A Compressed Sensing Parameter Extraction Platform for Radar Pulse Signal Acquisition
Summary (5 min read)
Introduction
- A principal goal in the design of modern electronic systems is to acquire large amounts of information quickly and with little expenditure of resources.
- In light of the ever growing demand to capture higher bandwidths, it would seem that a solution at the fundamental system level is needed to address these challenges.
- The requisite sampling rate is merely proportional to the information level, and thus CS provides a framework for sub-Nyquist rate signal acquisition.
- The authors complete system is capable of recovering radar pulse parameters within an effective instantaneous bandwidth (EIBW) spanning 100 MHz—2.5 GHz with a digitizing performance of 8 ENOB.
A. Compressed Sensing
- CS at its heart relies on two concepts: sparsity and incoherence [5].
- Incoherence captures the idea of dissimilarity between any two representations; two bases are said to be incoherent if any signal having a sparse expansion in one of them must be dense in the other.
- Fig. 1a shows the block diagram of the IC containing the input buffer driving the common node of the four RD channels, and the timing generator.
- After the integrator the signal bandwidth is reduced and the circuits are design to meet settling requirements.
- Finally, an output buffer is designed to the drive the ADC with the correct swing and common-mode voltage.
B. A Brief History and Description of the RMPI
- Almost simultaneously with the introduction of CS [2], a number of CS-based signal-acquisition architectures were proposed.
- The rows of each block contain ±1 entries, and the overall matrix will be composed of NTNyq/Tint = 20 blocks (one for each integration window).
- For the measurements presented in this paper, the authors construct a model of their system’s Φ matrix by feeding in sinusoidal tones and using the output measurements to characterize the system’s impulse response.
A. Architecture and Operation
- The RMPI presented in this work was realized with the proprietary Northrop Grumman (NG) 450 nm InP HBT bipolar process [26].
- The timing generator is responsible for generating the pseudo-random bit sequences (PRBS) and the clocking waveforms to coordinate the track-and-hold (T/H) and integration operations.
- The circuits following the integrator are designed to meet the settling requirements of the reduced bandwidth.
- In operation, the RMPI circuit takes the analog input signal, buffers it, and distributes the buffered signal to each of the 4 channels.
- Immediately after the signal is sampled, the capacitor begins discharging and the second capacitor begins integrating the next frame (see Fig. 1b).
B. Analog Signal Path
- The input buffer is a differential pair with emitter degeneration and 50 Ω termination at each single-ended input.
- Emitter degeneration is used on the bottom differential pair to improve linearity.
- At the end of the integration period the signal is sampled and then held for 26 CLKin cycles to allow the external ADC to digitize the signal for post-processing.
- The diodes act as switches to configure capacitors for integration or reset it based on the level of the control signal (SEL).
- The input clock buffer was biased with a relatively high power to reduce jitter and it has 4 separate output emitter followers to limit cross-talk.
C. PRBS & Timing Generator
- A master clock is applied to CLKin, from which all required timing signals are generated.
- The output pulse from PN6B is re-clocked with the pulse from PN6A to pr duce a sync pulse that is 52 CLKin cycles long once every 3276 cycles.
- Special attention was paid to the routing of the PRBS, T/H clocks, and select signals to inimize clock/data coupling among th four channels.
- Shown are (4) quadrature clocks for the T/H and (4) select signals for the interleaved capacitors.
D. Performance Analysis
- Simulation validation was done by performing transientbased two-tone inter-modulation distortion simulations in the Cadence design environment.
- Noise simulations were perform d using the peri i steady-state (PSS) mode of spectre.
- The RMPI sam ling system, including the off-chip ADCs consumed 6.1 W of power.
- The authors point out that this system was designed as a proof-of-concept and was not optimized for power.
- 4 Distribution Statement “A” (Approved for Public Release, Distribution Unlimited) [DISTAR case #18841].
