We describe a parallel iterative least squares solver named \textttLSRN that is based on random normal projection. \textttLSRN computes the min-length solution to $\min_{x \in \mathbb{R}^n} \|A x - b\|_2$, where $A \in \mathbb{R}^{m \times n}$ with $m \gg n$ or $m \ll n$, and where $A$ may be rank-deficient. Tikhonov regularization may also be included. Since $A$ is involved only in matrix-matrix and matrix-vector multiplications, it can be a dense or sparse matrix or a linear operator, and LSRN automatically speeds up when $A$ is sparse or a fast linear operator. The preconditioning phase consists of a random normal projection, which is embarrassingly parallel, and a singular value decomposition of size $\lceil \gamma \min(m,n) \rceil \times \min(m,n)$, where $\gamma$ is moderately larger than $1$, e.g., $\gamma = 2$. We prove that the preconditioned system is well-conditioned, with a strong concentration result on the extreme singular values, and hence that the number of iterations is fully predictable ...

Space–time waveform-encoding (STWE) SAR can receive echoes from multiple sub-swaths simultaneously with a single receive window. The echoes overlap each other in the time domain. To separate the echoes from different directions, traditional schemes adapt single-null steering techniques for digital receive beam patterns. However, the problems of spaceborne DBF-SAR, in practice, such as null extension loss, terrain undulation, elevation angle of arrival extension, and spaceborne antenna beam control, make the conventional scheme unable to effectively separate the echoes from different sub-swaths, which overlap each other in the time domain.A novel multi-null constrained echo separation scheme is proposed to overcome the shortcomings of the conventional scheme. The proposed algorithm can flexibly adjust the width of the notch to track the time-varying pulse extension angle with less resource consumption. Moreover, the hardware implementation details of the corresponding real-time processing architecture are discussed. The two-dimensional simulation results indicate that the proposed scheme can effectively improve the performance of echo separation. The effectiveness of the proposed method is verified by raw data processing instance of an X-band 16-channel DBF-SAR airborne system.

High-resolution wide swath (HRWS) imaging has become a research hotspot in the field of synthetic aperture radars (SARs) in recent years. Digital beamforming (DBF) denotes a powerful technique for obtaining the HRWS images. The DBF can be implemented in a spaceborne SAR in real time but at the cost of massive digital resources. To solve this problem, an intermediate frequency (IF) DBF real-time processing architecture has been proposed, but it has never been validated in practice. In this letter, the X-band 16-channel DBF-SAR and the C-band four-channel DBF-SAR are used to demonstrate the effectiveness of the IFDBF scheme in practice for the first time. The performance of the IFDBF scheme is verified by the detailed analysis of the signal-to-noise ratio (SNR) improvement and system complexity. The result shows that the IFDBF scheme can achieve the same SNR improvement as the DBF scheme. Moreover, by applying the IFDBF scheme, a spaceborne SAR can save more digital resources in real-time processing.

Digital beamforming (DBF) with scan-on-receive (SCORE) is a state-of-the-art technique for high-resolution and wide-swath observation in synthetic aperture radar (SAR) imaging. However, this technique has a problem with frequency dispersion. Most existing DBF methods treat the frequency as a constant, and little work has been devoted to the analysis of frequency dispersion. To address this shortcoming, this letter analyzes the dispersion effect using the raw data of two digital beamforming synthetic aperture radars (DBF-SARs). Moreover, this letter demonstrates in practice for the first time the effectiveness of the digital scalloped beamforming (DSBF), one of the candidates for solving the frequency dispersion problem in SCORE DBF, using the X-band sixteen-channel DBF-SAR and the C-band four-channel DBF-SAR. The analyses of the impulse response width extension and the signal-to-noise ratio (SNR) improvement are presented in detail to show the performance of the frequency dispersion compensation. The results show that the DSBF is effective in compensating for the frequency dispersion in the DBF technique. With DSBF, a higher SNR improvement can be obtained in DBF-SARs.

Digital beamforming (DBF) is an effective approach for accessing high-resolution wide-swath (HRWS) imaging in spaceborne synthetic aperture radar (SAR). By utilizing DBF, the performance of imaging, including signal to noise ratio (SNR) and system sensitivity, can be greatly improved. In actual missions, DBF for SAR imaging can be combined with various operating modes like squint-strip SAR, spotlight SAR and TOPSAR. In squint-looking scenarios, the receiving beam of antenna scans the scene not only along the vertical direction (elevation) but also along the horizontal direction (azimuth). For the first time, this paper proposes the application of DBF for squint SAR imaging, establishes a geometric model of beam scanning and derives the analytic expression of signal model. The performance of both the conventional DBF scheme and the digital scalloped beamforming (DSBF) scheme are analyzed in squint-looking scenarios. In order to further reduce the loss of gain when processing received signals with broadband widths and long pulse durations in the conventional DBF schemes, as well as to minimize the digital resource consumption in the DSBF scheme, where the resource usage is directly proportional to the number of sub-beams, a novel multi-beam digital beamforming scheme is proposed. Theoretical analysis and simulation results validate the effectiveness of the proposed scheme, making it as a more realistic technology for future spaceborne SAR.