High Resolution TOA Estimation Based On Compressed Sensing

The estimation of time of arrival (TOA) is the key issue for wireless positioningsystems. Other than being used in conventional navigation applications, the informationof user location can be used to help the communication systems allocate the resourcesmore efficiently.The conventional correlator based methods are widely used. However, theresolution is restricted by the system bandwidth, and can’t offer enough accuracy foractual needs. The deconvolution based methods can out put an impulse-like channelresponse, thus have better performance in separating closely spaced multipaths. On theother hand, it will suffer from severe noise amplification effect. The subspace basedsuper resolution methods can realize a high definition for TOA. However, itscomplexity is too high for practice use, and for low SNR, it suffers from a seriousdegradation in performance.Based on the theory of compressed sensing, a novel TOA estimation scheme withhigh resolution is proposed in this work. The inherent sparsity of the channel isexploited to give an accurate estimation of the channel response. Then an energy basedcriteria is used to determine the first arrival path, and consequently the TOA. Thetheoretical error bound of the estimated channel response is derived, and is shown to beproportional to the channel response sparsity and the noise level. Simulations show thatthe proposed scheme can achieve a sub-chip resolution, and outperforms the currentmethods both in error mean and variance.To further reduce the complexity of CS recovery in TOA estimation, a newiteration stopping criteria is proposed. In this method, the energy distribution of thesignal in each iteration is measured and the iteration is stopped once the signal supportset can be determined. Simulation shows that while keeping the mean of TOAestimation error nearly unchanged, and the standard deviation increased by nomore than40%, the number of iterations can be reduced by around50%.This work exploited the inherent sparsity of the channel and proposed a TOAestimation scheme with high resolution and good anti-noise property. As the solution can be get via liner programming, the scheme is not computationally expensive forpractical use.