## 2 Transmission Model and Simulation Conditions
### Transmission Model  
Figure 2 shows a transmission model of an OFDM-based higher-order modulation schemes in downlink with a single antenna branch. The transmitter includes an encoder, a QAM mapper, a pilot insertion, an inverse fast Fourier transform (IFFT), and a cyclic prefix (CP) insertion. Input baseband signals are encoded via turbo coding which is typically used in 4G systems. The encoded signals are converted to QAM mapper to produce a 1024- or 4096-QAM signal. Then, the IFFT forms OFDM signals. Finally, a CP in the form of a copy of the tail of a symbol placed at its beginning is inserted to reduce inter symbol interference. Pilot insertion is used to estimate the channel response at the receiver side under multipath fading conditions. At the receiver side, first the CP is removed and the FFT then separates the individual subcarrier components and converts them to QAM format. Each component signal is then demodulated by the QAM de-mapper. Finally, the soft-decision Viterbi decoding is used to output the original baseband signals. Channel estimation and channel equalization are used to compensate received signals distorted by multipath fading.  
Figure 1: Application example of higher-order modulation schemes such as 1024- and 4096-quadrature amplitude modulation (QAM) in backhaul links for pico-evolved node B (eNB) and a relay node. UE = user equipment.  
Figure 3 shows a block diagram of the turbo encoder (coding rate = 1/3), which uses two identical convolutional encoders (1 st and 2 nd encoders) with a constraint length of four and one internal interleaver. Figure 4 shows a block diagram of the soft-decision Viterbi decoder, which comprises two single soft-in soft-out (SISO) decoders that work iteratively, with the output of the first decoder (SISO decoder 1) feeding into the second decoder (SISO decoder 2) to form a turbo decoding iteration. During this process, interleaver and de-interleaver blocks re-order the data [28; 29].  
The computer simulation parameters are listed in Table 1. The IFFT/FFT size is 2048 which corresponds to a transmission bandwidth of 20 MHz, and the subcarrier spacing of OFDM is 15 kHz. The coding rates of the turbo encoder are assumed to be 1/3, 1/2, 2/3, 3/4, and 1, and the constraint length is fixed at four. QAM signals are mapped by the rule of Gray-code. The CP is produced using 1024  
Figure 4: Block diagram of soft-decision Viterbi decoder. SISO = soft-in soft-out.  
Figure 3: Block diagram of turbo encoder. \(\mathrm{x_{k}}\) is the first systematic bit (original input bit). \(\mathrm{z_{k}}\) and \(\mathrm{z_{k}}^{\prime}\) are the outputs of 1 st and 2 nd encoders, respectively.  
Figure 2: Transmission model of orthogonal frequency division multiplexing (OFDM)-based 1024- and 4096-QAM. IFFT = inverse fast Fourier transform; FFT = fast Fourier transform; AWGN = additive white Gaussian noise.  
samples for seven OFDM symbols, the first of which uses 160 samples as the CP, with the remaining six using 144 samples. This is referred to as normal CP in LTE mobile systems.  
The multipath fading channels specify the following two profiles, extended pedestrian A (EPA) and extended vehicular A (EVA), whose delay profiles represent low and medium delay spreads, respectively, as listed in Table 2[30]. Doppler frequency shift is an apparent change in the carrier frequency due to the relative motion of two objects (here, the eNB and UE). The maximum Doppler frequency shift is fixed at 5 Hz, assuming a UE velocity of 3 km/h for the carrier frequency band of 2 GHz.