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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

This paper describes the underlying methodology behind an adaptive multimodal radar sensor that is capable of progressively optimizing its range resolution depending upon the target scattering features. It consists of a test-bed that enables the generation of linear frequency modulated waveforms of various bandwidths. This paper discusses a theoretical approach to optimizing the bandwidth used by the multimodal radar. It also discusses the various experimental results obtained from measurement. The resolution predicted from theory agrees quite well with that obtained from experiments for different target arrangements.

Increasingly complex target scenarios call for sophisticated techniques such as waveform and sensing diversity for resolving individual targets or target scattering centers to aid in target identification and recognition. Waveform design is therefore an essential ingredient of modern radar systems [

Multifunction radio frequency (RF) systems have been studied for a long time [

Multifunction radar systems have also been developed [

The multimodal radar has the ability to provide target indication with a large range extent and can progressively switch to a narrow range extent mode for extracting recognizable target features. Primary requirements for such a radar include detection and location of stationary targets in severe ground clutter as well as the classification and recognition of these targets.

A multimodal radar has been designed and developed by us to address the above needs. It consists of a test-bed that enables the generation of linear frequency modulation (LFM) waveforms with varying bandwidths. A narrow bandwidth waveform is used initially to obtain a low range resolution (LRR) profile of the target. High range resolution (HRR) processing is then progressively performed using higher bandwidth waveforms within selected range cells wherein targets are declared.

Radar resolution has been the focus of research for a very long time. Woodward applied the two-dimensional matched filter response to the analysis of radar resolution [

This paper is organized as follows: Section 2 provides a description of the multimodal radar and its operation. In Section 3, the bandwidth optimization procedure is presented with examples. The field measurement results for various scenarios are discussed in Section 4. In Section 5, we show results of extensive simulations to characterize the multimodal radar system. Conclusions are discussed in Section 6.

In this section, we discuss the system block diagram, various design parameters, and the flowchart of operation of the multimodal radar.

Initially, the AWG transmits a low bandwidth waveform (40 MHz) and sweeps the range extent searching for targets generating low range resolution profiles. Range resolution Δ

The multimodal radar now restricts its attention to those LRR gates where the threshold is exceeded. HRR imaging begins on these identified LRR gates with the 80 MHz bandwidth waveform (1.875-m resolution). Imaging stops if the desired range resolution is obtained on a particular LRR gate to identify existing targets, else it continues with the next higher bandwidth (160 MHz → 320 MHz → 640 MHz). Range resolution is progressively enhanced until a minimum separation (in dB) is met between the peaks and its neighboring cells. This minimum separation may be decided based upon the required resolution and the expendable bandwidth. Thus, the multimodal radar continues to look at potential targets with narrower range extents until the desired resolution is obtained to detect target presence.

Measurements were also taken for scenarios where multiple target scenes are laid out in azimuthal fashion. The radar starts scanning the field for targets (by rotating the antennas about a vertical axis) beginning with the low bandwidth waveform. The first LRR profile is taken at

We consider the problem of determining the optimum bandwidth required for a target scene. The cost function for our optimization problem is the bandwidth which is same as the optimization variable. The separation between the peak and its neighboring cells can serve as the constraints. We would like to have 3-dB amplitude separations between the target peak and its neighboring cells. This should be adequate to provide a good representation of the range-related variability within the target scene. Using higher separation may increase the required bandwidth significantly.

The optimization problem can be stated as below:

minimize

subject to _{1}(

_{2}(

where

_{1} is the separation in dB between the peak and the neighboring cell towards the radar,

_{2} is the separation in dB between the peak and the neighboring cell away from the radar.

The above constraints can be rewritten as:
_{1} and _{2} change in an arbitrary fashion. However, if the gate containing the peak target is forced to be centered in the range dimension, then the above constraints can be approximated by convex functions. The accuracy with which the functions can represent the above constraints will greatly influence the correctness of the results.

The Lagrangian duality method was used to solve the problem [_{i}

The maximum of the dual function gives a lower bound on the optimum value of

A Target Scenario 1 is shown in

These constraints are plotted in

The dual function was obtained and its values for different values of Lagrangian multipliers are shown plotted in

Another Target Scenario 2 is shown in

In the above two examples, we see that the maximum occurs at a value where either _{1} or _{2} is zero. This signifies that one of the constraints is dominant and is masking the other constraint. Hence a symmetrical Target Scenario 3 was tried, as shown in _{1}, _{2}), some of which have both _{1} and _{2} non-zero. The dual function for this target scenario is shown in

For the previous discussion, we assumed that the targets were of equal strength. However, if the targets vary greatly in strength, a resolution value of half of the target separation is no longer accurate. In [

minimize

subject to _{1}(

_{1} is the separation in dB between the cell containing the weaker target and the neighboring cell towards the stronger target.

To solve the above problem, we first solve the simpler problem using _{req}

Let us consider an arbitrary target shown in _{1}, _{2}). We approximate the expected value of bandwidth based on the theory of point spread function. If _{1} and _{2} were equal, the resolution required would have been approximately _{1,2}/2. This corresponds to a bandwidth of _{1.2} = _{1.2}. When _{1} and _{2} are unequal, this can be adjusted to be equal to:

Looking at the other pairs of scattering centers, for a total of

When we consider just the pair of adjacent scattering centers, we neglect the effect of other scatterers. This can be justified from the fact that if a scatterer were close enough to make a substantial contribution, then the bandwidth required to resolve that scatterer from its neighbor would be much higher than the others in the expression above.

