1. EEE-752 Emerging Wireless Networks OFDM Riaz Hussain FA08-PCE-003 rhussain@comsats.edu.pk Ph.D. Student Department of Electrical Engineering COMSATS Institute of Information Technology Islamabad, Pakistan Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: OFDM1rhussain@comsats.edu.pk

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 Hussainrhussain@comsats.edu.pkEEE752-EWN: OFDM2rhussain@comsats.edu.pk

3. Orthogonality & Vector Space Two vectors are orthogonal if their inner product (dot product) is zero – e.g.: A = 4B = 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 Hussainrhussain@comsats.edu.pkEEE752-EWN: OFDM3rhussain@comsats.edu.pk

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 Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: OFDM4rhussain@comsats.edu.pk 0000 0001 0010 0011 0100 0101 0110 0111

5. Orthogonal Functions 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. f(x) = sin(ωx); g(x) = sin (2 ωx)f(x) = sin(ωx); g(x) = sin (3 ωx) f(x) = sin(ωx); g(x) = cos (ωx) Integration over a complete period Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: OFDM5rhussain@comsats.edu.pk

6. OFDM OFDM is the combination of modulation and multiplexing Frequency Spectrum – Use many carriers that are equally spaced: Mapping of information changes in the carrier phase, frequency, amplitude or combination Method of sharing bandwidth with other independent data channels k = 0, 1, …, N-1 T s = Symbol Time Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: OFDM6rhussain@comsats.edu.pk

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 Hussainrhussain@comsats.edu.pkEEE752-EWN: OFDM7rhussain@comsats.edu.pk

8. Advantages Carriers are orthogonal – No ACI Many carriers with small spacing – Long symbol time – Useful to reduce ISI ISI Symbol n-1 Symbol nSymbol n+1 Direct Path Delayed Path ISI = Inter Symbol Interference ISI Symbol n-1Symbol nSymbol n+1 Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: OFDM8rhussain@comsats.edu.pk

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 Hussainrhussain@comsats.edu.pkEEE752-EWN: OFDM9rhussain@comsats.edu.pk

10. Example Ofdm2.pdf p:5 Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: OFDM10rhussain@comsats.edu.pk

11. Issues With MultiCarrier Modulation 1. Large bandwidth penalty since the subcarriers can’t have perfectly rectangular pulse shapes and still be time-limited. 2. Very high quality (expensive) low pass filters will be required to maintain the orthogonality of the subcarriers at the receiver. 3. 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 Hussainrhussain@comsats.edu.pkEEE752-EWN: OFDM11rhussain@comsats.edu.pk Courtesy of: Shivkumar Kalyanaramand: RPI Google: “Shiv RPI”

12. OFDM Symbols 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 Hussainrhussain@comsats.edu.pkEEE752-EWN: OFDM12rhussain@comsats.edu.pk Courtesy of: Shivkumar Kalyanaramand: RPI Google: “Shiv RPI”

13. Circular Convolution & DFT/IDFT Circular convolution: q Detection of X (knowing H): (note: ISI free! Just a scaling by H) q Circular convolution allows DFT! Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: OFDM13rhussain@comsats.edu.pk Courtesy of: Shivkumar Kalyanaramand: RPI Google: “Shiv RPI”

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 y cp 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. Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: OFDM14rhussain@comsats.edu.pk Courtesy of: Shivkumar Kalyanaramand: RPI Google: “Shiv RPI”

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}. Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: OFDM15rhussain@comsats.edu.pk Courtesy of: Shivkumar Kalyanaramand: RPI Google: “Shiv RPI”

16. OFDM Implementation 1. 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. 2. In order to use a single wideband radio instead of L independent narrow band radios, the subcarriers are modulated using an IFFT operation. 3. 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. Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: OFDM16rhussain@comsats.edu.pk Courtesy of: Shivkumar Kalyanaramand: RPI Google: “Shiv RPI”

17. P/S QAM demod decoder invert channel = frequency domain equalizer S/P (QAM) encoder N -IFFT add cyclic prefix P/S D/A + transmit filter N -FFTS/P remove cyclic prefix TRANSMITTER RECEIVER N subchannels2N real samples N subchannels Receive filter + A/D multipath channel An OFDM Modem Bits 00110 Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: OFDM17rhussain@comsats.edu.pk Courtesy of: Shivkumar Kalyanaramand: RPI

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 Hussainrhussain@comsats.edu.pkEEE752-ETWN: OFDM18rhussain@comsats.edu.pk

19. OFDM in WiMAX Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: OFDM19rhussain@comsats.edu.pk Courtesy of: Shivkumar Kalyanaramand: RPI Google: “Shiv RPI”

20. OFDM in Wimax (Contd) Pilot, Guard, DC subcarriers: overhead Data subcarriers are used to create “subchannels” Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: OFDM20rhussain@comsats.edu.pk

21. OFDM Block Diagram OFDM modulation (IFFT) Channel coding / interleaving Guard interval I/Q Symbol mapping (modulation) Transmitter OFDM demod. (FFT) Decoding / deinter- leaving Guard interval removal Time sync. I/Q symbol de- mapping (detection) Channel est. Receiver 0101010010110 Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: OFDM21rhussain@comsats.edu.pk Courtesy of: Shivkumar Kalyanaramand: RPI Google: “Shiv RPI”

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 Hussainrhussain@comsats.edu.pkEEE752-ETWN: OFDM22rhussain@comsats.edu.pk

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 Hussainrhussain@comsats.edu.pkEEE752-EWN: OFDM23rhussain@comsats.edu.pk

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: B sc = B/L::: B = Nominal BW; L = Number of subcarriersdetermines size of FFT/IFFT – OFDM Symbol Time: T = T s (L + N g )::: Sampling Time (Ts) = 1/B; Guard Symbols (Ng) = GL Guard Fraction (G) = % of L for CPdetermines v Guard Time (Tg) = TsNgTo eliminate intra symbol interference among/within OFDM subcarriers – Data Subcarriers: L d = L – pilot subcarriers – null subcarriers – Guard-time: (To eliminate interference between OFDM symbols) Depends on the channel conditions --- delay spread of an OFDM symbol G T = % of T:::usualy 10% – 15% – Data Rate: R = (B/L)(L d log 2 (M)/(1 + G)) M = No. of discrete symbol level used in modulation

27. References Shivkumar Kalyanaraman: RPI lectures Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: OFDM27rhussain@comsats.edu.pk