Radar Waveform Optimization for Joint Radar Communications Performance
Abstract
:1. Introduction
1.1. Contributions
- Extend previously derived spectral mask shaping method to employ the continuous spectral WF algorithm to maximize communications performance
- Employ more computationally efficient optimization solvers for the spectral mask shaping algorithm
- Introduce constraints on autocorrelation peak side-lobe to main-lobe ratio and spectral leakage for the spectral mask shaping waveform design method
- Conduct a preliminary study to compare the performance of the extended waveform design method against previously derived spectral-mask shaping method
- Compare waveform properties of the optimally designed radar waveform with that of a LFM chirp waveform
- Derive a time-domain expression for a spectrally masked standard chirp signal
- Prove that the solution of the NLP waveform design problem is Pareto-optimal
1.2. Background
1.3. Problem Description
- Radar and communications operate in the same frequency allocation simultaneously
- Joint radar communications receiver is capable of simultaneously decoding a communications signal and estimating a target parameter
- Radar detection and track acquisition have already taken place
- Radar system is an active, single-input single-output (SISO), mono-static, and pulsed system
- Radar system operates without any maximum unambiguous range
- A single SISO communications transmitter is present
- Only one radar target is present
- Target range or delay is the only parameter of interest
- Target cross-section is well estimated
2. Joint Radar Communications Performance Metrics
2.1. Successive Interference Cancellation Receiver Model
2.2. Spectral Water-Filling SIC Data Rate
2.3. Global Radar Estimation Rate
3. Joint Waveform Design Problem
- Peak side-lobe to main-lobe ratio (constraint ): in [8], the estimation rate was extended to consider global estimation errors (errors occurring when the radar waveform autocorrelation side-lobe is confused for the main-lobe) using the method of interval errors [60]. However, the method of interval errors only considers the errors occurring due to the peak side-lobe and ignores the rest. If the other side-lobes are high enough, they can still have a significant contribution to the global estimation error. By limiting the peak side-lobe to main-lobe ratio to be below a certain threshold, we can reduce the effect the peak side-lobe as well as any other high side-lobes will have on the global estimation error. This constraint is mathematically defined in Equation (11).
- Spectral leakage (constraint ): Since the system can only receive signals whose spectrum lies within the system’s bandwidth, any electromagnetic radio frequency (RF) energy that leaks outside of the bandwidth will be lost. To minimize this loss of RF energy, we introduce a constraint on the amount of energy present in the radar spectrum at frequencies out of the system bandwidth range. We enforce this constraint by having the radar spectrum be below a thresholding spectral mask such as the one seen in Figure 5. This constraint is mathematically defined in Equation (11).
4. Method
- and
- and .
Time Domain Form of Spectrally-Masked Chirp
5. Simulation Results and Discussion
5.1. Spectral-Mask Shaping Method
5.2. Performance Comparison of Waveform Design Algorithms
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
BER | bit error rate |
NLP | Nonlinear Programming |
MMSE | Minimum Mean-Squared Error |
OFDM | Orthogonal Frequency-Division Multiplexing |
PSD | Power Spectral Density |
RMS | Root Mean Square |
RF | Electromagnetic Radio Frequency |
SIC | Successive Interference Cancellation |
SISO | Single-Input Single-Output |
SNR | Signal-to-Noise Ratio |
WF | Water-Filling |
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Variable | Description |
---|---|
Expectation | |
L2-norm or absolute value | |
Marcum Q-function | |
Dirac-delta function | |
f | Frequency |
t | Time |
B | Full bandwidth of the system |
Root-mean-squared radar bandwidth | |
Unit-variance transmitted radar signal | |
Radar signal frequency response | |
Radar power | |
Time delay to target | |
a | Target complex combined antenna, cross-section, and propagation gain |
T | Radar pulse duration |
Radar duty factor | |
Total communications power | |
Optimal communications transmit distribution | |
b | Complex combined antenna gain and communications propagation loss |
Receiver thermal noise | |
Post-SIC radar residual | |
Thermal noise power | |
Boltzmann constant | |
Absolute temperature | |
Variance of range fluctuation process | |
Cramèr-Rao lower bound or estimation error variance | |
Integrated radar SNR |
Parameter | Value |
---|---|
Bandwidth (B) | 5 MHz |
Center frequency | 3 GHz |
Effective temperature () | 1000 K |
Communications range | 10 km |
Communications power () | 1 W |
Communications antenna Gain | 20 dBi |
Communications receiver Side-lobe Gain | 10 dBi |
Radar target range | 11.2 km |
Radar antenna gain | 30 dBi |
Radar power () | 1 kW |
Target cross section | 10 m2 |
Target process standard deviation () | 100 m |
Time–bandwidth product () | 128 |
Radar duty factor () | 0.01 |
Performance Metric (Average Values) | CW Spectral-Mask Shaping | Spectral-Mask Shaping |
---|---|---|
Final objective value | ||
(b/s) | ||
(b/s) |
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Chiriyath, A.R.; Ragi, S.; Mittelmann, H.D.; Bliss, D.W. Radar Waveform Optimization for Joint Radar Communications Performance. Electronics 2019, 8, 1498. https://doi.org/10.3390/electronics8121498
Chiriyath AR, Ragi S, Mittelmann HD, Bliss DW. Radar Waveform Optimization for Joint Radar Communications Performance. Electronics. 2019; 8(12):1498. https://doi.org/10.3390/electronics8121498
Chicago/Turabian StyleChiriyath, Alex R., Shankarachary Ragi, Hans D. Mittelmann, and Daniel W. Bliss. 2019. "Radar Waveform Optimization for Joint Radar Communications Performance" Electronics 8, no. 12: 1498. https://doi.org/10.3390/electronics8121498
APA StyleChiriyath, A. R., Ragi, S., Mittelmann, H. D., & Bliss, D. W. (2019). Radar Waveform Optimization for Joint Radar Communications Performance. Electronics, 8(12), 1498. https://doi.org/10.3390/electronics8121498