This paper addresses the problem of joint angle and delay estimation(JADE) in a multipath communication scenario. A low-complexity multi-way compressive sensing(MCS) estimation algorithm is proposed. The received data are firstly stacked up to a trilinear tensor model. To reduce the computational complexity,three random compression matrices are individually used to reduce each tensor to a much smaller one. JADE then is linked to a low-dimensional trilinear model. Our algorithm has an estimation performance very close to that of the parallel factor analysis(PARAFAC) algorithm and automatic pairing of the two parameter sets. Compared with other methods, such as multiple signal classification(MUSIC), the estimation of signal parameters via rotational invariance techniques(ESPRIT), the MCS algorithm requires neither eigenvalue decomposition of the received signal covariance matrix nor spectral peak searching. It also does not require the channel fading information, which means the proposed algorithm is blind and robust, therefore it has a higher working efficiency.Simulation results indicate the proposed algorithm have a bright future in wireless communications. This paper addresses the problem of joint angle and delay estimation (JADE) in a multipath communication scenario. A low-complexity multi-way compressive sensing (MCS) estimation algorithm is proposed. The received data are pre- stacked up to a trilinear tensor model. To reduce the computational complexity, three random compression matrices are individually used to reduce each tensor to a much smaller one. JADE then is linked to a low-dimensional trilinear model. Our algorithm has an estimation performance very close to that of the parallel factor analysis Compared with other methods, such as multiple signal classification (MUSIC), the estimation of signal parameters via rotational invariance techniques (ESPRIT), the MCS algorithm requires neither eigenvalue decomposition of the received signal covariance matrix nor spectral peak searching. It also does not require the channel fading information, which means the proposed algorithm is blind and robust, therefore it has a higher working efficiency.Simulation results indicate the the proposed algorithm have a bright future in wireless communications.