IV. PULSE-DESCRIPTOR WORD (PDW) EXTRACTION
- Having described the acquisition system, the authors now present algorithms for detecting radar pulses and estimating their parameters, referred to as pulse-descriptor words (PDW), from randomly modulated pre-integrated (RMPI) samples.
- The detection process is based on familiar principles employed by detectors that operate on Nyquist samples.
- The authors algorithms use a combination of template matching, energy thresholding, and consistency estimation to determine the presence of pulses.
- The remainder of the section elaborates on the procedure and is arranged as follows.
- After describing how the authors can reliably estimate the carrier frequency of a signal from compressive measurements, they then explain how they use such estimations to form a detection algorithm that jointly uses energy detection and consistency of their frequency measurements.
A. General Parametric Estimation
- The authors general parameter estimation problem can be stated as follows.
- Given the measurements y = Φ[x0]+noise, the authors search for the set of parameters corresponding to the subspace which contains a signal which comes closest to explaining the measurements y.
- Tα is the orthogonal projector onto the column space of Vα.
- When the noise is correlated, the authors may instead pose the optimization in terms of a weighted least squares problem.
- In Sec. IV-B and Sec. IV-C below, the authors will discuss the particular cases of frequency estimation for an unknown tone, and time-of-arrival estimation for a square pulse modulated to a known frequency.
B. Carrier Frequency, Amplitude, and Phase
- The authors consider the task of estimating the frequency of a pure tone from the observed RMPI measurements.
- The algorithms developed here play a central role in the detection process as well, as the frequency estimation procedure is fundamental to determining the presence of pulses.
- The authors also describe how to estimate the amplitude and phase once the carrier frequency (CF) is known.
- The subspaces Since the authors have discretized the signal x(t) through its Nyquist samples, their measurement process is modeled through a matrix Φ, the rows of which are the basis elements φk.
- Rather than dealing with continuously variable frequency, the authors define a fine grid of frequencies between 0 and fnyq/2.
D. Pulse Detection
- With their estimation techniques explained the authors next describe a pulse detection algorithm that takes a stream of RMPI samples and classifies each as either having a “pulse present” or “no pulse present.”.
- The authors task is to determine how many pulses are present and to estimate the parameters of each pulse the authors find.
- If neighboring blocks have CF estimates that are consistent in value and tones at these frequencies account for a considerable portion of their measurement energies, then the authors are confident that a pulse is indeed present.
- Once the TOA, TOD, and CF estimates have been refined, the authors calculate their amplitude and phase estimates.
- Merge any segments that are close together in time and have similar CF estimate, also known as 7.
E. Complexity
- In fact, since Φ contains repetitions of Φ0 the authors need only take the FFT of the 252 rows of Φ0, which they may then shift through complex modulation.
- This calculation does not depend on the measurement data, and therefore can be done offline as a precomputation.
- For each window length L (typically between 5-11 RMPI samples) and each window shift, the authors have to compute.
- The authors can explicitly invert V Tf Vf using the 2×2 matrix inverse formula, and all other calculations involve a small number of 4L-point inner products.
- The number of frequencies the authors test is proportional to the number of Nyquist 8 Distribution Statement “A” (Approved for Public Release, Distribution Unlimited) [DISTAR case #18841] samples N , and thus the cost of the frequency estimation for each sliding window shift is O(NL).
F. Cancellation and multiple pulses
- The authors focus on how to remove contributions from certain frequency bands in the RMPI measurements.
- The operator Ψ can be used to remove the contributions of the interfering band in the measurements y when the authors run their estimation methods.
- Fig. 9 shows how the use of the nulling operator aids in removing interfering bands.
- During this second 1These are also known as Slepian sequences.
- Fig. 10 shows an example of the two-stage detector for overlapping pulse data.
A. Measurement Test Setup Description
- In order to test the performance of the radar-pulse parameter estimation system-composed of the RMPI sampling hardware and the PDW extraction algorithm §IV, the authors ran a set of over 686 test radar pulses composed of permutations of A0, θ0, CF, TOA and TOD through the RMPI and estimated the varied parameters from the compressed-samples digitized by the RMPI.
