LTE Physical Hybrid ARQ Indicator Channel (PHICH)

PHICH is the physical channel that carrier the Hybrid ARQ Indicator (HI).  The HI contains the Acknowledgement/Negative Acknowledgement (ACK/NACK) feedback to the UE for the uplink blocks received by the eNB.

PHICH group is the group of multiple PHICHs mapped to same set of resource elements, where PHICHs within the same PHICH group are separated through different orthogonal sequences.

 A PHICH resource is identified by the index pair [ n(group,PHICH), n(seq, PHICH)] , where  n(group, PHICH) is the PHICH group number and n(seq, PHICH) is the orthogonal sequence index within the group for frame structure type 1, the number of PHICH groups n(group, PHICH) is

constant in all subframes and given by where Ng is {1/6,1/2,1,2}   is provided by higher layers. The index n(group, PHICH) ranges from 0  to N(group, PHICH) - 1 For Normal Cyclic Prefix

Ng, NRB	1/6	1/2	1	2
6	1	1	1	2
15	1	1	2	4
25	1	2	4	7
50	2	4	7	13
75	2	5	10	19
100	3	7	13	25

The HARQ Indicator undergoes repetition coding to create a HARQ indicator codeword made up of three bits, 

HARQ Indicator	HARQ Indicator Codeword
0 – Negative acknowledgement	<0,0,0,>
1 – Positive acknowledgement	<1,1,1>

The HARQ Indicator codeword undergoes BPSK modulation. The block of modulated symbols is bit-wise multiplied with an orthogonal sequence and a cell-specific scrambling sequence.  The three modulated symbols  are repeated   times and scrambled to create a sequence of six or twelve symbols depending on whether a normal or extended cyclic prefix is used. As resource element groups (REGs) contain four resource elements (each able to contain one symbol) the blocks of scrambled symbols are aligned to create blocks of four symbol.