advanced telecommunications for wireless systems investigating ofdm by mathcad n.
Skip this Video
Loading SlideShow in 5 Seconds..
Advanced telecommunications for wireless systems Investigating OFDM by MathCAD PowerPoint Presentation
Download Presentation
Advanced telecommunications for wireless systems Investigating OFDM by MathCAD

Advanced telecommunications for wireless systems Investigating OFDM by MathCAD

206 Vues Download Presentation
Télécharger la présentation

Advanced telecommunications for wireless systems Investigating OFDM by MathCAD

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

  1. Advanced telecommunications for wireless systemsInvestigating OFDM by MathCAD Timo Korhonen, Communications Laboratory, TKK

  2. Motto • If you tell me – I forget • If you show me – I will remember • If you involve me – I can understand- a Chinese proverb

  3. Topics • The objective of workshop OFDM module is to get familiar with OFDM physical level by using MathCAD for system studies. • Topics: • OFDM Signal in time and frequency domain • Channel model and associated effects to OFDM • Windowing • Cyclic prefix • Peak-to-average power ratio (PAPR) • OFDM transceiver • Water-pouring principle • System modeling: Constellation diagram, error rate • System impairments

  4. References for exercises • • Bahai, Ahmad R. S: Multi-Carrier Digital Communications : Theory and Applications of OFDM • Hara, Shinsuke: Multicarrier Techniques for 4G Mobile Communications • Prasad, Ramjee: OFDM for Wireless Communications Systems • Xiong, Fuqin: Digital Modulation Techniques. Norwood, MA, USA •

  5. Exercise: Using MathCAD • Plot the sinc-function • Create a script to create and draw a rectangle waveform. • Demonstrate usage of FFT by drawing a sin-wave and its spectra. • Determine Fourier-series coefficients of a sinusoidal wave and plot the wave using these coefficients • Prepare a list of problems/solutions encountered in your tasks.

  6. Rect

  7. Spectra of a sinus

  8. Fourier transformation of a sinusoidal

  9. Introduction

  10. Background • Objectives: High capacity and variable bit rate information transmission with high bandwidth efficiency • Limitations of radio environment, also Impulse / narrow band noise • Traditional single carrier mobile communication systems do not perform well if delay spread is large. (Channel coding and adaptive equalization can be still improve system performance)

  11. OFDM • Each sub-carrier is modulated at a very low symbol rate, making the symbols much longer than the channel impulse response. • Discrete Fourier transform (DFT) applied for multi-carrier modulation. • The DFT exhibits the desired orthogonality and can be implemented efficiently through the fast fourier transform (FFT) algorithm.

  12. Basic principles • The orthogonality of the carriers means that each carrier has an integer number of cycles over a symbol period. • Reception by integrate-and-dump-receiver • Compact spectral utilization (with a high number of carriers spectra approaches rectangular-shape) • OFDM systems are attractive for the way they handle ISI and ICI, which is usually introduced by frequency selective multipath fading in a wireless environment. (ICI in FDM)

  13. Drawbacks of OFDM • The large dynamic range of the signal, also known as the peak-to-average-power ratio (PAPR). • Sensitivity to phase noise, timing and frequency offsets (reception) • Efficiency gains reduced by guard interval. Can be compensated by multiuser receiver techniques (increased receiver complexity)

  14. Examples of OFDM-systems • OFDM is used (among others) in the following systems: • IEEE 802.11a&g (WLAN) systems • IEEE 802.16a (WiMAX) systems • ADSL (DMT = Discrete MultiTone) systems • DAB (Digital Audio Broadcasting) • DVB-T (Digital Video Broadcasting) OFDM is spectral efficient, but not power efficient (due to linearity requirements of power amplifier=the PAPR-problem). OFDM is primarily a modulation method; OFDMA is the corresponding multiple access scheme.

