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# OFDM

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# OFDM

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### OFDM

1. 1. OFDM Transmitter & Receiver Guide: Dr. Vijaya Prakash A.M. Professor, ECE Department Group members: Shriram Shridhar Shanbhag(1BI12EC101) Shubham Dhingra (1BI12EC103) Supreem H(1BI12EC111) Mohammed Ibrahim Adilshah(1BI13EC407) BANGALORE INSTITUTE OF TECHNOLOGY ELECTRONICS & COMMUNICATIONS ENGINEERING Project Seminar on
2. 2. Agenda / Topics • Introduction to OFDM • Single carrier modulation v/s Multi-carrier modulation • Block Diagram • Constellation Mapper • Role of IFFT block • Cyclic Prefix • Design of Constellation Mapper • Design of IFFT block • Simulation Results • Conclusion • References
3. 3. Introduction to OFDM  Multi Carrier modulation technique  Subcarrier frequencies are chosen so that the subcarriers are orthogonal to each other  Two signals are said to be orthogonal to each other if the integral of the product of two signals is zero over a time period  Orthogonality is defined by: 0 𝑇 cos(2𝜋𝑛𝑓0 𝑡)cos(2𝜋𝑚𝑓0 𝑡)𝑑𝑡 = 0 (𝑛 ≠ 𝑚)  For OFDM, T is one symbol period and f0 set to 1/T for optimal effectiveness  Orthogonality prevents interference between overlapping carriers
4. 4. Basis for OFDM – Multi Carrier Modulation(MCM)  Operates by dividing the data stream to be transmitted into a number of lower data rate data streams  Each of the lower data rate streams is then used to modulate an individual carrier  MCM is being used as a modulation format for high data rate transmissions Single Carrier Modulation v/s MCM – An example  Usually, symbol period must be greater than delay time to avoid ISI  Generally, delay time Td = 2-3 μs Say, bandwidth B = 10Mhz Case (i) Single Carrier Modulation Symbol time, T = 1/B = 1/10M = 0.1μs T < Td which implies there will be ISI Case (ii)Multi-Carrier Modulation Suppose , there are 1000 sub-carriers, i.e. N=1000 Symbol time, T = 1/(B/N) = 1/(10M/1000) = 100μs T>>Td which implies there will be no ISI B . . .. . . Transmission in MCM systems 0 B/N 2B/N-B/N-2B/N
5. 5.  OFDM signal consists of a number of closely spaced modulated carriers (until they are actually overlapping) Spectrum overlap in OFDM  Because of orthogonal carriers, inter carrier guard bands are not required and hence provides high bandwidth efficiency compared to FDM  Doesn’t require filter at the receiver side as in the case of FDM Fig.(A)Spectrum of FDM showing guard bands Fig.(B)Spectrum of OFDM showing overlapping carriers
6. 6. Block Diagram of OFDM Serial to Parallel Constellation Mapper (QPSK/QAM) IFFT Parallel to Serial Channel Serial to Parallel Delete Cyclic Prefix FFT Constellation demapper (QPSK/QAM) Parallel to Serial d0,d1,d2,… OFDM signal Cyclic Prefix (xN-Ncp ,xN-Ncp-1,….,xN-1) s0 s1 sn-1 X0 X1 Xn-1 x0 x1 xn-1 r0 r1 rn-1 R0 R1 Rn-1 s0 s1 sn-1 d0,d1,…
7. 7. Constellation mapper Constellation mapper is nothing but the modulator that takes word as an input and maps it to a point on the constellation diagram The size of the word depends on the type of modulation used In case of QPSK the size is 2 bits/word, in 16-QAM it’s 4 bits/word and in case of 64-QAM it’s 6 bits/word The use of phase shift keying produces a constant amplitude signal while QAM produces signal with variable amplitude Hence PSK modulators are easier in terms of implementation
