A compressed sensing/sparse-recovery procedure is adopted to obtain enhanced range resolution capability from the processing of data acquired with narrow-band SFCW radars. A mathematical formulation for the proposed approach is reported and validity limitations are fully discussed, by demonstrating the ability to identify a great number of targets, up to 20, in the range direction. Both numerical and experimental validations are presented, by assuming also noise conditions. The proposed method can be usefully applied for the accurate detection of parameters with very small variations, such as those involved in the monitoring of soil deformations or biological objects.

The application of radar devices for the remote detection and diagnostics of objects with high resolution capability is a strong focused point nowadays in many different contexts, going from soil deformation monitoring [

The most attractive configuration in these cases is given by the stepped-frequency continuous-wave (SFCW) radar [

low acquisition rate is typically provided, due to the slow scan over the radar bandwidth;

conventional SFCW data processing, based on the application of the Inverse Fourier Transform (IFT) [

By exploiting or enforcing the sparsity nature of the scenario, a compressed sensing (CS [

The possibility to enhance the radar resolution with CS has been recently highlighted in [

In this work, a detailed formulation of a CS-based processing algorithm able to identify close targets (in the range direction) by using narrow-band SFCW radar is presented. The effective range resolution enhancement is theoretically demonstrated, and a detailed discussion on the mathematical limits constraining the validity of the approach is presented, by revealing the possibility to identify a significant number of close targets (up to 20). Numerical simulations on both noiseless and Gaussian corrupted data are reported. Furthermore, experimental validations are presented on a real scenario composed by two metal plates (test targets) with a small separation distance of just 10 cm, accurately retrieved by adopting the CS-based processing algorithm to measured data obtained by a C-band (500 MHz) SFCW radar, fully designed at the Microwave Laboratory of University of Calabria.

With reference to a monostatic radar configuration [

The signal received by the radar, as due to the interaction with a single target located in the field of view, can be expressed as follows:

The received signal (

In the general case of

After applying the IFT to (

Equation (

When adopting an SFCW radar, only

From (

This latter equation, well known in radar theory [

Now, let us express (

It is easy to observe that system (

When applying the Fourier Transform (FT) operator to both sides of (

If imposing a range resolution

It must be noted that the number of data

In the realistic case where noise is added to data, the sparsest solution of undetermined system (

The first condition in (

It should be noted that (

As a matter of fact, under limit (

When applying constraint (

This latter expression suggests that, once fixing the radar operating bandwidth

In order to highlight the above mathematical limitations of the proposed CS approach, numerical simulations of (

Behavior of (

Behavior of (

Behavior of (

Behavior of (

It can be easily observed that, in the presence of a reduced number of targets to be solved (

Another important aspect, strongly influencing the validity of the CS approach (

The above choice is considered in the present work to perform the numerical tests discussed in the next section.

In order to assess the validity of the CS approach outlined in Section

As a first step, (

Behavior of (

From the above simulations, it can be easily observed that, for values of parameter

In order to demonstrate the range resolution enhancement offered by the proposed CS technique, two different target scenarios are assumed, including, respectively, a number

Firstly, ideal noiseless simulations are performed, whose corresponding results are illustrated in Figures

Range profile obtained from standard IFT algorithm (first scenario:

Range profile obtained from CS procedure (first scenario:

Range profile obtained from standard IFT algorithm (second scenario:

Range profile obtained from CS procedure (second scenario:

By examining the above results, it can be easily observed that standard radar processing algorithm is able to identify only two targets (over four) for the first scenario (Figure

To verify the robustness of the proposed CS approach with respect to noisy data, additional simulations are performed by assuming the signals to be corrupted with additive Gaussian noise giving an SNR ratio equal to 20 dB. For these noisy tests, the

The comparisons between the reconstructed radar range profiles with and without noise are reported in Figures

Range profile obtained from CS procedure (comparison between noiseless and Gaussian corrupted case, first scenario: 4 targets): only the second target is missed in the presence of noise (SNR = 20 dB).

Range profile obtained from CS procedure (comparison between noiseless and Gaussian corrupted case, second scenario: 6 targets): all targets are revealed in the presence of noise (SNR = 20 dB).

For the first scenario (Figure

As a further assessment test, experimental validations on a laboratory noisy scenario are performed by adopting a C-band SFCW radar fully designed and realized at the Microwave Laboratory of the University of Calabria, in the framework of project PON 01-01503 for landslides monitoring, financed by the Italian Ministry of University and Research. The radar is characterized by an operating bandwidth

Test setup into the Microwave Laboratory at University of Calabria.

Prior to performing the tests, a preliminary calibration procedure is applied, in the absence of targets, to properly identify the reflection peak due to the overall radar system delay. It results in being positioned at a distance approximately equal to 5 m.

When applying the standard (IFT) SFCW processing algorithm, the two targets are not distinguished but identified as a single object at a distance equal to 6.2 m (5 m + 1.2 m), as indicated by the arrows on the radar intensity profile of Figure

Radar intensity profile obtained from standard radar processing (IFT): experimental scenario of Figure

The CS algorithm outlined in Section

As a matter of fact, the radar range profile in Figure

Radar intensity profile obtained from CS processing algorithm: experimental scenario of Figure

The enhancement of range resolution, when adopting a CS approach for the processing of data coming from narrow-band radars, has been theoretically demonstrated, and a CS-based target reconstruction procedure has been properly formulated.

Mathematical aspects concerning the validity of the proposed sparse-recovery method are discussed, and the ability to reconstruct a great number of targets, up to 20, is demonstrated. Both numerical and experimental validations, illustrating the enhanced range profile reconstruction, have been reported. Concerning future work, the application of the proposed technique to fast and real-time monitoring of very small displacements, such as those occurring in soil deformations or bioradiolocation field, will be considered.

The author declares that there is no conflict of interests regarding the publication of this paper.