This paper proposes a compressed sensing radar system that achieves higher resolution than classical radar by exploiting sparsity and incoherence. The system discretizes the time-frequency plane into an N×N grid and assumes a small number of targets (K << N²). A sufficiently "incoherent" pulse is transmitted, and compressed sensing techniques are used to reconstruct the target scene. Theoretical bounds on sparsity K are presented, and numerical simulations show improved performance in practice. The key ideas include using an Alltop sequence for incoherence, avoiding matched filters, and leveraging sparsity constraints for target recovery. The paper introduces a matrix identification approach using compressed sensing, where an unknown matrix H is represented as a linear combination of basis elements. The goal is to identify the coefficients of this representation. The coherence of the dictionary is analyzed, and it is shown that the Alltop sequence provides maximal incoherence, enabling efficient recovery of sparse signals. The paper also discusses the time-frequency basis for radar systems, showing that any matrix can be represented using time-frequency shifts. The Alltop sequence is used to construct a Gabor frame with maximal incoherence, which is essential for compressed sensing radar. Theoretical results show that compressed sensing radar can achieve better resolution than classical radar, especially when the number of targets is much smaller than N². Numerical simulations demonstrate that the theoretical bounds on sparsity can be relaxed, and compressed sensing radar can successfully recover target scenes even in the presence of noise. The paper compares compressed sensing radar with classical radar, showing that compressed sensing radar can achieve higher resolution by leveraging sparsity and incoherence. The results highlight the potential of compressed sensing in radar systems for improved resolution and performance.This paper proposes a compressed sensing radar system that achieves higher resolution than classical radar by exploiting sparsity and incoherence. The system discretizes the time-frequency plane into an N×N grid and assumes a small number of targets (K << N²). A sufficiently "incoherent" pulse is transmitted, and compressed sensing techniques are used to reconstruct the target scene. Theoretical bounds on sparsity K are presented, and numerical simulations show improved performance in practice. The key ideas include using an Alltop sequence for incoherence, avoiding matched filters, and leveraging sparsity constraints for target recovery. The paper introduces a matrix identification approach using compressed sensing, where an unknown matrix H is represented as a linear combination of basis elements. The goal is to identify the coefficients of this representation. The coherence of the dictionary is analyzed, and it is shown that the Alltop sequence provides maximal incoherence, enabling efficient recovery of sparse signals. The paper also discusses the time-frequency basis for radar systems, showing that any matrix can be represented using time-frequency shifts. The Alltop sequence is used to construct a Gabor frame with maximal incoherence, which is essential for compressed sensing radar. Theoretical results show that compressed sensing radar can achieve better resolution than classical radar, especially when the number of targets is much smaller than N². Numerical simulations demonstrate that the theoretical bounds on sparsity can be relaxed, and compressed sensing radar can successfully recover target scenes even in the presence of noise. The paper compares compressed sensing radar with classical radar, showing that compressed sensing radar can achieve higher resolution by leveraging sparsity and incoherence. The results highlight the potential of compressed sensing in radar systems for improved resolution and performance.