EEE-752 Emerging Wireless Networks OFDM

1. EEE-752Emerging Wireless NetworksOFDM Riaz Hussain FA08-PCE-003 rhussain@comsats.edu.pk Ph.D. Student Department of Electrical Engineering COMSATS Institute of Information Technology Islamabad, Pakistan Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 1

2. OFDM • FDM • Division on the basis of frequency • But a very special case • Orthogonal • Carefully selecting the frequencies that are orthogonal • In FDM • Divided bands must be separate • In fact should have some guard band • To prevent cross-talk among modulated signals • To prevent adjacent channel interference (ACI) • In OFDM • Bands can overlap • Still signals can be separated • No fear of ACI Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 2

3. Orthogonality & Vector Space • Two vectors are orthogonal if their inner product (dot product) is zero • e.g.: A = 4 B = 3i A . B = |A| |B| Cosθ = 0 • In 2- or 3-dimensionl Euclidean space, two vectors are orthogonal if their dot product is zero, i.e. they make an angle of 90° or π/2 radians. • e.g.: The vectors (1, 3, 2), (3, −1, 0), (1/3, 1, −5/3) are orthogonal to each other Since (1)(3) + (3)(−1) + (2)(0) = 0, (3)(1/3) + (−1)(1) + (0)(−5/3) = 0, (1)(1/3) + (3)(1) − (2)(5/3) = 0 Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 3

4. Orthogonality in OFDM In geometry orthogonal is synonym to perpendicular, but here orthogonality has no geometric significance When you trough a ball in a projectile does its horizontal velocity change? --- assuming no friction. NO Why Not? when gravitation force is acting on it? Example: Orthogonal CDMA Codes So in OFDM orthogonality signifies that no component of one signal contributes to the other signal 0000 0001 0010 0011 0100 0101 0110 0111 Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 4

5. Orthogonal Functions f(x) = sin(ωx); g(x) = sin (2 ωx) f(x) = sin(ωx); g(x) = sin (3 ωx) Integration over a complete period f(x) = sin(ωx); g(x) = cos (ωx) • In mathematics, two functions f and g are called orthogonal if their inner product is zero. ∫ f*(x) g(x) dx = 0 Here, the star is the complex conjugate. Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 5

6. Mapping of information changes in the carrier phase, frequency, amplitude or combination OFDM Method of sharing bandwidth with other independent data channels k = 0, 1, … , N-1 Ts = Symbol Time OFDM is the combination of modulation and multiplexing • Frequency Spectrum • Use many carriers that are equally spaced: Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 6

7. OFDM System Multiplexing is applied to independent signals, but these independent signals are a sub-set of one main signal Signal is split into independent channels Each modulated by the data Remultiplexed to create OFDM carrier Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 7

8. Advantages Direct Path Symbol n Symbol n+1 Symbol n-1 Delayed Path Symbol n-1 Symbol n Symbol n+1 ISI ISI ISI = Inter Symbol Interference • Carriers are orthogonal • No ACI • Many carriers with small spacing • Long symbol time • Useful to reduce ISI Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 8

9. Pulse Shaping • In FDM • sinc-shaped pulse is applied in time domain to each individual symbol to reduce the ACI • as a byproduct it also results in reduced ISI • In OFDM • sinc-shaped pulse is applied in frequency domain of each channel that maintains the orthogonality of the sub-carriers --- conquering ISI Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 9

10. Example Ofdm2.pdf p:5 Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 10

11. Issues With MultiCarrier Modulation Courtesy of: Shivkumar Kalyanaramand: RPI Google: “Shiv RPI” • Large bandwidth penalty since the subcarriers can’t have perfectly rectangular pulse shapes and still be time-limited. • Very high quality (expensive) low pass filters will be required to maintain the orthogonality of the subcarriers at the receiver. • This scheme requires L independent RF units and demodulation paths. • OFDM overcomes these shortcomings by using DFT • FFT/IFFT an highly efficient computational technique • Can create large number of orthogonal subcarriers using single radio Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 11

12. OFDM Symbols Courtesy of: Shivkumar Kalyanaramand: RPI Google: “Shiv RPI” • Group L data symbols into a block known as an OFDM symbol. • An OFDM symbol lasts for a duration of T seconds, where T = LTs. • Guard period > delay spread • OFDM transmissions allow ISI within an OFDM symbol, but by including a sufficiently large guard band, it is possible to guarantee that there is no interference between subsequent OFDM symbols. • The next task is to attempt to remove the ISI within each OFDM symbol --- Circular Convolution Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 12

13. Circular convolution allows DFT! Circular Convolution & DFT/IDFT • Circular convolution: • Detection of X (knowing H): (note: ISI free! Just a scaling by H) Courtesy of: Shivkumar Kalyanaramand: RPI Google: “Shiv RPI” Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 13

14. Cyclic Prefix: Eliminate intra-symbol interference! • In order for the IFFT/FFT to create an ISI-free channel, the channel must appear to provide a circular convolution • If a cyclic prefix is added to the transmitted signal, then this creates a signal that appears to be x[n]L, and so y[n] = x[n] * h[n]. • The first v samples of ycp interference from preceding OFDM symbol => discarded. • The last v samples disperse into the subsequent OFDM symbol => discarded. • This leaves exactly L samples for the desired output y, which is precisely what is required to recover the L data symbols embedded in x. Courtesy of: Shivkumar Kalyanaramand: RPI Google: “Shiv RPI” Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 14

15. Cyclic Prefix (Contd) • These L residual samples of y will be equivalent to • By mimicking a circular convolution, a cyclic prefix that is at least as long as the channel duration (v+1)… • … allows the channel output y to be decomposed into a simple multiplication of the channel frequency response H = DFT{h} and the channel frequency domain input, X = DFT{x}. Courtesy of: Shivkumar Kalyanaramand: RPI Google: “Shiv RPI” Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 15

