# A Low-Complexity Pilot-Based Frequency-Domain Channel Estimation for ICI Mitigation in OFDM Systems
## 2 System Model
### Link Simulator  
Figure 1 illustrates the functional blocks related to the link simulator that is used to assess the performance of the proposed ICI mitigation mechanism. On the transmitter side, the source block generates bits grouped in transport blocks (TBs) that are transmitted in different sub-frames. The overhead of reference signals (pilots) is taken into account to generate each TB, since the number of data bits depends on the number of pilots symbols and pilots tones per sub-frame. The bits are mapped into IQ symbols that belong to a M-QAM modulation in the modulator block. This block groups the bits in vectors of \(\log_{2}(M)\) bits that are mapped into a complex constellation symbol, \(s\in\mathbb{C}\), with unit power \(\mathbb{E}[|s|^{2}]=1\). Gray mapping is considered to map the bits into complex symbols. Then, the sub-carrier mapper block inserts reference signals for channel estimation on different OFDM symbols and sub-carriers depending on the chosen pilot pattern. The resource grid of LTE-A and 5G NR has been considered, and thus, each sub-frame corresponds to 1 ms that spans over 14 OFDM symbols. On the frequency domain, resources are divided in physical resource blocks (PRBs) that consist of 12 sub-carriers, each of them named as resource elements (REs) in the context of LTE-A and 5G NR. Different pilot patterns can be analyzed in this paper, including: (i) Cell Specific Reference Signal (CRS) pattern of LTE-A ([28] figure 6.10.1.2-1); (ii) comb-type pattern [29], where a set of sub-carriers has reference signals on each OFDM symbol; and (iii) our proposed pilot pattern defined in Section 3. For comb-type pattern, the parameter \(F_{\text{spac}}\) defines the pilot density on the frequency domain, since 1 sub-carrier out of \(F_{\text{spac}}\) sub  
Figure 1: Functional blocks of the simulator. Blocks related to the transmitter are drawn in blue whereas blocks related to the receiver are drawn in green. Blocks related to Bit Error Rate (BER) metric computation and wireless channel are in orange. carriers will be reserved for reference signals with this scheme. Nevertheless, since every symbol has pilots, the degradation due to outdated channel estimation is minimal. Once the resource grid related to a given sub-frame is completed, IQ constellation symbols are used by the OFDM modulator block, which generates the 14 OFDM symbols of each sub-frame, adding the CP to each of them. As seen with (1) for each of the 14 OFDM symbols, the OFDM modulator receives a block of \(N\) complex symbols. Figure 2 illustrates a block diagram of the OFDM modulator. There are \(N_{A}\) active sub-carriers and \(N_{v}=N-N_{A}\) guard band sub-carriers. Hence, the complex symbols, \(X_{k}^{(m)},\ k\in[0,N-1]\), can be either allocated to active sub-carriers (containing pilots tones and/or data) or they can be guard bands with zero power (null symbols) to avoid out of band emissions. The symbol \(\underline{X}_{k},\ k\in[0,N_{A}]\) refers to the complex symbols related to active sub-carrier. To perform the OFDM modulation, the block of complex symbols \(X_{k}^{(m)},\ k\in[0,N-1]\) is delivered to an inverse FFT (IFFT) block. Then, in order to add the CP, the \(G\) time-samples that fall within the interval \(n\in[N-G,N-1]\) are copied at the beginning of the OFDM symbol, i.e., on time instants \(n\in[-G,-1]\). The generated time domain waveform undergoes time and frequency selective fast fading by the wireless channel block, which can simulate an arbitrary power-delay profile. On the receiver side, the signal feeds the synchronization block, which implements time and frequency synchronization by using the redundancy added with the CP [30]. This frequency synchronization allows to mitigate carrier frequency offsets related to a line-of-sight (LOS) component of the channel, if present. The synchronized signal passes through the OFDM de-modulator block, which subtracts the CP and performs FFT to get IQ complex symbols on frequency domain.