The Physical Hybrid-ARQ Indicator Channel (PHICH) in the downlink carries Hybrid ARQ (HARQ) acknowledgements (ACK/NACK) for uplink data transfers. PHICHs are located in the first OFDM symbol of each subframe. (Note that our discussion focuses on the FDD frame structure and the normal PHICH duration). A PHICH is carried by several Resource Element Groups (REGs). Multiple PHICHs can share the same set of REGs and are differentiated by orthogonal covers; PHICHs which share the same resources are called a PHICH group. Consequently, a specific PHICH is identified by two parameters: the PHICH group number, and the orthogonal sequence index within the group.

How many REGs does a PHICH need? The channel coding for HARQ ACK/NACKs is straight forward: an ACK is 111, and a NACK is 000 (3 bits each). PHICHs use BPSK modulation, so 3 modulation symbols are generated for each ACK or NACK. Next, these 3 modulation symbols are multiplied by the orthogonal cover, which has the spreading factor (SF) of 4 for the normal cyclic prefix, resulting in a total of 12 symbols. Each REG contains 4 resource elements (REs) and each RE can carry one modulation symbol, so 3 REGs are needed for a single PHICH.

Let's look at the illustration below for an
example of how PHICHs are mapped to resources; three PHICH groups are shown
here. The three REGs that support a PHICH group are evenly distributed within
the system bandwidth to provide frequency diversity. (Note that the Physical
Control Format Indicator Channel (PCFICH) also appears in the first symbol of
each subframe, and always occupies 4 REGs regardless of system bandwidth. These
4 REGs are evenly distributed across the system bandwidth).

How many PHICHs can a PHICH group include? A total of 8 orthogonal sequences have been defined (3GPP TS 36.211 Table 6.9.1-2), so each PHICH group can carry up to 8 PHICHs.

How many PHICH groups are supported in a system? That depends on the specific configuration. The actual number of PHICH groups can be derived from the downlink bandwidth and the parameter (Ng), both of which are broadcast in the Master Information Block (MIB). The formula is defined in 3GPP TS 36.211 section 6.9 as shown below. Assume that the downlink channel bandwidth is 10 MHz and that Ng = 1; in this case, there will be a total of 7 PHICH groups available. The total number of PHICHs supported per subframe would then be 7 PHICH groups x 8 PHICHs per PHICH group = 56 PHICHs. The total number of resource elements (REs) needed is 7 PHICH groups x 3 REGs per PHICH group x 4 REs per REG = 84 REs.

We know that each PHICH carries HARQ ACK/NACKs for uplink data transfers. How does a UE know where to look for its PHICH? In the time domain, if the uplink transmission occurs in subframe n, the corresponding PHICH will be in subframe n+4. In the frequency domain, it is indicated by the uplink resource allocation with DCI format 0, where the specific PHICH (PHICH group number, orthogonal sequence index within the group) is derived from the lowest uplink PRB index in the first slot of the corresponding PUSCH transmission and the DMRS cyclic shift. For details on this calculation, please refer to 3GPP TS 36.213 section 9.1.2.

Why is it necessary to have Ng in the MIB? Why not include it in the System Information Block (SIB)? The reason that the UE needs to know the PHICH configuration at the very beginning of the system acquisition process is because of the "chicken-and-egg" problem. On one hand, the UE needs to decode PDCCH to know where to find SIB on PDSCH. On the other hand, PDCCH and PHICH and PCFICH share the resources in the control region of a subframe and the set of the available resources for PDCCH depends on the PHICH configuration (PCFICH resources are fixed and known).