ECE637 : Fundamentals of Wireless Communications

ECE637 : Fundamentals of Wireless Communications Lecture 13,14,15,16: Multi-carrier Modulation OFDM Aliazam Abbasfar

Outline • Multi-carrier Modulation • Digital Multi-tone (DMT)/OFDM

Multi-carrier Modulation • Used in wideband systems • Frequency selective fading • B >> Wc • Divide data stream into N sub stream, each transmitted over a sub-channel with BN=B/N bandwidth • If N is big enough • Narrowband/flat fading modulation • BN < Wc • TN (sub-channels) >> Tm (delay spread) • FDM system • Multiple carrier frequencies • Guard bands • Spectrally inefficient • Roll-off factor • Time-limited pulses • N independent TX/RX • Sharp filter in RX

Orthogonal sub-channels • Sinusoids with different frequencies (in a period of T) • Df = n/T • N complex sinusoids • Multiple Sinc functions in spectrum • Overlapping spectrums • Sub-channels are not band-limited • Bigger guard band • Time and frequency offset problems • Early HF modems (1970) • OFDM/DMT foundation

Band-limited sub-channels • Orthonormal sets • ISI free – Nyquist functions • Root raised cosine functions • If g(t) is a Nyquist function, • {g(t-kT)}k is an orthonormal set • {g(t-kT) cos(wct)}k • {g(t-kT) cos(wit+fi)}k,i • ISI and ICI free • QAM modulation possible • Staggered I and Q • Sensitive to delay and phase • Spectrally efficient

Digital Multi-Tone (DMT)Orthogonal Frequency Division Multiplexing (OFDM) • Send N symbols {dn} over N orthogonal sinusoids in a period of TN • OFDM symbol • {dn} can be complex symbols • x(t) is baseband signal • {x(k/N TN)} is IDFT of {dn} • Transmitted signal :

Cyclic prefix • Discrete channel response : {h[0], h[1], …, h[L-1]} • Extended TX signal samples : {x[N-L:N-1], x[0:N-1]} • {x[N-L], …, x[N-1]} is cyclic prefix • Cyclic prefix changes linear convolution to circular convolution • y(t) = h(t)  x(t)  y[n] = h[n]  x[n]; n=0, …, N-1 • DFT{y[n]} = DFT{h[n]} . DFT{x[n]} = {H[n] . d[n]} • The first L-1 samples of y(t) are discarded • Eliminates ISI form previous OFDM symbol • Cyclic prefix is a guard time between OFDM symbols • CP overhead : L • Data rate reduction : N/(N+L) 1 – (L/N)

Zero prefix • Sends nothing (zero) instead of cyclic prefix • No ISI • Less transmitted power • Add the received tail of each symbol to its beginning to make circular convolution work • Additional noise : (N+L)/N = 1 + L/N

OFDM in matrix form • y = H W d + n • H is convolution matrix • With cyclic prefix : yN = Hc W d + n • Hc is circulant matrix : Hc = W L WH

Frequency equalization • yN = Hc (Wd) + n = W L d + n • Frequency domain equalization • Y = WHyN = L d + WH n • L-1 WH Y = d + L-1 WH n • Noise enhancement • Pre-coding • yN = Hc (W L-1 d) + n = Wd + n • WH Y = d + WH n • Channel response needed in the TX • Power allocation and bit loading needed

OFDM system block diagram • Transmitter • Receiver

OFDM performance • Independent sub-channels • Pi : signal power in ith sub-channel • Ni0 : noise power in ith sub-channel • dmin is a function of Pi and the constellation in ith sub-channel • (dmin/2)2 = 3 Pi /(M2-1) (M-ary PAM)

Power allocation • Power allocation to sub-channels • Maximize capacity subject to power constraint • Lagrangian technique • Water filling • Bit loading • Power and data rate allocation • Adaptive in fading channels • Commonly used in ADSL

Channel estimation • Channel estimate when data is known • Using preamble • Frequency domain • WH y = L WH x + n • Time domain • y = X h + n • h = (XHX)-1 XH y • Time and Frequency domain • Tracking • Pilot tones • Time and • Frequency interpolation

OFDM in fading channels • Flat fading for sub-channels • Coding in time, frequency, and space • Diversity • MIMO OFDM

Synchronization issues • Timing acquisition and Coarse frequency offset estimation • Pilot symbols • Timing offset • timing synchronization errors • Data rotation • Carrier phase offset • Data rotation • Carrier frequency offset • mismatched oscillators, Doppler frequency shifts • Causes attenuation and ICI • y = diag{wak}kWLd; a=Dw/w0 • Sampling frequency offset : x[k] = y( k(TN+dt)/N) • y = W’Ld; w’ = w(1+a); a=dt/TN

Windowing • Mitigates frequency offset problem • Raised cosine • Gaussian • Done after cyclic extension • Power spectrum

Peak to average power ratio • Linear operation is needed for OFDM symbols • Average power : N Ps = N A2 • Assume the same power for sub-channels (Ps = A2) • Peak power = (NA)2 • PAPR = N • Limiting when N is large • Large back-off in power amps (PA) • PAPR distribution

PAPR reduction • Clipping • distortion (increase Pe) • Spectral regrowth • Symbol selection • Peak cancellation • Coding

Case study – 802.11a/11g • Wireless LAN • Band 5 GHz (11g operates in 2.4 GHz) • B = 20 MHz • N = 64 • 48 used for data • 12 outer tones not used • 4 used as pilot tones • BN = 20 MHz/64 = 312.5 KHz • CP = 16 samples (16/20 = 0.8 usec) • Delay spread < 0.8 usec • OFDM symbols = 80 samples (80/20 = 4 usec) • CP overhead = 20% • The same modulation and coding for all sub-carriers • Modulations : BPSK, QPSK, 16QAM, and 64 QAM • Convolutional code : Rates ½, 2/3, and ¾ • Date rates • Rmin = 48x 1/2 x 1 / 4usec = 6 Mbps • Rmax = 48x 3/4x 6 / 4usec = 54 Mbps

Reading • Ch. 12 Goldsmith • Ch. 1, 2 Bahai

ECE637 : Fundamentals of Wireless Communications