). In this system, the code of length 2/sup k/ is cyclically shifted, then truncated and transmitted. Although shortened, the truncated code still represents k bits of information, thus leading to an increased data rate. We evaluate radiometer detection of TCCSK and it is shown that the probability of detection is increased compared with the detection of CCSK.

A Wideband Wavelet Based Estimator Correlator and its Properties

Maximum likelihood detectors of narrowband, non-stationary random echos in Gaussian noise can be efficiently implemented in the time-frequency domain. When the transmitted signals have large time-bandwidth products, the natural implementation of estimators and detectors is in the time-scale or wavelet transform domain. This paper presents a wideband wavelet transform domain implementation of an estimator-correlator (EC) detector and details the components of this processor, including weighted wavelet transforms and cascaded scattering functions. Key properties associated with this wavelet based wideband EC are also presented. The theoretical developments of the processor are based on group theory which provides a unified approach to detector development for both narrowband and wideband processors. The group theoretic concepts provide a powerful analysis tool for complex signal processing problems.

The fourth-order cumulant spectrum of a filtered linear frequency-modulated source in motion

The goal of a sonar system is to extract information from received pressure signals emanating from a source. Typical methods employed are usually first-order or second-order functions of the received pressure. This paper develops an analytical method to extract information from the received pressure using the fourth-order cumulant spectrum. The analysis begins with a far-field solution of the wave equation for an acoustic point source in motion. The source is modeled as a filtered linear frequency-modulated signal. The objective is to extract the impulse response of the source characterized by the filter. But due to the motion of the source the response of the extracted filter is modified by the Doppler component. For the given source model, a scaled Doppler component, and both the phase and a scaled magnitude of the Doppler modified filter, can be extracted directly from the fourth-order cumulant spectrum assuming a large time bandwidth product.

Reciprocal radar waveforms

Digitally coded radar waveforms can be used to obtain large time-bandwidth products (pulse compression ratios). It is demonstrated that periodic radar waveforms with zero sidelobes or almost zero sidelobes can be defined. A perfect periodic code is a periodic code whose autocorrelation function has zero sidelobes and whose amplitude is uniform (maximum power efficiency=1). An asymptotically perfect periodic code has the property that as the number of elements in the code goes to infinity the autocorrelation function of the code has zero sidelobes and its power efficiency is one. The authors introduce a class of radar waveforms that are either perfect or asymptotically perfect codes. These are called reciprocal codes because they can be derived through a linear transformation of known codes. The aperiodic performance of the reciprocal code is examined. >

Interferometric scanning acoustooptic spectrum analyzer

An interferometric scanning acoustooptic (AO) spectrum analyzer is described. The instantaneous detector array is replaced by an AO Bragg cell driven by a short rf pulse and a single fast photodetector, and the diffracted beam is mixed with a local oscillator. The temporal modulation of the heterodyne signal gives the spectrum of the input signal with linear characteristics. Using this architecture, a dynamic range of 70 dB can be achieved with a large time-bandwidth product (1000) and high speed (50 micros/spectrum).

Optical matched filter with log-constant false alarm detection

We have demonstrated and analyzed an analog electronic constant false alarm rate processor that discriminates against distributed clutter for an acoustooptic correlator of a potentially large time-bandwidth product.

Resolution of the ocean wave propagation direction in SAR imagery

There is an inherent 180 degrees ambiguity in the derived wave propagation direction when using conventional spectral analysis techniques on standard synthetic aperture radar (SAR) image products. Three different techniques are successfully used to resolve this ambiguity in propagation direction using a single pass of airborne SAR data. The fact that the SAR is characterized by a large time-bandwidth product is used to advantage. A sequence of individual looks extracted from the Doppler spectrum represents images of the scene collected at a sequence of discretely delayed intervals of time. The techniques utilized include cross-correlation-based motion analysis of a pair of looks, phase weighting based upon a pair of looks and the ocean wave dispersion relation, and a three-dimensional spectral analysis. The phase weighting technique is also demonstrated for a Seasat SAR scene. >

Correction factor for strongly reflecting U-path RACs

An equation from the literature describing multiple reflections in a U-path surface-acoustic-wave (SAW) reflective array compressor (RAC) is simplified for RACs with a large time-bandwidth product, yielding a very convenient expression consisting of the relation for weakly reflecting RACs plus phase and amplitude correction factors. The quantitative effect of multiple reflections is immediately apparent, so that the designer has a better understanding of how various parameters affect the final performance. A down-chirp, which is more common in practical devices, is described. Empirical extensions to higher-order and variable weighing are deduced and verified numerically, while the possibility of variable chirp is discussed.

Attaining the ideal detection limit using random multiplication

The effect of measurement time and the detection system bandwidth product in determining the signal-to-noise ratio is formulated. Results are derived for both cases when the detector is operated in the deterministic limit and the random limit. A comparison suggests that for level detection, when the measurement accuracy is limited by the finite time constant of the detection system, the random limit operation results in superior performance. For pulse detection, the random limit operation makes it possible to approach the ideal performance limit for large time bandwidth products. Also, the random scheme can attain the ideal performance limit even in the presence of gain fluctuations of the detector. The principle of random multiplication therefore provides an alternative approach to realizing ideal photodetectors.

