ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING FOR WIRELESS CHANNELS LEONARD J. CIMINI, JR. YE (GEOFFREY) LI AT&T LABS - RESEARCH ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING FOR WIRELESS CHANNELS Leonard J. Cimini, Jr. AT&T Labs – Research 100 Schulz Dr., Rm. 4-146 Red Bank, NJ 07701-7033, USA Email: [email protected] Tel/Fax: 1-732-345-3129/3039 Ye (Geoffrey) Li AT&T Labs – Research 100 Schulz Dr., Rm. 4-152 Red Bank, NJ 07701-7033, USA Email: [email protected] Tel/Fax: 1-732-345-3132/3039 ABSTRACT Orthogonal frequency division multiplexing (OFDM) has been shown to be an effective technique to combat multipath fading in wireless communications. It has been successfully used for HF radio applications and has been chosen as the standard for digital audio broadcasting and digital terrestrial TV broadcasting in Europe and high-speed wireless local areas networks. In this tutorial, we present the basic principles of OFDM and discuss the problems, and some of the potential solutions, in implementing an OFDM system. Techniques for peak-to-average power ratio reduction, time and frequency synchronization, and channel estimation will be discussed. We conclude with a brief overview of current application areas BIOGRAPHIES OF PRESENTERS: Leonard J. Cimini, Jr., received the B.S.E. (summa cum laude), M.S.E. and Ph.D. degrees in electrical engineering from the University of Pennsylvania in 1978, 1979, and 1982, respectively. During the graduate work he was supported by a National Science Foundation Fellowship. Since 1982, he has been employed at AT&T, where his research interests are in wireless communications systems. Dr. Cimini is a member of Tau Beta Pi and Eta Kappa Nu. He has been very active in the IEEE Communications Society and is Editor-in-Chief of the IEEE J-SAC: Wireless Communications Series. He is also an Adjunct Professor at the University of Pennsylvania. Ye (Geoffrey) Li received the B.Eng and M.Eng degrees in 1983 and 1986, respectively, from the Department of Wireless Engineering, Nanjing Institute of Technology, Nanjing, China, and the Ph.D. degree in Electrical Engineering in 1994, Auburn University, Alabama. Since May 1996, he has been with AT&T Labs - Research. His current research interests are in statistical signal processing and wireless communications. He has served as a guest editor for a special issue on Signal Processing for Wireless Communications for the IEEE J- SAC and is an editor for Wireless Communication Theory for the IEEE Transactions on Communications. OUTLINE • Introduction • Basic Concepts • Peak-to-Average Power Ratio Reduction • Time and Frequency Synchronization • Channel Estimation • Applications • Summary • References OUTLINE • Introduction • Basic Concepts • Peak-to-Average Power Ratio Reduction • Time and Frequency Synchronization • Channel Estimation • Applications • Summary • References INTRODUCTION • Motivation • Radio Environment • Brief History MOTIVATION • High-bit-rate wireless applications • Limitations caused by the radio environment • OFDM can overcome these inherent bit rate limitations PATH LOSS MODEL • Path Loss • Shadow Fading • Multipath • Flat fading • Doppler spread • Delay spread • Interference PATH LOSS MODEL • Different, often complicated, models are used for different environments. • A simple model for path loss, L, is P 1 = r = L K α Pt d where Pr is the local mean received signal power, Pt is the transmitted power, and d is the transmitter receiver distance. The path loss exponent α = 2 in free space; 2 ≤≤ααα≤≤ 4 in typical environments. SHADOW FADING • The received signal is shadowed by obstructions such as hills and buildings. • This results in variations in the local mean received signal power, (()) = (())+ Pr dB Pr dB GS (()σ2 ) ≤ σ ≤ where GS ~ N 0, S ,4 S 10dB. • Implications – nonuniform coverage – increases the required transmit power MULTIPATH Received Power t Delay Spread θ (()))(= j i δ(()− ) h t ∑aie t ti i Constructive and destructive interference of arriving rays 10 0 dB With Respect -10 to RMS Value -20 0.5λ -30 00.5 1 1.5 t, in seconds 01020 30 x, in wavelength FLAT FADING • The delay spread is small compared to the symbol period. • The received signal envelope, r, follows a Rayleigh or Rician distribution. P (()dB) = P (dB) + G + 20 log r r r S Received Signal Power (dB) path loss shadow fading Rayleigh fading log (distance) • Implications – increases the required transmit power – causes bursts of errors DOPPLER SPREAD • A measure of the spectral broadening caused by the channel time variation. v f ≤ D λ Example: 900 MHz, 60 mph, fD = 80 Hz 5 GHz, 5 mph, fD = 37 Hz • Implications – signal amplitude and phase decorrelate after a time period ~ 1/fD DELAY SPREAD TIME DOMAIN INTERPRETATION Two-ray model τ = rms delay spread 2τ Power Received Delay Channel Output τ Channel Input small T 0T 2T 1 1 0 T2T τ large T 0T 2T τ small negligible intersymbol interference • T τ • large significant intersymbol interference, T which causes an irreducible error floor DELAY SPREAD FREQUENCY DOMAIN INTERPRETATION H(f) Bs = signal bandwidth ≈ 1/T Bs 1 f 2τ τ small flat fading • T τ • large frequency-selective fading T BIT RATE LIMITATIONS • ISI causes an irreducible error floor. 