8. 8. The constellation diagram for QPSK, 16-QAM and 64-QAM are shown below
9. 9. Role of IFFT block • In OFDM we divide the available bandwidth into N orthogonal carriers • If Xi is the symbol to be transmitted on ith subcarrier, transmitted signal equation can be written as Si = Xi*ej2*pi*i*(B/N)*t where B is the total bandwidth • The set of symbols transmitted can be written as S = Σ Xi*ej2*pi*i*(B/N)*t • The above expression is nothing but IFFT(X)
10. 10. Pictorially, it can be represented as follows :
11. 11. Cyclic Prefix • Usually to minimize the ISI we increase the symbol time • But even after increasing symbol time, some effects are not removed
12. 12. • To eliminate this problem, we have to find a way to recover the lost part • One way to do this is duplicating the initial part of the symbol and append it to the end of the symbol • This increases the overall length of the symbol but the gains outweigh the increase in length
13. 13. • From the figure below, it can be seen that with cyclic prefix the problem no longer exists • The length of the cyclic prefix should be large enough to eliminate the effects of multipath components but short enough to keep the symbol time low
14. 14. Design of constellation mapper QPSK rst in Out_real Out_im Binary Mapping points Hexadecimal 00 0.707 + j0.707 3fe6 3fe6 01 -0.707 + j0.707 bfe6 3fe6 10 -0.707 –j0.707 bfe6 bfe6 11 0.707 – j0.707 3fe6 bfe6 16 16 clk
15. 15. ROM MODULE 4x32 4x32 ROM rst address Out 2 clk 32 Address Value 00 3fe63fe6 01 bfe63fe6 10 bfe6bfe6 11 3fe6bfe6
16. 16. SIPO 4x32 ROM ROM Clk rst address Out_real clk 2 16 16 32 /2 in din rst Out_img
17. 17. Design of IFFT block X(0) = x(0)+ x(4)+ x(2)+ x(6)+ x(1)+ x(5)+ x(3)+ x(7) X(4) = x(0)+ x(4)+ x(2)+ x(6)- x(1)- x(5)- x(3)- x(7) X(2) = x(0)+ x(4)- x(2)- x(6)+ jx(1)+ jx(5)- jx(3)- jx(7) X(6) = x(0)+ x(4)- x(2)- x(6)- jx(1)- jx(5)+ jx(3)+ jx(7) X(1) = x(0) - x(4) + jx(2) - jx(6) + 0.7071x(1) + j0.7071x(1) - 0.7071x(5) - j0.7071x(5) - 0.7071x(3) - j0.7071x(3) + 0.7071x(7) + j0.7071x(7) X(5) = x(0) - x(4) + jx(2) - jx(6) - 0.7071x(1) - j0.7071x(1) + 0.7071x(5) + j0.7071x(5) + 0.7071x(3) + j0.7071x (3) - 0.7071x(7) - j0.7071x(7) X(3) = x(0) - x(4) - jx(2) - jx(6) - 0.7071x(1) + j0.7071x(1) + 0.7071x(5)- j0.7071x(5) + 0.7071x(3) - j0.7071x(3) - 0.7071x(7) + j0.7071x(7) X(7) =x(0)- x(4) - jx(2) - jx(6) + 0.7071x(1) - j0.7071x(1) - 0.7071x(5) + j0.7071x(5) - 0.7071x(3)+ j0.7071x(3)+ 0.7071x(7)- j0.7071x(7)
18. 18. Design of IFFT Block Pass Path0 Path1 Path2 Path5 Path3 Path4 Path6 Path7 X0 X1 X2 X3 X4 X5 X6 X6 x(0) x(1) x(2) x(3) x(4) x(5) x(6) x(7)
21. 21. Path 1, 3, 5 & 7 X(1) = x(0) - x(4) + jx(2) - jx(6) + 0.7071x(1) + j0.7071x(1) - 0.7071x(5) - j0.7071x(5) - 0.7071x(3) -j0.7071x(3) + 0.7071x(7) + j0.7071x(7) X(5) = x(0) - x(4) + jx(2) - jx(6) - 0.7071x(1) - j0.7071x(1) + 0.7071x(5) + j0.7071x(5) + 0.7071x(3) + j0.7071x (3) - 0.7071x(7) - j0.7071x(7) X(3) = x(0) - x(4) - jx(2) - jx(6) - 0.7071x(1) + j0.7071x(1) + 0.7071x(5)- j0.7071x(5) + 0.7071x(3) - j0.7071x(3) - 0.7071x(7) + j0.7071x(7) X(7) =x(0)- x(4) - jx(2) - jx(6) + 0.7071x(1) - j0.7071x(1) - 0.7071x(5) + j0.7071x(5) - 0.7071x(3)+ j0.7071x(3)+ 0.7071x(7)- j0.7071x(7) • Each expression contains 12 products and sum of those product terms. • So the path can be split into 2 modules one to find the products, and one to add them up.