Correction factor for low-loss 180 degrees reflecting linear chirp arrays in SAW devices

Low-loss, 180 degrees -reflecting linear chirps with constant or slowly varying weighting and large time-bandwidth product are analyzed. Multiple reflections are fully taken into account, giving a universal correction factor as a function of array parameters. This should enable such chirps to be designed without making iterations. Surface acoustic-wave (SAW) device layouts making use of the 180 degrees arrays are suggested.

Wide-band packet radio technology

Advances in signal processing and architectural design for high-performance packet radio are described. The scope of the work roughly encompasses the data-link and physical levels of standardized layered-network architectures. A hardware-function layering approach is used, including the purposeful design of an interface to provide a structured control environment for a demonstration packet radio. The advanced signal processing provides a robust, flexible data link to service demanding network environments, and uses 100-MHz-bandwidth surface-acoustic-wave (SAW) convolvers as large time-bandwidth product matched filters for communication with nonrepeating pseudonoise waveforms. The convolvers are combined with a binary-quantized postprocessor to implement a hybrid correlator which provides high processing gain for detection, demodulation, and ranging measurements. Data rates can be selected, in response to varying channel conditions, over a range from 1.45 Mbits/s down to 44 bits/s with an almost ideal tradeoff in processing gain for interference rejection and privacy ranging from 18 dB up to 61 dB. Future enhancements are proposed that will advance both the signal processing and the architecture.

Phase comparison time delay estimation using wideband signals

First Page

Locally Optimum and Suboptimum Detector Performance in a Non-Gaussian Interference Environment

Since the normally assumed white Gaussian interference is the most destructive in terms of minimizing channel capacity, substantial improvement can usually be obtained if the real-world interference environment (non-Gaussian) is properly taken into account. In this paper, the performance of the locally Bayes detector (LOBD) is compared to the performance of various ad hoc nonlinear detection schemes. The known results are reviewed, and then it is demonstrated that these theoretical results may be misleading due to the assumptions that are required in order to derive them analytically. For a particular type of broad-band impulsive noise, the critical assumptions of sufficiently small signal level and large number of samples (large time-bandwidth product so that the central limit theorem applies) are removed; the first analytically, and the second by computer simulation. The thus-derived performance characteristics are then compared, especially as the signal level increases. One result is that there are situations where the bandpass limiter outperforms the LOBD as the signal level increases; that is, the locally detector may not remain near optimum in actual operational situations.

Scanning Acoustic Microscope Utilizing SAW-BAW Conversion

A 1WMHz acoustic microscope using an integrated grat- ing acoustic scanner is studied. The resolution of the system is approx- imately 68 pm. The real-time acoustic images obtained from this mi- croscope demonstrate the feasibility of the approach. The dependency of the energy velocity of acoustic waves on the propagation direction in the saggital plane of a Y-cut Z-propagating LiNbO, crystal was studied, and piezoelectric effects were included. The energy of velocity disper- sion was calculated and the results were employed for designing the tap positions of a large time-bandwidth product, nonlinear chirp fflter to obtain a large aperture and spherical aberration-free operation. Theoretical analysis reveals that for a given chirped waveform, the sur- face acoustic wave (SAW) propagating in the positive 2 direction gives better resolution than that in the negative 2 direction. Focusing the bulk acoustic wave in the transverse direction is achieved with the curved grooves or metallic strips, and the focus phase error using the curved structure are studied. to reduce the attenuation loss, and the crystals used are normally anisotropic. We had also previously reported a high-frequency GAS device (8) and demonstrated its fo- cusing and scanning capabilities. Electronic focusing in the axial direction was augmented by transverse focusing using an external lens that was massive and bulky. This device was operated at a rather high frequency, approximately 100 MHz, and the anisotropic effect of the substrate was included in the design. In Section I1 the de- sign of the GAS using an anisotropic substrate will be dis- cussed. In Section I11 we will discuss methods for focus- ing the bulk acoustic wave in the transverse direction without the external lens. We also analyze the focus phase error, which is important for obtaining high resolution. To obtain large aperture operation and spherical aber- ration-free focusing, energy velocity dispersion in LiNb03 was calculated (given in the Appendix) and employed for designing the tap positions of a large time-bandwidth product, nonlinear chirp generator. The GAS was used in conjunction with a computer-controlled mechanical scan- ner, which scanned the sample in the transverse direction to the GAS to obtain two-dimensional images. This had not been achieved previously due to the lack of a stable mechanical scanner.

Optical Fiber Delay-Line Signal Processing

Single-mode optical fiber is an attractive delay medium for processing microwave frequency signals due to its extremely low loss (<0.1 dB/µs) and large available time-bandwidth product (in excess of 10/sup 5/). Recent progress in the efficient tapping of light from single-mode fibers has made it possible to construct recirculating and nonrecirculating (tapped) delay-line structures that can perform a variety of important signal processing functions. These functions include coded sequence generation, convolution, correlation, matrix-vector multiplication, and frequency filtering. This paper presents the fundamental properties of single-mode fiber delay lines and reviews recent experimental results that demonstrate the feasibility of fiber delay-line devices for broad-band signal-processing applications.