This paper proposes a novel method for two-dimensional (2-D) direction-of-arrival (DOA) estimation of multiple signals employing a sparse L-shaped array structured by a sparse linear array (SLA), a sparse uniform linear array (SULA) and an auxiliary sensor. In this method, the elevation angles are estimated by using the SLA and an efficient search approach, while the azimuth angle estimation is performed in two stages. In the first stage, the rough azimuth angle estimates are obtained by utilizing a noise-free cross-covariance matrix (CCM), the estimated elevation angles and data from three sensors including the auxiliary sensor. In the second stage, the fine azimuth angle estimates can be achieved by using the shift-invariance property of the SULA and the rough azimuth angle estimates. Without extra pair-matching process, the proposed method can achieve automatic pairing of the 2-D DOA estimates. Simulation results show that our approach outperforms the compared methods, especially in the cases of low SNR, snapshot deficiency and multiple sources.

The decoders, which improve the error-correction performance by finding and correcting the error bits caused by channel noise, are a hotspot for polar codes. In this paper, we present a threshold based D-SCFlip (TD-SCFlip) decoder with two improvements based on the D-SCFlip decoder. First, we propose the LLR fidelity criterion to define the LLR threshold and investigate confidence probability to calculate the LLR threshold indirectly. The information bits whose LLR values are smaller than the LLR threshold will be excluded from the range of candidate bits, which reduces the complexity of constructing the flip-bits list without the loss of error-correction performance. Second, we improve the calculation method for flip-bits metric with two perturbation parameters, which locates the channel-induced error bits faster, thus improving the error-correction performance. Then, TD-SCFlip-ω decoder is also proposed, which is limited to correcting up to ω bits in each extra decoding attempt. Simulation results show that the TD-SCFlip decoding is slightly better than the D-SCFlip decoding in terms of error-correction performance and decoding complexity, while the error-correction performance of TD-SCFlip-ω decoding is comparable to that of D-SCFlip-ω decoding but with lower decoding complexity.