22. 22. Path 1, 3, 5 & 7 Path 5 x0 x3 x1 x2 x4 x6 x7 XR XI 16bits 8bits x5
23. 23. Product Generator clk start x0 x3 x4 x1 x2 x5 x6 x7 Cascade of adders p1 p2 p3 p4 p5 p10 p11 p12 p6 p7 p8 p9 XR XI 8bits 16bits busy enable
24. 24. M1 a b p M2 M11 M3 M12 . . . . . . . . . . . . . . . .start clk busy multiplier clk inputs outputs busy
25. 25. Tools Used • MATLAB R2014a • Xilinx 9.2i • ModelSim-Altera 10.1d (quartus 13.1)
26. 26. Results Simulation of constellation mapper
27. 27. RTL schematics of QPSK constellation mapper
28. 28. Simulation of path 0
29. 29. Simulation of path 2
30. 30. Simulation of path 5
31. 31. Comparison of Transmitted signal with the received signal using OFDM system simulated in MATLAB with SNR = 10 dB
32. 32. BER v/s SNR for different modulation schemes
33. 33. Fig.(A) SNR = 30 dB Fig.(B) SNR = 20 dB Fig.(C) SNR = 10 dB
34. 34. Conclusion Because of orthogonal carriers, inter carrier guard bands are not required and hence OFDM provides higher bandwidth efficiency compared to FDM OFDM overcomes even severe intersymbol interference through the use of the IFFT and a cyclic prefix BER v/s SNR curve shows BER reduces at low SNR values for QPSK while it reduces to the same levels at relatively higher SNR in case of QAM Data rates of 16-QAM is twice of QPSK and that of 64-QAM, it’s thrice of QPSK Choice of modulation is a trade-off between accuracy and speed
35. 35. References • “HDL Programming (VHDL and Verilog)” Nazeih Botros- 2008 edition • Foisal Ahmed,1,* Md. Liakot Ali,2 and Mohammad Imam Hasan Bin Asad2 “Design of high speed ofdm transmitter and receiver” 8th International Conference on Electrical and Computer Engineering 20-22 December, 2014, Dhaka, Bangladesh • “Hardware implementation of ofdm trasnmitter and receiver using fpga” Shabaz Abbasi and Shazer Baig National University of Computer and Emerging Sciences Fast June 2008 • “OFDM SIMULATION in MATLAB” by Paul Gaunming Lin California Polytechnic State University • “Implementation the Technique of Orthogonal Frequency Division Multiplexing Using 16-Point Fast Fourier Transform and Inverse Fast Fourier Transform” Muhammad Waqas – Sharad institute of science and information technology, Peshawar, Pakistan • “Design and Implementation of Orthogonal Frequency Division Multiplexing (OFDM) Signaling” Alan C. Brooks and Stephen J hoelzer. • Mathuranathan Viswanathan, “Introduction to OFDM”, June 2015; https://www.gaussianwaves.com
36. 36. References • https://www.rf-wireless.com • Charan Langton, “Orthogonal Frequency Division Multiplex (OFDM, DMT)”, July 2015; https://www.complextoreal.com • Krishna Sankar M, “Cyclic Prefix in Orthogonal Frequency Division Multiplexing”, July 2015; https://www.dsplog.com • Matlab help (https://www.mathworks.com)
37. 37. THANK YOU