  15. OFDM Signal

  16. Multiplexing techniques

  17. OFDM signal in time domain OFDM TX signal = Sequence of OFDM symbols gk(t) consisting of serially converted complex data symbols The k:th OFDM symbol (in complex LPE form) is where N = number of subcarriers, TG + TS= symbol period with the guard interval, and an,k is the complex data symbol modulating the n:th subcarrier during the k:th symbol period. In summary, the OFDM TX signal is serially converted IFFT of complex data symbols an,k

  18. Orthogonality of subcarriers Definition: Orthogonality over the FFT interval: Phase shift in any subcarrier - orthogonality over the FFT interval should still be retained:

  19. Exercise: Orthogonality • Create a MathCAD script to investigate orthogonality of two square waves • #1 Create the rect-function • #2 Create a square wave using #1 • #3 Create a square wave with a time offset • #4 Add the waves and integrate

  20. Exercise: Orthogonality of OFDM signals • Create and plot an OFDM signal in time domain and investigate when your subcarriers are orthogonal • #1 Create a function to generate OFDM symbol with multiple subcarriers • #2 Create a function to plot comparison of two subcarriers orthogonality (parameter is the frequency difference between carriers) • Note: also phase continuity required in OFDM symbol boarders • #3 Inspect the condition for orthogonality and phase continuity


  22. OFDM Spectra

  23. OFDM in frequency domain TG TFFT Square-windowed sinusoid in time domain => "sinc" shaped subchannel spectrum in frequency domain See also A.13 in Xiong, Fuqin. Digital Modulation Techniques. Norwood, MA, USA: Artech House, Incorporated, 2006. p 916.

  24. Spectra for multiple carrier Single subchannel OFDM spectrum Subcarrier spacing = 1/TFFT Spectral nulls at other subcarrier frequencies

  25. Next carrier goes here!

  26. Exercise: Analytical spectra • Draw the spectra of OFDM signal by starting its frequency domain presentation (the sinc-function). Plot the spectra also in log-scale • #1 Plot three delayed sinc(x) functions in the range x = -1…2 such that you can note they phase align correctly to describe the OFDM spectra • #2 Plot in the range from f = -20 to 20 Hz an OFDM spectra consisting of 13 carriers around f=0 in linear and log-scale

  27. Ofdm

  28. Exercise: Spectra modified • Investigate a single OFDM carrier burst and its spectra by using the following script: • How the spectra is changed if the • Carrier frequency is higher • Symbol length is altered

  29. OFDM Spectra by MathCAD for a single carrier ofdm spectra by rect windowed

  30. Spectral shaping by windowing

  31. Exercise: Windowed spectra • The next MathCAD script demonstrates effect of windowing in a single carrier. • How the steepness of the windowing is adjusted? • Why function win(x,q) is delayed by ½? • Comment the script

  32. burst windowing and ofdm

  33. Modeling OFDM Transmission

  34. Transceiver • Some processing is done on the source data, such as coding for correcting errors, interleaving and mapping of bits onto symbols. An example of mapping used is multilevel QAM. • The symbols are modulated onto orthogonal sub-carriers. This is done by using IFFT • Orthogonality is maintained during channel transmission. This is achieved by adding a cyclic prefix to the OFDM frame to be sent. The cyclic prefix consists of the L last samples of the frame, which are copied and placed in the beginning of the frame. It must be longer than the channel impulse response.

  35. OFDM and FFT ~ Aalborg-34-lecture13.pdf

  36. Exercise: Constellation diagram of OFDM system • Steps • #1 create a matrix with complex 4-level QAM constellation points • #2 create a random serial data stream by using outcome of #1. Plot them to a constellation diagram. • #3 create complex AWGN channel noise. Calculate the SNR in the receiver. • #4 form and plot the received complex noisy time domain waveform by IFFT (icfft-function) • #5 detect outcome of #4 by FFT and plot the resulting constellation diagram

  37. Exercise : Constellation diagram of OFDM Ofdm