Orthogonal frequency-division multiplexing (OFDM), also known as multicarrier modulation [Cim85, Bin90, LAB95, SKJ95, ZW95, KH00, WG00], relies on the concept of parallel data transmission in the frequency domain, and mainly owes its success to the easy equalization for linear time-invariant (LTI) frequency-selective channels. In OFDM systems, the data symbol stream is split into L parallel flows, which are transmitted on equispaced frequencies called subcarriers, each one characterized by a transmission rate that is 1/L times lower than the original data rate. This is obtained by splitting the original data stream into multiple blocks, which are transmitted in consecutive time intervals, where each symbol of a block is associated to a specific subcarrier. This frequency-domain multiplexing can be efficiently performed by means of fast Fourier transform algorithms. Thanks to the use of orthogonal (equispaced) subcarriers, OFDM systems with LTI frequency-selective channels avoid the so-called intercarrier interference (ICI) among the data symbols of the same OFDM block. Differently from conventional frequencydivision multiplexing, a frequency overlapping among the spectra associated to different substreams is permitted, resulting in a significant reduction of the bandwidth requirements. Moreover, for LTI frequency-selective channels, the absence of ICI allows an easy channel equalization, which can be performed on a per-subcarrier basis by means of scalar divisions. The intersymbol interference (ISI)1 among data symbols of different OFDM blocks, induced by multipath propagation, is avoided by a suitable cyclic extension of each OFDM block, usually referred to as cyclic prefix (CP) [SKJ95, ZW95, WG00]. The ISI is also known as interblock interference, while the OFDM blocks are also known as OFDM symbols. However, when the channel experiences a non-negligible time variation, each subcarrier undergoes a Doppler spreading effect that destroys the subcarrier orthogonality, producing significant ICI [RS95, RK99, SF00]. Dually to the ISI in single-carrier systems, the ICI power reduces the signal-to-interference-plus-noise ratio (SINR) and, when left uncompensated, impairs the performance of OFDM systems. A simple method that reduces the ICI is the shortening of the OFDM block duration. This way the channel becomes (almost) constant over each block. However, the block-length shortening is capacity inefficient, because the CP has to be inserted more frequently. Therefore, other ICI mitigation techniques are necessary. These techniques are reviewed in Section 7.2. In addition, the rapid time variation of the channel makes its estimation more complicated. This issue is discussed in Section 7.3. In this section, we first set up the system model and review the behavior of OFDM systems with LTI channels, focusing on the most popular OFDM wireless standards. Successively, we show the effects of rapidly time-varying channels on conventional OFDM systems by analyzing the ICI power, the SINR degradation, and the bit-error rate (BER) performance loss. Finally, we extend the system model to multiantenna OFDM systems.

### OFDM Communications over Time-Varying Channels

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*RUGINI, LUCA;BANELLI, Paolo;*

##### 2011

#### Abstract

Orthogonal frequency-division multiplexing (OFDM), also known as multicarrier modulation [Cim85, Bin90, LAB95, SKJ95, ZW95, KH00, WG00], relies on the concept of parallel data transmission in the frequency domain, and mainly owes its success to the easy equalization for linear time-invariant (LTI) frequency-selective channels. In OFDM systems, the data symbol stream is split into L parallel flows, which are transmitted on equispaced frequencies called subcarriers, each one characterized by a transmission rate that is 1/L times lower than the original data rate. This is obtained by splitting the original data stream into multiple blocks, which are transmitted in consecutive time intervals, where each symbol of a block is associated to a specific subcarrier. This frequency-domain multiplexing can be efficiently performed by means of fast Fourier transform algorithms. Thanks to the use of orthogonal (equispaced) subcarriers, OFDM systems with LTI frequency-selective channels avoid the so-called intercarrier interference (ICI) among the data symbols of the same OFDM block. Differently from conventional frequencydivision multiplexing, a frequency overlapping among the spectra associated to different substreams is permitted, resulting in a significant reduction of the bandwidth requirements. Moreover, for LTI frequency-selective channels, the absence of ICI allows an easy channel equalization, which can be performed on a per-subcarrier basis by means of scalar divisions. The intersymbol interference (ISI)1 among data symbols of different OFDM blocks, induced by multipath propagation, is avoided by a suitable cyclic extension of each OFDM block, usually referred to as cyclic prefix (CP) [SKJ95, ZW95, WG00]. The ISI is also known as interblock interference, while the OFDM blocks are also known as OFDM symbols. However, when the channel experiences a non-negligible time variation, each subcarrier undergoes a Doppler spreading effect that destroys the subcarrier orthogonality, producing significant ICI [RS95, RK99, SF00]. Dually to the ISI in single-carrier systems, the ICI power reduces the signal-to-interference-plus-noise ratio (SINR) and, when left uncompensated, impairs the performance of OFDM systems. A simple method that reduces the ICI is the shortening of the OFDM block duration. This way the channel becomes (almost) constant over each block. However, the block-length shortening is capacity inefficient, because the CP has to be inserted more frequently. Therefore, other ICI mitigation techniques are necessary. These techniques are reviewed in Section 7.2. In addition, the rapid time variation of the channel makes its estimation more complicated. This issue is discussed in Section 7.3. In this section, we first set up the system model and review the behavior of OFDM systems with LTI channels, focusing on the most popular OFDM wireless standards. Successively, we show the effects of rapidly time-varying channels on conventional OFDM systems by analyzing the ICI power, the SINR degradation, and the bit-error rate (BER) performance loss. Finally, we extend the system model to multiantenna OFDM systems.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.