1 Principles and Experiments of Communications Weiyao Lin Dept. of Electronic Engineering Shanghai Jiao Tong University Textbook: Chapter 11 Lecture 06: Multicarrier modulation and OFDM
Multicarrier Modulation Multipath channels cause intersymbol interference (ISI) when the reciprocal of the symbol rate is smaller than the dispersion of the nonideal channel. A solution: Subdivide the available channel bandwidth into a number of equal-bandwidth subchannels; The frequency response characteristics of each subchannel are nearly ideal.
Subdivision of Channel Bandwidth 1 D f = T where T is the symbol interval 3
Orthogonal Frequency Division Multiplexing (1/) Each subchannel associate a carrier k ( ) = cos p, = 0,1,!, -1 x t f t k N k Orthogonal Frequency Division Multiplexing (OFDM) The subcarriers are orthogonal over the symbol interval; Independently of the relative phase relationship between subcarriers. ò T 0 ( p f ) ( p f ) cos f t + cos f t + dt = 0 i i j j 4
Orthogonal Frequency Division Multiplexing (/) 5
Modulation Each OFDM symbol is the sum of signals modulated by subcarriers. OFDM symbol can express as N -1 ì é æ i + 0.5 ö ùü s( t) = Re í å d N exp jp fc ( t ts) t i s t ts T + ê ç - - ý + i=-n ú î ë è ø ûþ equivalent baseband signal N -1 é i ù s( t) = å d N exp jp ( t ts) t i s t ts T + ê - + i=-n ë T ú û 6
For the k th signal Demodulation ^ N -1 1 ts + T k- N i k = exp s N exp t i s Tò p - å - - + s T i=-n T é ù é ù d ê j ( t t ) ú d ê j p ( t t ) ú dt ë û ë û N -1 1 ts + T é i- k+ N å N exp p i+ ò t ê s i=-n T ù = d j ( t - ts) dt T ë ú û = d k 7
Modulation and Demodulation of OFDM System 8
FFT and IFFT Inverse DFT and IDFT are critical in the implementation of an OFDM system N -1 1 IDFT x[n]= å xke [ ] N DFT N -1 å n= 0 n= 0 x[k]= x[ n] e p j kn N p - j kn N IFFT and FFT algorithms are the fast implementation for the IDFT and DFT 9
Modulation Using IDFT OFDM equivalent baseband signal can implement with IDFT. let 0, N -1 é i ù s( t) = å d N exp jp ( t ts) t i s t ts T + ê - + i=-n ë T ú û t s = t = kt, k = 0,1,!, N -1 N N -1 ækt ö æ p ki ö s( k) = sç = å di expç j 0 k N -1 è N ø i= 0 è N ø s( k) is IDFT of d i 10
At the receiver Demodulation Using DFT N -1 æ p ki ö di = å s( k) expç - j 0 i N -1 k = 0 è N ø Modulating the transmitted signal and demodulating the received signal is equivalent to the computation of the IDFT and its inverse. 11
OFDM via the FFT Algorithm Algorithm complexity DFT/IDFT: FFT/IFFT: ( ) O N æ N ö Oç log ( N) è ø Implement the OFDM system via the FFT algorithm instead of DFT algorithm can be achieved more easily. 1
Eliminate ISI (1/) To eliminate ISI, we need to insert guard interval between OFDM symbols. If the guard interval is larger than the delay spread, the multipath component of a symbol does not interfere with adjacent symbols. 13
Eliminate ISI (/) An alternative approach is to append cyclic prefix to each OFDM symbol Since the ISI in any pair of successive signal transmission block only affects the cyclic prefix, we discard the affected samples of received signal to eliminate ISI 14
3 cases: Cyclic Prefix and Delay Spread (a) Delay Spread < Cyclic Prefix (b) Delay Spread is 3% over Cyclic Prefix (c) Delay Spread is 10% over Cyclic Prefix 15
Multicarrier OFDM Comunication System 16
The AWGN Channel Model The channel is assumed to corrupt the signal by the addition of white Gaussian noise as shown in the following figure. 17
OFDM System Performance over AWGN Channel (1/3) 18
QAM OFDM System Performance over AWGN Channel (/3) M-ary PSK ( M - ) ( M )! p( c I) ( M ) p( c II) p( c III) 1 ì 1 pe, M -QAM = 1 é í - - + 4 - + 4 log M î M êë a = 3Es 1 é æ a öù p( c I) = ê1- Q ú ê ç N ë è 0 øúû é ùé ù æ a ö æ a ö p( c II) = ê1-q úê1-q ú ê ç N ç 0 N ë è øúê ûë è 0 øúû é æ a öù p( c III) = ê1- Q ú ê ç N ë è 0 øúû æ Es æ p öö pe» erfc ç sin ç N0 èm ø è ø ùü úý ûþ 19
OFDM System Performance over AWGN Channel (3/3) BER versus SNR curves for the OFDM system in AWGN channel using BPSK/QPSK, 16QAM, 64QAM, 56QAM 0
SNR per subchannel The SNR per subchannel can be defined as: SNR k = TP C k s k nk In subchannels with high SNR, we transmit more bits/symbol. Thus, the bit rate on each subchannel can be optimized 1
Spectra of OFDM Signal (1/) OFDM signals are orthogonal in the time domain but have significant overlap in frequency domain.
Spectra of OFDM Signal (/) The large spectral overlap of the OFDM signals causes intersubchannel interference (ICI) when the communication channel is a fading channel OFDM may not be as robust as a single carrier system in radio communications where the receiving terminal is moving at high speed 3
Peak-to-Average Power Ratio Major problem: high PAPR Large peaks occurs when the signals in the K subchannels add constructively in phase. Such large signal peaks may saturate the power amplifier at the transmission, thus, causing intermodulation distortion in the transmitted signal. Solution: Insert different phase shifts in each of the subcarriers; Modulate a small subset of the subcarriers with dummy symbol. 4
Applications of OFDM Digital audio broadcasting (DAB) Digital video broadcasting (DVB) Digital subscriber lines (DSL) Wireless local area networks (LANs) 5
Advantages and disadvantages Advantages: High data rate Immunity to delay spread Efficient bandwidth Disadvantages: of OFDM The problem of Synchronization Need FFT units at transmitter, reciver The problem of high peak to average power ratio (PAPR) 6