Field measurements were performed for a number of different scenarios. The measurement setup is shown in ^{2} (+17.6 dBsm) at 1 GHz to 155.5 m^{2} (+21.9 dBsm) at 1.64 GHz. We consider a range of 37.5 m which is slightly greater than the maximum radar range. This results in 10 LRR gates each of extent of 3.75 m. The RCS values of the targets are normalized with respect to the target with the highest RCS. The algorithm continues with higher resolution passes until 3-dB separations are obtained between the peaks and their neighboring cells.

The following results were obtained when the multimodal radar system was operated in the staring mode.

Field data were acquired to study the variation in bandwidth required based on difference in target strength. Multiple corner reflectors were placed side by side to increase the resultant RCS.

An extended target was simulated by placing corner reflectors at appropriate positions. One corner reflector is placed at 8.2 m, and two each at 10.7 m and 12.2 m. After normalizing with respect to strength and distance, the resulting extended target is as shown in

In this section, we look at certain results obtained from simulations. We also try to understand how the number of passes required by the multimodal radar would change with respect to external conditions.

Simulations were performed to generate the receiver operating characteristics (ROC) curves for the multimodal radar. The probability of detection (_{d}_{f}

Different targets may experience different number of passes. The _{f}_{f}

_{f}_{d}_{f}_{d}_{d}_{d}_{d}

We explore the effect of separation between the targets. We consider two targets and note the number of passes required as the separation between them is gradually reduced. The result is plotted in

We also simulated the effect of signal-to-noise ratio (SNR) on the performance of the multimodal radar. The target scenario was kept the same while the SNR was varied. It was observed that a higher number of passes is required to resolve a target scene as the SNR is decreased. The result is plotted in

The methodology of a multimodal radar system with progressive resolution enhancement is described. This radar makes it possible to look at different target scenes with the appropriate bandwidth required to resolve the target features. The saved bandwidth can be made available for use by other applications. Experimental results were provided to give a demonstration of the multimodal radar algorithm in operation. Simulation results were shown to provide further insight into the performance characteristics of the radar. A theoretical method was discussed to optimize the bandwidth required by the multimodal radar. It was seen that this bandwidth increases significantly when the targets differ greatly in strength.

Several other considerations also come to mind. For example, there may be an overriding need to reserve a significant portion of the available spectrum for other applications, such as essential communications. In such a case, there may be an upper limit to the bandwidth available for the radar. In addition, if a specific smaller portion of the spectrum needs to be reserved for alternate applications, the radar may need to search for available contiguous spectrum for its operation within the entire band while avoiding the reserved subband. These issues require additional study. With the advent of software-defined RF technology, future multimodal radar systems can be designed to be reconfigurable, and therefore highly flexible and adaptive [

Notional block diagram of the multimodal radar.

Flowchart for operation of multimodal radar in staring mode.

Flowchart for operation of multimodal radar in scanning mode.

Representation of constraints by quadratic equations.

Dual function for a Target Scenario 1.

Dual function for a Target Scenario 2.

Dual function for a Target Scenario 3.

Dependance of bandwidth required for resolution on target strength ratio.

Scattering centers of an extended target.

Field measurement setup for multimodal radar.

Imaging results for Target Scenario 4. (

Imaging results for Target Scenario 5. (

Diagrammatic representation of Target Scenario 6.

HRR images for Target Scenario 6. (

Diagrammatic representation of Target Scenario 7.

HRR Images for a Target Scenario 7. (

Dependance of bandwidth on target strength ratio.

An extended target using corner reflectors.

Receiver operating characteristics.

Variation in required number of passes as a function of target separation.

Variation in required number of passes as a function of SNR.

Radar system parameters.

Radar waveform | Linear frequency modulated pulse |

Radar bandwidth | 40–640 MHz |

Pulse width | 16 |

Transmit power | Approx. 0.5 W |

Maximum radar range | Approx. 25 m |

Bandwidth and resolution for each pass of the multimodal radar.

1 | 40 | 3.75 |

2 | 80 | 1.87 |

3 | 160 | 0.93 |

4 | 320 | 0.46 |

5 | 640 | 0.23 |

Target Scenario 1.

1 | 8.2 | 1 |

2 | 10.7 | 1 |

Target Scenario 2.

1 | 11.5 | 1 |

2 | 12.1 | 1 |

Target Scenario 3.

1 | 8.2 | 1 |

2 | 10.7 | 1 |

3 | 13.2 | 1 |

Target Scenario 4.

1 | 8.2 | 3 | 1 |

2 | 10.7 | 3 | 1 |

3 | 15.8 | 5 | 1 |

Target Scenario 5.

1 | 11.5 | 4 | 1 |

2 | 12.1 | 4 | 1 |

3 | 22.1 | 7 | 4 |

Target Scenario 6.

1 | 40 | 8.5 | 3 | 2 |

45 | 9.5 | 3 | 2 | |

2 | 140 | 15.8 | 5 | 4 |

Target Scenario 7.

1 | 30 | 8.2 | 3 | 1 |

2 | 75 | 11.3 | 4 | 1 |

80 | 12.2 | 4 | 1 | |

3 | 145 | 8.2 | 3 | 1 |

150 | 15.2 | 5 | 2 |

Field results for Scenario WITH varying relative RCS

1 | 1 | 0.345 | 4.62 | 180 |

1 | 2 | 0.69 | 1.62 | 140 |

1 | 3 | 1.035 | 0.15 | 110 |

1 | 4 | 1.38 | 1.4 | 110 |

2 | 1 | 0.172 | 7.62 | 180 |

2 | 2 | 0.345 | 4.62 | 150 |

2 | 3 | 0.518 | 2.86 | 150 |