to a waveform shaper 46 an output of the waveform shaper 46 is input to a digital to analog d a converter 48 an output of the d a converter 48 is input to a radio frequency r f amplifier 50 that is connected to an antenna 52 in a preferred embodiment the ofdm transmitter 30 complies with ieee section 802 11 a referring now to fig3 an ofdm receiver 60 receives the rf signals that are generated by the ofdm transmitter 30 the receiver 60 includes antennas 62 1 and 62 2 a switch 64 selects one of the antennas 62 based upon the strength of the rf signal detected by the antenna 62 an amplifier 66 is connected to an output of the switch 64 an analog to digital a d converter 68 is connected to an output of the amplifier 66 an automatic gain control agc antenna diversity and packet detection circuit 70 is connected to an output of the a d converter 68 when the gain of the agc decreases a packet is detected a symbol timing and carrier frequency offset circuit 74 according to the present invention is connected to an output of the circuit 70 the symbol timing and carrier frequency offset circuit 74 identifies a carrier frequency offset u03c9 u03b4 a starting time n g of a guard interval and phase noise as will be described more fully below the circuit 74 typically multiples the samples by e u2212 j u03c9 u03b4 n where n is a sample time index a cyclic prefix remover 76 is connected to.