In this section, the procedure to generate the PHY signal for the downlink is described and illustrated in Figure 13. It consists of Error correction coding, scrambling, Modulation mapping, layer mapping, pre coding and OFDM signal Generation.

i) Error correction encoding: In LTE Cyclic Redundancy Check (CRC), Convolution coding and Turbo coding is done for different information. They are briefly described as follows,

a) Cyclic Redundancy Check:The encoding of the information is performed using CRC. For each transport block, a CRC of length 24 bits (or, 16 or 8 bits under some circumstances) is computed. It is calculated for each block of data for one transmission time interval from the following code polynomials,

$G(D) = D^8 + D^7 + D^4 + D^3 + D + 1 \quad \quad \text {For 8 bit CRC}$

$G(D) = D^{16} + D^{12} + D^5 + 1 \quad \quad \text {For 16 bit CRC}$

$G(D) = D^{24} + D^{23} + D^6 + D^5 +D + 1 \quad \quad \text {For 24 bit CRC}$

$G(D) =D^{24} + D^{23} + D^{18}+ D^{17} + D^{14}+ D^{11}+ D^{10}+ D^7 + D^6 + D^5 + D^4 + D^3 + D + 1 \quad \quad \text {For 24 bit CRC (alternative)}$

and this CRC is attached at the end of the block.

b) Convolutional Codes: Convolutional codes are used in LTE only for the encoding of control information such as Broadcast Channel (BCH), DCI, UL control information not for the actual payload data. In particular, the standard defines a length-7 tail-biting convolutional code with the following code polynomials.

$G1(D) = 1 + D^2 + D^3 + D^5 + D^6$

$G2(D) = 1 + D + D^2+ D^3 + D^6$

$G3(D) = 1 + D + D^2 + D^4 + D^6$

c) Turbo Codes: In LTE, Turbo codes are applied to the Uplink Shared CHannel (UL-SCH) and Downlink Shared CHannel (DL-SCH), Paging CHannel (PCH), and Multicast CHannel (MCH). In contrast to WCDMA, there is no option to encode payload data with convolutional codes; only turbo codes are allowed. This is mainly due to the fact that turbo codes are now so well established, and receivers are sufficiently optimized that there is no need for the slightly simpler (but worse-performing) convolutional codes anymore. The turbo encoder is the same as in WCDMA, with the exception of the interleaver.

ii) Scrambling of coded bits: The bits of all transport channels are scrambled by multiplication with a Pseudo Noise (PN) (Gold) sequence. It is important to note that unlike in WCDMA in LTE bits are scrambled and not the complex-valued symbols.

iii) Modulation of scrambled bits to generate complex-valued modulation symbols: The modulation formats used for data transmission are Quadrature Phase Shift Keying (QPSK), 16- Quadrature Amplitude Modulation (QAM), and 64-QAM, with Gray mapping (i.e., signal points located next to each other are distinguished only by 1 bit) as illustrated in Figure 14. The choice of the modulation format depends on the quality of the propagation channel. In order to achieve higher signal-to-interference and Signal-to-Noise Ratio (SNR), higher order modulation can be employed.

iv) Mapping of the modulation symbols onto the transmission layers: In LTE symbols are mapped in to multiple spatial streams with multiple antennas to achieve diversity gain.

v) Precoding of the symbols on each layer for transmission on the antenna ports: This step is also related to multiple-antenna transmission technique.

vi) Mapping of symbols to Resource Elements (REs): In this step assignment of symbols is performed to time frequency. More specifically, which symbols are to be transmitted in which time/frequency resource (i.e., time and subcarrier) is determined and allocated. In the case of multiple transmit antennas; this mapping is done at each antenna port separately.

vii) Generating the time domain OFDM signal: Finally time domain OFDM signal is generated.