LTE cell search

Up to three base stations transmit on the same frequency, as neighbouring LTE cells do. Each has a physical cell ID from 0 to 503, split into a group N_ID⁽¹⁾ (0 to 167) and an identity within the group N_ID⁽²⁾ (0 to 2): ID = 3 × N_ID⁽¹⁾ + N_ID⁽²⁾. Unless you give them the same frame timing, they are not synchronized: each cell's 10 ms frames start at a different moment and carry a different frame number. The phone captures 50 ms of their sum and has to untangle it. This table is the truth the receiver does not see.

Received RSRP is the true reference-signal power after this capture's fading, relative to a cell at 0 dB with no fading. The CRS shift, ID mod 6, sets which subcarriers carry the reference signals.

LTE sends data on subcarriers 15 kHz apart, in OFDM symbols of about 71 µs. A 10 ms frame has 10 subframes of 14 symbols. Each small square is one resource element: one subcarrier for one symbol. The signals a phone needs for cell search sit in the middle 72 subcarriers, whatever the channel bandwidth. The PSS and SSS appear twice per frame, in subframes 0 and 5. The broadcast channel (PBCH) fills the first four symbols of the second half of subframe 0. Reference signals are spread across the whole band.

The phone samples the central 1.08 MHz at 1.92 million samples per second, so each OFDM symbol is 128 samples plus a cyclic prefix of 9 or 10. Here is the magnitude of the first 10 ms of the capture: the cells, multipath, a frequency offset and noise all added together. Nothing in this trace says where a frame starts.

The primary synchronization signal (PSS) is one of only three known sequences, one per N_ID⁽²⁾. The receiver slides each of them along the capture and measures how well they match. A peak says a cell is there, which of the three sequences it uses, and where its symbol boundary is. The PSS repeats every 5 ms, so the receiver adds four half-frames together. A frequency offset smears the peaks, so the search runs at five trial frequencies 7.5 kHz apart and keeps the best.

The phone's oscillator is a few parts per million off, several kilohertz at LTE frequencies, a large fraction of the 15 kHz subcarrier spacing. The receiver estimates it in three steps. The cyclic prefix is a copy of the symbol's end, so the phase turn between the two copies gives the offset modulo 15 kHz. Then the PSS, checked at whole-subcarrier shifts, resolves which multiple of 15 kHz. Once the cell is known, its reference signals give a fine correction. The whole capture is then counter-rotated.

One OFDM symbol before each PSS sits the secondary synchronization signal (SSS), built from two interleaved length-31 sequences whose shifts encode N_ID⁽¹⁾. The two halves swap between subframe 0 and subframe 5, so the SSS also tells the receiver which half of the frame it is looking at, and so where the 10 ms frame starts. The PSS just found serves as a channel reference, so the detection is coherent. All 168 groups × 2 half-frames are tested.

With the cell ID known, the receiver can generate that cell's reference signals and compare them with what arrived. The ratio at each reference-signal subcarrier is the channel there. Reference signals from two slots are averaged, and the channel is interpolated across the 72 subcarriers. Each antenna has its own reference signals on different subcarriers, so the two channels can be measured separately. Pairs of reference-signal measurements half a millisecond apart, taken over the whole capture, give the reference signal received power (RSRP) and the noise-plus-interference level.

The broadcast channel carries the Master Information Block: 24 bits giving the bandwidth, the PHICH configuration and the top 8 bits of the 10-bit frame number. It is coded to 1920 bits and spread over four frames (40 ms). Each frame's 480 bits can be decoded alone, so the receiver does not know which quarter it is holding. It descrambles, equalizes, reverses the rate matching and runs a Viterbi decoder, trying each 40 ms phase. The CRC is masked by the number of transmit antennas, so the mask that makes it pass reveals the antenna count. The phase that decodes gives the last 2 bits of the frame number. If one frame is not enough, it combines several.

Every candidate from the PSS search goes through the whole chain. A cell counts as found when its MIB passes the CRC. Found cells are ranked by RSRP, and a phone would normally camp on the strongest. Weak neighbours drown in the stronger cells' signals: their signal-to-interference ratio is negative even when the noise is low. Click a row to follow that cell in stages 5 to 8.