Joint timing‐offset and channel estimation for physical layer network coding in frequency selective environments

Abstract

Abstract 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 maximum‐likelihood (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.

Keywords

• Codes
• Communication channel equalisation and identification
• Radio links and equipment
• Error statistics (inc. error probability)