Multi-Carrier and Spread Spectrum Systems: From OFDM and MC ...

Multi-Carrier Modulation and Demodulation 137(−1) lDelayIoscillatorf c −1/(2T samp ) Sampling frequency2/T samp(−1) l1/T sampLow pass filterA/DDe-MuxLocal1/T sampr(2l+1) r(2l)FIR FilterQN c -pointFFT(complexdomain)Figure 4-7Digital I/Q generation using FIR filtering with a single analogue demodulatorwhere T samp is the sampling period of each I and Q component. By doubling the samplingrate to 2/T samp we get the sampled signalr(l) = I(l)cos(πl/2) + Q(l) sin(τl/2). (4.13)This stream can be separated into two sub-streams with rate 1/T samp by taking the evenand odd samples:r(2l) = I(2l)cos(πl) + Q(2l)sin(πl)r(2l + 1) = I(2l + 1) cos(π(2l + 1)/2) + Q(2l + 1) sin(π(2l + 1)/2). (4.14)It is straightforward to show that the desired output I and Q components are related tor(2l) and r(2l + 1) byI(l) = (−1) l r(2l) (4.15)and the Q(l) outputs are obtained by delaying (−1) l r(2l + 1) by T samp /2, i.e. passing the(−1) l r(2l + 1) samples through an interpolator filter (FIR). The I(l) components have tobe delayed as well to compensate the FIR filtering delay.In other words, at the transmission side this method consists (at the output of thecomplex digital IFFT processing) of filtering the Q channel with an FIR interpolatorfilter to implement a 1/2 sample time shift. Both I and Q streams are then oversampledby a factor of 2. By taking the even and odd components of each stream, only onedigital stream at twice the sampling frequency is formed. This digital signal is convertedto analogue and used to modulate the RF carrier. At the reception side, the inverseoperation is applied. The incoming analogue signal is down-converted and centered ona frequency f samp /2, filtered, and converted to digital by sampling at twice the samplingfrequency (i.e. 2f samp ). It is de-multiplexed into the two streams r(2l) and r(2l + 1) at ratef samp = 1/T samp . The I and Q channels are multiplied by (−1) l to ensure transposition ofthe spectrum of the signal into baseband [1]. The Q channel is filtered using the same FIRinterpolator filter as the transmitter while the I components are delayed by a correspondingamount so that the I and Q components can be delivered simultaneously to the digitalFFT processing unit.