LTE PDCCH introducton

PDCCH is also called heart of LTE. 1 PDCCH consist of 1, 2, 4 or 8 CCEs. 1 CCE = 9 REG, 1 REG = 4REs, with QPSK modulation, 1 RE could carry 2 bits information. In total, 1CCE has 36RE * 2 bits = 72 bits. There are 4 different PDCCH formats mapped to 4 different CCE aggregation levels (1, 2, 4, 8).

Search Space is defined Sk = L * {(Yk + m') mod floor(NCCE,k/L)} + i

For common search space, L is 4 or 8; For UE-specific search space, L is 1, 2, 4 or 8
NCCE,k is total number of CCEs in subframe k
i = 0, 1, ...... L-1
For common search space, m' = m; For UE-specific search space, if no carrier indicator field is configured on UE, m' = m; else m' = m + M(L) * nCI,  wehre nCI is the value of carrier indicator, M(L) is the number of PDCCH candidates to monitor in the given search space.
m = 0, 1, ..... M(L)-1

Following table is quoted from 3GPP 36.213 9.1.1

For common search space, Yk is set to 0 for L = 4 or 8
For UE-specific search space, Yk = (A * Yk-1) mod D, where Y-1 = nrnti, A = 39827, D = 65537, k = floor(ns/2), ns is the slot number in a radio frame.

Following is an example of calculating C-RNTI = 135, UE-specific search space starting point:
For k=0 (ns = 0 or 1, subframe 0),