10-1 Coherent Detection + BPSK QPSK OQPSK Modulation x MSK x 10-2 b x x + + x Irreducible P + 10-3 + x + 10-4 10-2 10-1 100 rms delay spread τ = symbol period T The rms delay spread imposes a limit on the maximum bit rate. For example, for QPSK τ Maximum Bit Rate Mobile (rural) 25 µsec 8 kbps Mobile (city) 2.5 µsec 80 kbps Microcells 500 nsec 400 kbps Large Building 100 nsec 2 Mbps INTERFRENCE • Frequencies are reused often to maximize spectral efficiency. R BASE STATION D • For interference-limited systems, the noise floor is dominated by co-channel interference. α S S 1 D ≈ = I + N I 6 R • Implications – high reuse efficiency requires interference mitigation HISTORY • Military HF radio (1950’s - 1960’s) – Kineplex – Kathryn • Wireline modem (Telebit, Gandalf) • Cellular modem (Telebit) • Digital audio and terrestrial TV broadcasting (Europe) • Asymmetric digital subscriber line (DMT) • Wireless LANs – IEEE802.11 - National Information Infrastructure – HIPERLAN TYPE II OUTLINE • Introduction • Basic Concepts • Peak-to-Average Power Ratio Reduction • Time and Frequency Synchronization • Channel Estimation • Applications • Summary • References BASIC CONCEPTS • Multicarrier • Basic OFDM • Impairments • Alternative forms MULTICARRIER • The transmission bandwidth is divided into many narrow subchannels which are transmitted in parallel. • Ideally, each subchannel is narrow enough so that the fading it experiences is flat ⇒ no ISI. Transmitter R/N b/s d0(t) QAM filter f0 R/N b/s d1(t) QAM filter RF D(t) f1 R/N b/s dN-1(t) QAM filter fN-1 Bandlimited signals f0 f1 f2 Receiver filter f0 QAM f filter 0 f1 QAM RF f1 filter QAM fN-1 fN-1 • Disadvantage: - Requires filter bank at receiver - Spectrally inefficient Horizontal slide here BASIC OFDM RECEIVER d(0) ∫ f0 d(1) parallel ∫ to RF serial QAM f1 converter d(N-1) ∫ fN-1 • Subchannel separation 1 – choose fn = f0 +n∆f, with ∆f= NT ^ – integrate over NT, then d(m) = d(m) • A guard interval can virtually eliminate ISI (or, interblock interference) ⇒ lower spectral or power efficiency. PASSBAND VERSUS BASEBAND • Passband N−1 π + ∆ = ℜ [[]] j2 (fc k f)t ≤ ≤ xp (t) ∑ a k e , 0 t Ts k=0 • Baseband N−1 = [[]] j2πk∆ft ≤ ≤ xb (t) ∑ a k e , 0 t Ts k=0 DFT IMPLEMENTATION TRANSMITTER • Transmitted signal can be obtained using a Discrete Fourier Transform N−1 = [[]] j2πk∆ft ≤ ≤ xb (t) ∑ a k e , 0 t Ts k=0 • If sampled at a rate of Ts /N, N−1 n π ∆ [[]] = = [[]] j2 nk fTs / N xb n xb TS ∑ a k e N k=0 ∆ • For orthogonality, fTs = 1, N−1 [[]]][= [[]]][j2πnk / N = {{}[[]]} xb n ∑ a k e IDFT a k k=0 • Efficient FFT implementation DFT IMPLEMENTATION RECEIVER [[]]][= {{}[[]]} aˆ k DFT xb n N−1 = 1 [[]] − j2πnk / N ∑ xb n e N n=0 N−1 N−1 1 π − = ∑∑∑∑ a[[]m] e j2 n(m k) / N N n=0 m=0 N−1 N−1 1 π − = ∑ a[[]m]∑ e j2 n(m k) / N N m=0 n=0 1 N−1 = ∑ a[[]m]][Nδ[[]m − k] N m=0 = a[[]k] PERFORMANCE IMPROVEMENT • Coding across subchannels ⇒ works best with large delay spread • Adaptive loading – More bits/symbol where SNR is sufficient – Could also adapt transmit power in each subchannel – Requires reliable feedback channel and accurate channel information • Frequency equalization and coherent detection ⇒ requires accurate channel estimation SAMPLE DESIGN • Goal – Transmit 1.2 Mbits/sec using QPSK with B=800 kHz bandwidth channel – Delay span up to 40 µsec (max 5 kbaud for single carrier) • Design – Choose subchannel width so that there is no ISI in each subchannel ⇒ ∆ f = 6.25 kHz ⇒ N = B/∆f = 128 subchannels ∆ µ – OFDM symbol duration Ts=1/ f = 160 sec µ – Guard interval Tg = 40 sec µ – OFDM block length: Tf = Ts +Tg = 200 sec – Assuming 4 guard channels on each end, there are 120 data subchannels, each transmitting 2 bits in 200 µsec 120 x 2bits R = = 1.2 Mbits / sec b 200 µ sec IMPAIRMENTS • Time-varying fading, frequency offset, and timing mismatch impair the orthogonality of the subchannels. • Large amplitude fluctuations can be a serious problem when transmitting through a nonlinearity. TIME-VARYING IMPAIRMENTS • General expression: aˆ[[]k]][=DFT{{}χ [[]n]} = a[[]k]][K[[]k,k]][+ a[[]n]][K[[]n,k] b LOM ON ∑ Ln≠k OMO ONO attenuated & rotated ICI • Frequency offset – For a frequency offset between the transmitter and receiver, N−1 (()) = [[]] j2π(()k∆f−δf )t ≤ ≤ xb t ∑ a k e , 0 t Ts k=0 δ f δ sinπn − k − jπn−k− f ∆ f ∆f K[[]n,k] = e δf πn − k − ∆f δf sinπ δf ∆ jπ [[]] = f ∆f K k,k δ e π f ∆f TIMING MISMATCH • Timing offset smaller than the guard interval results in a phase shift.