operator [ ] denotes concatenation of sequences, and an and bn represent a complementary pair of length 2n. The number of different Golay sequences is large and increases rapidly with N, the sequence length. The number of different sequences of length 2N is N! 2N/2. Golay sequences have very good aperiodic autocorrelation properties. Golay sequences have the property that their spectral peaks are no more than 3 dB larger than the average of the spectrum [42]. 9.11 Pilot-based channel estimation Primary/Secondary Preambles MIMO Midambles Switching Gap UIDDLDLDLUL Structure of the MIMO Midamble in Time Sub-band 1 Sub-band 2 Sub-band n Antenna Antenna Antenna Port 1 Antenna Port 2 Port 3 Port 4 Sub-carrier Structure of the MIMO Midamble in Frequency FIGURE 9-39 Structure of MIMO midamble in time and frequency [2] is derived from the secondary preamble. The physical structure of MIMO midamble is shown in Figure 9-39 for four transmit antennas and IDcell = 0. 9.11 PILOT-BASED CHANNEL ESTIMATION While perfect knowledge of the radio channel can be used to find an upper bound for system perfor- mance, such knowledge is not available in practice, and the channel needs to be frequently estimated. Channel estimation can be performed in various ways using frequency and/or time correlation properties of the wireless channel, blind or pilot (reference signal) based, adaptive or non-adaptive, etc. Non- parametric methods attempt to estimate the frequency response without relying on a specific channel model. In contrast, the parametric estimation methods assume a certain channel model and determine the parameters of this model. Spaced-time and spaced-frequency correlation functions, discussed earlier, are specific properties of the channel that can be incorporated in the estimation method, improving the quality of estimations. Pilot-based estimation methods are the most commonly used methods in OFDM systems, and are applicable in systems where the sender transmits some known signal. Blind estimation, on the other hand, relies on