Radar Signal Processing: Echo Wave Analysis and Target Detection

The echo wave reflected by the targets received at the BS can be expressed as:

Yecho = ∑k=1K αka(θk)aT(θk)X˜k + Z, (1)

where Z represents the noise plus interference, with the variance σ2r, αk denotes the complex-valued reflection coefficient of the kth target, θk is the kth target’s azimuth angle, with a(θ) being the steering vector of the transmit antenna array.

In the case of ULA, the steering vector can be written in the form

a(θ) = [1, ej2πλdsin(θ),...,ej2πλd(NBS−1)sin(θ)]T ∈CNBS×1, (2)

where d and λ denote the antenna spacing and the signal wavelength. Without loss of generality, we set d = λ/2.

For notational convenience, we arrange the steering vectors into a steering matrix A(Θ) = [a(θ1),..., a(θK)], Θ = {θ1, θ2,...,θK}, and denote [α1,...,αK]T as α. Note that the received signal Yecho is a linear combination of the target reflections, weighted by their reflection coefficients and the steering vectors of the transmit antenna array.

The goal of radar signal processing is to estimate the reflection coefficients of the targets and their azimuth angles based on the received signal Yecho. This is typically done using techniques such as matched filtering, beamforming, and angle estimation. The accuracy of the estimates depends on factors such as the signal-to-noise ratio (SNR), the number of targets, and the array geometry.

In addition to target detection and localization, radar signal processing can also be used for tasks such as tracking moving targets, imaging objects, and detecting changes in the environment. These applications require more sophisticated algorithms and processing techniques, but the basic principles of radar signal processing remain the same.