16. OFDM Implementation Break a wideband signal of bandwidth B into L narrowband signals (subcarriers) each of bandwidth B/L. The L subcarriers for a given OFDM symbol are represented by a vector X, which contains the L current symbols. In order to use a single wideband radio instead of L independent narrow band radios, the subcarriers are modulated using an IFFT operation. In order for the IFFT/FFT to decompose the ISI channel into orthogonal subcarriers, a cyclic prefix of length v must be appended after the IFFT operation. The resulting L + v symbols are then sent in serial through the wideband channel. Courtesy of: Shivkumar Kalyanaramand: RPI Google: “Shiv RPI” Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 16

17. An OFDM Modem N subchannels 2N real samples S/P (QAM) encoder N-IFFT add cyclic prefix P/S D/A + transmit filter Bits 00110 TRANSMITTER multipath channel RECEIVER N subchannels 2N real samples Receive filter + A/D P/S QAM demoddecoder N-FFT S/P remove cyclic prefix invert channel = frequency domain equalizer Courtesy of: Shivkumar Kalyanaramand: RPI Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 17

18. OFDM Applications • WiFi • 802.11a (54 Mbps; 5 GHz ISM) • 802.11g(54 Mbps; 2.4 GHz ISM) • WIMAX • 3G-LTE (UMB) • DAB • DVB • 4G (Proposed Modulation Technique) Riaz Hussain rhussain@comsats.edu.pk EEE752-ETWN: OFDM 18

19. OFDM in WiMAX Courtesy of: Shivkumar Kalyanaramand: RPI Google: “Shiv RPI” Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 19

20. OFDM in Wimax (Contd) • Pilot, Guard, DC subcarriers: overhead • Data subcarriers are used to create “subchannels” Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 20

21. I/Q I/Q Channel coding / interleaving Symbol mapping (modulation) OFDM modulation (IFFT) Guard interval 0110 010101001 Receiver Decoding / deinter-leaving symbol de-mapping (detection) OFDM demod. (FFT) Guard interval removal I/Q I/Q Channel est. Time sync. OFDM Block Diagram Transmitter Courtesy of: Shivkumar Kalyanaramand: RPI Google: “Shiv RPI” Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 21

22. Other Versions of OFDM • VOFDM (Vector OFDM = MIMO-OFDM) • WOFDM(Wideband) • develops spacing between channels large enough so that any frequency errors between transmitter and receiver have no effect on performance • Flash OFDM • uses multiple tones and fast hopping to spread signals over a given spectrum band • COFDM (Coded) Riaz Hussain rhussain@comsats.edu.pk EEE752-ETWN: OFDM 22

23. MIMO-OFDM Multiple Input, Multiple Output Orthogonal Frequency Division Multiplexing is a technology developed by Iospan Wireless that uses multiple antennas to transmit and receive radio signals. MIMO-OFDM will allow service providers to deploy a Broadband Wireless Access (BWA) system that has Non-Line-of-Sight (NLOS) functionality. Specifically, MIMO-OFDM takes advantage of the multipath properties of environments using base station antennas that do not have LOS. According to Iospan, "In this environment, radio signals bounce off buildings, trees and other objects as they travel between the two antennas. This bouncing effect produces multiple "echoes" or "images" of the signal. As a result, the original signal and the individual echoes each arrive at the receiver antenna at slightly different times causing the echoes to interfere with one another thus degrading signal quality. The MIMO system uses multiple antennas to simultaneously transmit data, in small pieces to the receiver, which can process the data flows and put them back together. This process, called spatial multiplexing, proportionally boosts the data-transmission speed by a factor equal to the number of transmitting antennas. In addition, since all data is transmitted both in the same frequency band and with separate spatial signatures, this technique utilizes spectrum very efficiently. Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 23

24. Summary (1) • Multicarrier • Orthogonality • Reduced • ISI • ACI • Multipath fading • Requirements • L-independent RF units and demodulation paths • Maintenance of orthogonality among subcarriers

25. Summary (2) • Fulfills Requirements: • In order to use a single wideband radio instead of L independent narrow band radios, the subcarriers are modulated using an IFFT operation. • In order for the IFFT/FFT to decompose the ISI channel into orthogonal subcarriers, a cyclic prefix of length v (channel duration) must be appended after the IFFT operation. The resulting L + v symbols are then sent in serial through the wideband channel. -------------------- the alternative to this was to design a very high quality low pass filter --- not practically implementable • OFDM transmissions allow ISI within an OFDM symbol, to ensure no interference between subsequent OFDM symbols a guardband is introduced

26. Summary (3) • Design Issues: • Subcarrier Bandwidth: Bsc = B/L ::: B = Nominal BW; L = Number of subcarriers determines size of FFT/IFFT • OFDM Symbol Time: T = Ts(L + Ng) ::: Sampling Time (Ts) = 1/B; Guard Symbols (Ng) = GL Guard Fraction (G) = % of L for CP determines v Guard Time (Tg) = TsNg To eliminate intra symbol interference among/within OFDM subcarriers • Data Subcarriers: Ld = L – pilot subcarriers – null subcarriers • Guard-time: (To eliminate interference between OFDM symbols) • Depends on the channel conditions --- delay spread of an OFDM symbol GT = % of T ::: usualy 10% – 15% • Data Rate: R = (B/L)(Ldlog2(M)/(1 + G))M = No. of discrete symbol level used in modulation

27. References Shivkumar Kalyanaraman: RPI lectures Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 27