A three-stage padding configuration providing a larger continuous virtual aperture and achieving more degrees-of-freedom (DOFs) for the direction-of-arrival (DOA) estimation is presented. The improvement is realized by appropriately cascading three-stages of an identical inter-element spacing. Each stage advantageously exhibits a continuous virtual array, which subsequently produces a hole-free resulting uniform linear array. The geometrical approach remains applicable for any existing sparse array structures with a hole-free coarray, as well as designed in the future. In addition to enlarging the continuous virtual aperture and DOFs, the proposed design offers flexibility so that it can be realized for any given number of antennas. Moreover, a special padding configuration is demonstrated, which further increases the number of continuous virtual sensors. The precise antenna locations and the number of continuous virtual positions are benefited from the closed-form expressions. Experimental works are carried out to demonstrate the effectiveness of the proposed configuration.

This letter proposes the use of a novel time-modulated array structure to estimate the direction of arrival (DOA). Such a time-modulated coprime array (TMCA) is obtained by exchanging a coprime array's phase shifter for a radio frequency (RF) switch. Compared with a traditional coprime array, the TMCA's structure is much simpler, and it has a higher degree of freedom and resolution compared with a time-modulated uniform linear array (TMULA) due to its exploitation of the virtual array's equivalent signals. Theoretical analysis and experimental results have validated the effectiveness of the proposed structure and method and have confirmed that a TMCA's DOA performance is better than that of a TMULA using the same number of antennas.

Using local time frames to treat non-stationary real world signals as stationary yields Quasi-Stationary Signals (QSS). In this paper, direction of arrival (DOA) estimation of uncorrelated non-circular QSS is analyzed by applying a novel technique to achieve larger consecutive lags using coprime array. A scheme of virtual extension of coprime array is proposed that exploits the difference and sum co-array which can increase consecutive co-array lags in remarkable number by using less number of sensors. In the proposed method, cross lags as well as self lags are exploited for virtual extension of co-arrays both for differences and sums. The method offers higher degrees of freedom (DOF) with a larger number of non-negative consecutive lags equal to MN+2M+1 by using only M+N-1 number of sensors where M and N are coprime with congenial interelement spacings. A larger covariance matrix can be achieved by performing covariance like computations with the Khatri-Rao (KR) subspace based approach which can operate in undetermined cases and even can deal with unknown noise covariances. This paper concentrates on only non-negative consecutive lags and subspace based method like Multiple Signal Classification (MUSIC) based approach has been executed for DOA estimation. Hence, the proposed method, named Virtual Extension of Coprime Array imbibing Difference and Sum (VECADS), in this work is promising to create larger covariance matrix with higher DOF for high resolution DOA estimation. The coprime distribution yielded by the proposed approach can yield higher resolution DOA estimation while avoiding the mutual coupling effect. Simulation results demonstrate its effectiveness in terms of the accuracy of DOA estimation even with tightly aligned sources using fewer sensors compared with other techniques like prototype coprime, conventional coprime, Coprime Array with Displaced Subarrays (CADiS), CADiS after Coprime Array with Compressed Inter-element Spacing (CACIS) and nested array seizing only difference co-array.