Most current and upcoming communication systems like 802.11x, WiMAX etc. deploy some variant of Orthogonal Frequency Division Multiplexing as their physical layer technology. Symbol timing acquisition is the first operation performed at the receiver after which other signal processing, such as orthogonalizing the received data into parallel streams using Fast Fourier Transform (FFT), can take place. To ensure reliable communication, extensive work has been done in designing robust algorithms that estimate the symbol timing with high accuracy. Most of these works assume that there is some total bandwidth which is utilized by a single user. However in future cognitive radio systems, the spectrum access will be dynamic and multiple devices in a geographical region will sense a common pool of spectrum for the presence of vacant frequency bands to transmit in. In the OFDM context, this means that a device may transmit in non contiguous tones (termed as Non-Contiguous OFDM or NC-OFDM). It is not clear how the existing symbol timing acquisition algorithms will perform in this situation. The current research around cognitive radios is mostly focused on the sensing and resource allocation aspects but to our knowledge the symbol timing acquisition issues have not yet been studied. In this work we study the performance of cyclic prefix correlation based symbol timing acquisition algorithms for NC-OFDM transmission. We first derive the ML estimator when the channel is frequency non-selective and show that it has high computational complexity. Consequently we study the performance of low complexity, sub-optimal approaches both for frequency non-selective and frequency selective channels. Our simulations indicate that in some likely situations such as the users occupying multiple discontiguous sub-bands and having large differences in the timing offsets between their transmitters and receivers, cyclic prefix based timing acquisition algorithms can perform quite poorly. This points to the need for better algorithms of reasonable complexity, or entirely different approaches to symbol timing acquisition, for example based on the periodic transmission of known sequences.
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