Detector Design and Complexity Analysis for Cooperative Communications in Intersymbol Interference Fading Channels

Table 1

The dependencies between 𝑥[0] and related output signal.

Related output signal	Symbols to be recorded
𝑠[0]=𝑓(𝐡0,𝑥[0],𝑥[−𝐾],𝑥[−𝐿+1])	𝑥[0]
𝑠[𝐾]=𝑓(𝐡𝐾,𝑥[𝐾],𝑥[0],𝑥[𝐾−𝐿+1])	𝑥[0],𝑥[𝐾]
𝑠[𝐿−1]=𝑓(𝐡𝐿−1,𝑥[𝐿−1],𝑥[𝐿−1−𝐾],𝑥[0])	𝑥[0],𝑥[𝐾],𝑥[𝐿−1]
𝑠[2𝐾]=𝑓(𝐡2𝐾,𝑥[2𝐾],𝑥[𝐾],𝑥[2𝐾−𝐿+1])	𝑥[𝐾],𝑥[𝐿−1],𝑥[2𝐾]
𝑠[𝐾+𝐿−1]=𝑓(𝐡𝐾+𝐿−1,𝑥[𝐾+𝐿−1],𝑥[𝐿−1],𝑥[𝐾])	𝑥[𝐾],𝑥[𝐿−1],𝑥[2𝐾],𝑥[𝐾+𝐿−1]
𝑠[2𝐿−2]=𝑓(𝐡2𝐿−2,𝑥[2𝐿−2],𝑥[2𝐿−2−𝐾],𝑥[𝐿−1])	𝑥[𝐿−1],𝑥[2𝐾],𝑥[𝐾+𝐿−1],𝑥[2𝐿−2]
𝑠[3𝐾]=𝑓(𝐡3𝐾,𝑥[3𝐾],𝑥[2𝐾],𝑥[3𝐾−𝐿+1])	𝑥[2𝐾],𝑥[𝐾+𝐿−1],𝑥[2𝐿−2]
𝑠[2𝐾+𝐿−1]=𝑓(𝐡2𝐾+𝐿−1,𝑥[2𝐾+𝐿−1],𝑥[𝐾+𝐿−1],𝑥[2𝐾])	𝑥[2𝐾],𝑥[𝐾+𝐿−1],𝑥[2𝐿−2]
𝑠[𝐾+2𝐿−2]=𝑓(𝐡𝐾+2𝐿−2,𝑥[𝐾+2𝐿−2],𝑥[2𝐿−2],𝑥[𝐾+𝐿−1])	𝑥[𝐾+𝐿−1],𝑥[2𝐿−2]