EE359 – Lecture 18 Outline Announcements Review of Last Lecture Last HW posted today, due Friday 12/9 at noon. Final Exam is Wed., 12/14, 9:30-11:30, in MCCULL115, Final Review most likely 12/12, time/room TBD. More details Monday. OHs today are 4-5, extra Ohs next week. Review of Last Lecture FFT Implementation of OFDM (DMT) Challenges in OFDM Overview of Spread Spectrum Direct Sequence Spread Spectrum ISI and Interference Rejection PN Sequences and Maximal Linear Codes

Review of Last Lecture S ISI Countermeasures: Equalizers, MCM, SS Multicarrier Mod.: B/N=BN=(1+b)/TN <<Bc Can overlap subcarriers (separation of 1/TN) Correction: This is twice as efficient for b=1 (not b=0) For fading across subcarriers, equalization doesn’t help, can precode or do adaptive loading Adaptive loading same as in flat-fading and MIMO R/N bps QAM Modulator x cos(2pf0t) cos(2pfNt) S R bps Serial To Parallel Converter R/N bps QAM Modulator f0 fN-1 2BN

FFT Implementation (DMT) Efficient IFFT structure at transmitter Reverse structure (with FFT) at receiver IFFT performs frequency modulation Cyclic prefix turns makes linear convolution circular: removes ISI between blocks Received symbols scaled versions of transmitted symbols X0 x0 Serial To Parallel Converter R bps Add cyclic prefix and Parallel To Serial Convert QAM Modulator x cos(2pfct) D/A IFFT XN-1 xN-1

OFDM Challenges Peak-to-average power ration Intercarrier Interference Adding multiple substreams can result in high peak signal values Impacts amplifier efficiency Solutions include clipping and coding Intercarrier Interference Frequency and timing offset causes interference between carriers Mitigated by minimizing the number of subcarriers and non-rectangular pulse shaping

Pseudorandom Sequences Autocorrelation determines ISI rejection Ideally equals delta function Maximal Linear Codes No DC component Large period (2n-1)Tc Linear autocorrelation Recorrelates every period Short code for acquisition, longer for transmission In SS receiver, autocorrelation taken over Tb Poor cross correlation (bad for MAC) 1 -1 2n-1 Tc -Tc

Direct Sequence Spread Spectrum Bit sequence modulated by chip sequence Spreads bandwidth by large factor (K) Despread by multiplying by sc(t) again (sc(t)=1) Mitigates ISI and narrowband interference S(f) s(t) sc(t) Sc(f) S(f)*Sc(f) 1/Tb 1/Tc Tc Tb=KTc 2

ISI and Interference Rejection Narrowband Interference Rejection Multipath Rejection (Two Path Model) S(f) I(f) S(f)*Sc(f) Info. Signal Receiver Input Despread Signal I(f)*Sc(f) aS(f) S(f) S(f)*Sc(f)[ad(t)+b(t-t)] bS’(f) Info. Signal Receiver Input Despread Signal

Main Points OFDM efficiently implemented using FFTs OFDM challenges are PAR and timing/frequency offset. Spread spectrum spreads signal over wide bandwidth for ISI/interference rejection DSSS rejects interference by spreading gain DSSS rejects ISI by code autocorrelation Maximal linear codes have good autocorrelation properties but poor cross correlation