Back Projection (BP) Algorithm Source Code for MIMO Array Implementation

The Back Projection (BP) algorithm is a widely used processing technique in radar imaging applications, particularly well-suited for handling Multiple-Input Multiple-Output (MIMO) array data. Its core principle involves reprojecting received signals based on time delays and spatial positions back to the imaging area, thereby constructing two-dimensional or three-dimensional images of targets.

For MIMO arrays, the Back Projection algorithm's advantage lies in its flexibility to adapt to various antenna configurations while effectively utilizing multi-channel signals to improve imaging resolution. The algorithm workflow can be divided into the following key implementation stages:

Signal Acquisition: Each transmitter antenna in the MIMO array sequentially emits signals while all receiver antennas simultaneously record echo data. Code implementation typically involves managing multiple data channels and synchronizing transmission-reception sequences.

Range Compensation: Time delay compensation is applied to each received signal to account for distance variations between targets and different antenna pairs. This requires precise calculation of propagation paths using geometric transformations and interpolation functions.

Coherent Summation: Compensated signals are coherently summed pixel by pixel to enhance useful signals and suppress noise. This critical step involves phase alignment and complex amplitude accumulation across all antenna channels.

Image Reconstruction: By accumulating data from all transmitter-receiver channel combinations, the algorithm ultimately generates high-resolution radar images. The implementation typically uses nested loops iterating through image pixels and antenna pairs.

Compared to traditional matched filtering or FFT-based methods, the BP algorithm has higher computational complexity but offers superior adaptability, especially for non-uniform sampling or complex scenarios in MIMO radar imaging.

For optimization, parallel computing or GPU acceleration can significantly improve BP algorithm execution efficiency, making it suitable for real-time or near-real-time imaging requirements. Implementation strategies may include dividing the image grid into parallel processing blocks and utilizing CUDA kernels for GPU operations. Additionally, combining sparse array optimization techniques can further enhance MIMO system imaging performance through advanced antenna pattern design and computational efficiency improvements.