- 9 Distribution Statement “A” (Approved for Public Release, Distribution Unlimited) [DISTAR case #18841] Fig. 12 shows a block diagram for the test setup used for the RMPI.
- An Arbitrary Waveform Generator AWG with an output sampling rate of 10 Gsps was used to output the pulses of interest.
- The stimulus was input into the RMPI whose outputs were then sampled by external ADCs located on a custom digitizing PCB shown in Fig. 11b: the RMPI IC is mounted on a a low-temperature co-fired ceramic (LTCC) substrate shown in Fig. 11a which is placed in the center of the digitizing board.
- The digitized samples were then transferred to a PC where the PDW extraction algorithm was used to estimate the signal parameters.
B. Parameter Estimation
- For each pulse, the authors estimated the CF only from measurements corresponding to times when the signal was active.
- The authors then estimated the TOA from RMPI samples corresponding to noise followed by the front end of the pulse.
- The authors repeated the procedure for the TOD, using RMPI samples corresponding to the end of the pulse followed by noise only.
- Fig. 13 shows the distribution of their estimation errors for CF, TOA, and TOD.
- Additionally, Table I shows statistics on the errors for each of the three parameters.
C. Pulse Detection
- The authors tested the pulse detection system by generating 60 test cases containing 12 pulses each (for a total of 720 pulses) with varying amplitudes (ranging over 60 dB), phases, 10 Distribution Statement “A” (Approved for Public Release, Distribution Unlimited) [DISTAR case #18841] durations (100 ns—1 µs), carrier frequencies (100 MHz— 2.5 GHz), and overlaps.
- All pulse rise times were approximately 10 ns.
- Table III shows the detection rate and standard deviation of the parameter estimate errors as a function of the pulse amplitudes.
- To test the robustness of the detection and estimation system, the authors repeated their detection experiment and included a constant-frequency interferer at set amplitudes in each experiment.
- The authors tested 6 interferer strengths, running 60 experiments with 12 pulses per experiment, for a total of 720 pulses per interferer strength.
VI. CONCLUSION
- The authors have presented a detailed overview of the design of both hardware and software used in a novel radar-pulse receiver in which information is extracted without performing full signal reconstruction.
- This novel approach obtains desired information with high accuracy while considerably reducing the back-end computational load.
- The system was validated using parameter estimates obtained from testing with a large and exhaustive set of realistic radar pulses spanning the parameter space.
- The physically measured results generated from this prototype proof-ofconcept system demonstrates the feasibility of the approach.
- In addition, the data obtained provides ample motivation for further investigation of the merit of CS-based signal acquisition schemes in general.
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Citations
2 citations
Cites methods from "A Compressed Sensing Parameter Extr..."
...As it shows great advantages in reduction of the data amount in transmission, CS method enlightens an efficient way to achieve wider bands with lower hardware device costs, and great progress has been made in last decades [2-4]....
[...]
2 citations
2 citations
Cites background from "A Compressed Sensing Parameter Extr..."
...Especially, the works in [5]–[7] have exploited the benefits of CS to radar systems....
[...]
2 citations
Cites methods from "A Compressed Sensing Parameter Extr..."
...Several AICs have been suggested for sampling radar echoes at range dimension, such as random sampling [2], RMPI [3], Xampling [4] and QuadCS [5]....
[...]
...Several AICs have been suggested for sampling radar echoes in the range dimension, such as random sampling [2], RMPI [3], Xampling [4] and QuadCS [5]....
[...]
1 citations
References
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"A Compressed Sensing Parameter Extr..." refers background in this paper
...Index Terms—Compressed sensing, Indium-Phosphide, Parameter Estimation, Random-Modulation Pre-Integration I. INTRODUCTION A principal goal in the design of modern electronic systems is to acquire large amounts of information quickly and with little expenditure of resources....
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...In short, the CS theory states that signals with high overall bandwidth but comparatively low information level can be acquired very efficiently using randomized measurement protocols....
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