Lock detectors for timing recovery

We present two lock detectors associated with the Gardner (1986) timing error detector (GA-TED). The first one (detectors A) requires an oversampling frequency of 4/T at the receiver, where 1/T is the symbol rate. The second (detector B) uses the same signal samples needed to implement the GA-TED, and thus, an oversampling frequency of 2/T is sufficient. Performance analysis shows that detector A matches to the GA-TED which means that independently of the channel impulse response, the optimal sampling instant obtained by the GA-TED corresponds to the optimal instant of the lock detector, i.e., it leads to the maximum average output. Unless, the channel transfer function has Hermetian symmetry, detector B does not match to the GA-TED. However, we show by computer simulations, that the performance degradation caused even by severe channel distortion remains negligible. The paper describes the basic principle of these lock detectors, analyzes their performance and discusses some points related to their implementation.