Fixed Delay Tree Search with Decision Feedback

FDTS is a suboptimal detection algorithm that performs maximum likelihood detection on a fixed and finite number of observation samples. This is in contrast to the MLSD detector which performs maximizes the sequence likelihood over all received samples. Detector decisions are made by computing the Euclidean distances of all possible tau+1 samples sequences from the tau+1 observation samples. The set of possible sequences can be represented as a tree as shown to the right (tau=2). There are 2^tau+1 possible sequences, the top half of which correspond to a_k-2=+1 and the other half to a_k-2=-1. After a decision is made, the other half of the tree is discarded and a new level of branches is grown onto the remaining half. In this way, the tree paths always remain consistent with previous decisions. For most practical cases, the length of the channel impulse response f(D) is greater than tau+1. To reduce the effective length of this response, a decision feedback equalizer eliminates from the observations intersymbol interference (ISI) associated with past decisions.

For more information, see

• J. Moon and L. R. Carley, " Performance comparison of detection methods in magnetic recording," IEEE Trans. Magn., vol. 26, no. 6, pp. 3155-3172, Nov. 1990.
  
  
• J. Moon and L. R. Carley, "Apparatus and method for fixed delay tree search," U.S. Patent 5,136,593, Aug. 4, 1992.