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Mobile Computing 1 07/03/16 BMGC Section 4 Orthogonal Frequency Division Multiplexing (OFDM) Relatively new modulation scheme. Used for DAB, ADSL & more recently wireless computer networks (IEEE 802.11a and Hiperlan2). It is said to be a "multi-carrier" modulation scheme OFDM has very many, say 64 or even 1024, carrier frequencies evenly spaced out over a range of frequencies. A vector-modulator can take i(t) + jq(t) as a complx b-b signal. Multiplying cos(2fCt) by i(t) & sin(2fCt) by q(t) & summing is: Real { (i(t) +jq(t)) exp(2jfCt) } Instead of one carrier, IEEE802.11a takes 64 carrier frequencies over the range fC to fC + 20 MHz: fC + 0, fC + fD, fC + 2fD, … , fC +63fD with fD = 20MHz / 64 =312.5 kHz. We do the OFDM modulation in two stages: (1) Apply PSK, QPSK, QAM (or other) to 64 'sub-carriers' of frequencies: 0 , fD, 2fD , …, 63fD (2) Vector-modulate fC with sum of modulated sub-carriers. Mobile Computing 2 07/03/16 BMGC There are 64 modulating signals: X0(t) = I0(t) + jQ0(t) : modulating 0 Hz X1(t) = I1(t) + jQ1(t) : modulating fD X2(t) = I2(t) + jQ2(t) : modulating fD …. X63(t) = I63(t) + jQ63(t). : modulating 63fD With QPSK, each Xi represents 2 bits. (IEE802.11a makes X0-X5 & X58-X63 all zero and uses 4 others for "pilot tones", leaving 48 to use.). Adding these together we obtain: 63 x(t) = Xk(t) exp (2jkfD t ) : -<t<. k=0 Sampling at 20MHz, (i.e. T = 0.05 us) this becomes: 63 x(nT) = x[n] = Xk(nT) exp (2jk fD nT ) k=0 Make Xk[nT] =Xk : constant for 0<n<79, i.e. 4 us. 63 x[n] = Xk exp(jk(2/N)n) : k=0 0<n<79 Mobile Computing 3 07/03/16 BMGC Generates a set {x[0], x[1], …, x[79]} of complx numbers. Time-domain OFDM "symbol" lasting 4us. Shape of pulse tell us the information. With QPSK on 48 carriers, 248 x 2 = 4 x 10 14 different shapes. 250,000 symbols /s can be strung together. Real part multiplies cos(2fCt) & imag pulse sin(2fCt). Complex multiplication gives one sideband. Expression for {x[n]} is "inverse DFT" of {X0, X1, …., X63} . Normally generates complex sequence {x[0], x[1], …., x[63]} With 63 samples, {x[0], x[1], …., x[63]}, no information lost. {x[n]}0,63 contains all the information in {Xk}0,63 . DFT of {x[n]}0,63 gets back exactly to {X0, X1, …., X63}. OFDM demodulator is DFT followed by detectors But we calculate {x[0], x[1], …, x[63], x[64], …, x[79]} Inverse DFT repeats cyclically for n > 63. So x[64] = x[0], x[65]=x[1], …, x[79]=x[15]. x[64] to x[79] is the "cyclic extension". "Guard interval" between one symbol & the next; Useful for carrier and symbol synchronisation at receiver. Due to cyclic extension & cyclic nature of DFT and its inverse, even if exact synchronisation is not achieved at the receiver, exact data can still be recovered with a phase shift. With 64 = 26 sub-carrier frequencies, inverse DFT can be carried out very efficiently by an "fast Fourier transform" (FFT). OFDM works because of orthogonality of the 64 carriers. Mobile Computing 4 07/03/16 BMGC Very good for channels affected by frequency selective fading for several reasons. First, information can be spread out across the sub-carriers in very intelligent ways so that when some are lost due to fading, others will compensate. This can even be done adaptively. Second the guard-band allows for ISI, so that if one 4us OFDM symbol rings on for a while, it only affects the beginning of the next symbol, and this information is repeated at the end. (Can have cyclic "prefix" instead). So no pulse-shaping necessary! Third (most importantly) equalisation much easier than with single carrier systems. Adaptive filtering is complicated OFDM equalisation done frequency-domain after FFT. Multiplies the FFT spectrum by a weighting function. Multiplication much easier than adaptive filtering. Works because of cyclic extension. -----------------------------------------------------------------------------------