# Of michigan ik jqk expj 2 kf0 t k 0 fall 2011 october

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Unformatted text preview: jQk ) exp(j 2π kf0 t ) k =0 Fall 2011 October 22, 2012 18 / 31 Lecture Notes 13 OFDM Signals Consider now generating samples of this signal. Assume we generate N samples during the time interval [0, T ]. Suppose also that f0 T = 1. Then N −1 s[n] = s((n/N )T )) = ℜ (Ik + jQk ) exp(j 2π kf0 (n/N )T ) k =0 N −1 =ℜ (Ik + jQk ) exp(j 2π kn/N ) k =0 = N (IFFT [Ik + jQk ]) . EECS 455 (Univ. of Michigan) Fall 2011 October 22, 2012 19 / 31 Lecture Notes 13 OFDM Parameters N carriers Total data rate is Rb . Data rate on each carrier is Rb /N . Duration of each data bit is N /Rb . Carrier Separation is Rb /N Hz. Cyclic Preﬁx of Length P added EECS 455 (Univ. of Michigan) Fall 2011 October 22, 2012 20 / 31 Lecture Notes 13 OFDM Transmitter Implementation Data Source Serial to Parallel IFFT Parallel EECS 455 (Univ. of Michigan) to Serial Fall 2011 Cyclic Preﬁx October 22, 2012 21 / 31 Lecture Notes 13 OFDM Receiver Remove Cyclic Preﬁx EECS 455 (Univ. of Michigan) Serial to Parallel FFT Parallel to Sink Serial Fall 2011 Data October 22, 2012 22 / 31 Lecture Notes 13 OFDM Spectrum OFDM Power Spectrum 1 0.8 0.6 0.4 0.2 0 EECS 455 (Univ. of Michigan) −1 −0.5 0 frequency (Hz) Fall 2011 0.5 1 6 x 10 October 22, 2012 23 / 31 O F O f Lecture Notes 13 OFDM Spectrum 5 0 −5 −10 −15 −20 −25 −30 −35 −40 −1.5 −1 −0.5 0 0.5 1 1.5 6 x 10 Lecture Notes 13 OFDM Spectrum OFDM/Single Carrier Power Spectrum (dB) 20 10 0 OFDM Spectrum −10 Single Carrier Spectrum −20 −30 −40 −50 −60 −3 EECS 455 (Univ. of Michigan) −2 −1 0 frequency (Hz) Fall 2011 1 2 3 6 x 10 October 22, 2012 25 / 31 Lecture Notes 13 OFDM Signal and Spectrum (M =1) M=1 M=1 30 OFDM Power Spectrum (dB) 40 1.5 OFDM Signal and Envelope 2 1 0.5 0 −0.5 −1 −1.5 −2 0.8 20 10 0 −10 −20 −30 −40 1 time (s) EECS 455 (Univ. of Michigan) 1.2 Fall 2011 −50 50 100 frequency (Hz) October 22, 2012 150 26 / 31 Lecture Notes 13 OFDM Signal and Spectrum (M =4) M=4 M=4 6 40 30 OFDM Power Spectrum (dB) OFDM Signal and Envelope 4 rms value 2 0 −2 20 10 0 −10 −20 −30 −4 −40 −6 0 1 2 3 −50 50 time (s) EECS 455 (Univ. of Michigan...
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