A receiver produces complex data samples from a demodulated received signal. The data samples, which may form a preamble identifying a wireless LAN data burst, are arranged in a sequence comprising sub-sequences having a predetermined relationship with each other. A tuning frequency offset is determined by delaying the complex data samples by a plurality of different delay periods, auto-correlating the complex data samples using said different delay periods in order to produce respective auto-correlation outputs, determining a plurality of phase-dependent values each dependent upon phase errors in a respective auto-correlation output and calculating a value representing frequency offset by combining the phase-dependent values in a weighted manner. The preamble can be recognised by using the same delay means. One matched filter is used to detect a particular sub-sequence, the output is fed to the delay means, and a second matched filter receives the outputs of the delay means to detect sub-sequences having the correct timing relationship.
