s, which are used for different purposes by a receiving device. While perfect knowledge of the radio channel can be used to find an upper bound for system performance, such knowledge is not available in practice and the channel needs to be frequently estimated. Channel estimation can be performed in various ways including the use of frequency and/or time correlation properties of the wireless channel, blind or pilot-based channel estimation, and adaptive or non-adaptive channel estimation. Non-parametric methods attempt to estimate the frequency response without relying on a 414 Chapter 4 specific channel model. In contrast, the parametric estimation methods assume a certain channel model and determine the parameters of this model. Spaced-time and space- d-frequency correlation functions, discussed in the previous chapter, are specific properties of channel that can be incorporated in the estimation method, improving the quality of estima- tions. Pilot-based estimation methods are the most commonly used in OFDM systems which are applicable in systems where the sender transmits some known signals to the receiver. A pilot-based channel estimation is defined as the use of the channel samples estimated at the pilot tones to reconstruct channel samples at the remaining data/control-bearing subcar- riers. As a result, the pilot pattern design is essentially a conventional sampling rate selec- tion problem in the two-dimensional signal processing space. To avoid aliasing during reconstruction of the channel time-frequency function, the pilot tone selection should follow the two-dimensional sampling theorem. When multiple antennas are used, the receiver must estimate the channel impulse response (or the transfer function) from each of the transmit antennas to correctly detect the signal. This is achieved through distributing reference sig- nals (or pilot tones) among the transmit antennas. Let Af = 1/Tu and Tsymbol = Tg denote the subcarrier spacing (SCS) and the OFDM symbol duration (inclusive of the guard interval), re