This paper considers the problem of joint timing-offset and channel estimation for physical-layer network coding systems operating in frequency-selective environments. Three different algorithms are investigated for the joint estimation of the channel coefficients and the fractional timing offset. The first algorithm is based on the maximumlikelihood (ML) criterion assuming baud-rate (BR) sampling. The second algorithm also assumes BR sampling and is based on the special properties of Zadoff-Chu training sequences. In the third algorithm, oversampling at double the baud-rate (DBR) is used and the least-squares (LS) estimation criterion applied. While the above algorithms assume that the integer timing offset is known, three generalized-likelihood-ratio tests (GLRTs) are also considered for integer offset error correction that integrate very well with the proposed estimation algorithms. Our simulation studies show that the DBR-LS estimator provides the highest estimation accuracy, significantly outperforming both BR estimators and performing very close to the corresponding Cramer-Rao bound. A gain of 4 dB is observed in symbol-error-rate performance using the DBR-LS algorithm. The DBR-GLRT also provides substantially higher probability of error correction.
INTRODUCTIONPhysical-layer network coding (PLNC) [1] is an important communication paradigm that continues to attract the interest of many researchers. The appeal of PLNC lies in exploiting the superposition of electromagnetic waves and the broadcast nature of wireless channels during its multiple access phase and broadcast phase, to achieve superior spectral efficiency. PLNC is capable of achieving 100% improvement in throughput over traditional scheduling that is based on point-to-point transmissions, and 33% improvement over conventional network coding schemes [2]. The PLNC framework provides an attractive solution to meet the demands of various applications envisaged for 5th generation (5G) wireless networks. In particular, PLNC can play an important role in facilitating efficient device-to-device (D2D) communication [3,4], where the numerous inactive users can be exploited as relays to extend the range of D2D communication. Other promising applications of PLNC include multiway relaying [2], cognitive relay networks [5] and visible light communication (VLC) [6].This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.