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hemant choubey

This document summarizes research on reducing peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. It discusses using a companding technique with Gaussian distribution to compress the signal before transmission and decompress it upon reception. The key aspects covered are: applying a compander and decompander with Gaussian distribution parameters at the transmitter and receiver; how the central limit theorem allows the sum of subcarriers to approximate a Gaussian distribution for large numbers; and how this technique reduces PAPR by increasing average power while keeping peak power the same. Performance is analyzed by simulating PAPR and bit error rate with and without companding under different parameters.

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DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING PRESENTED BY :- HEMANT CHOUBEY SISTEC-E RATIBAD DEPARTMENT OF ELECTRONICS AND COMMUNICATION www.sistec.ac.in EFFICIENT PAPR REDUCTION IN OFDM SYSTEM BASED ON A COMPANDING TECHNIQUE WITH GAUSSIAN DISTRIBUTION
Literature survey 1 .S. H. Han and J. H. Lee, “An overview of peak-to-average power ratio reduction techniques for multicarrier transmission,” IEEE Wireless Commun., vol. 12, pp. 56– 65, Apr. 2005. 2. T. Jiang and Y.Wu, “An overview: Peak-to-average power ratio reduction techniques for OFDM signals,” IEEE Trans. Broadcast., vol. 54, no. 2, pp. 257–268, Jun. 2008. 3. C. P. Li, S. H. Wang, and C. L. Wang, “Novel low-complexity SLM schemes for PAPR reduction in OFDM systems,” IEEE Trans. Signal Process., vol. 58, no. 5, pp. 2916–2921, May 2010.
 The Basic Principles of OFDM ◦ FFT-based OFDM System ◦ Serial and Parallel Concepts ◦ Modulation/Mapping  M-ary Phase Shift Keying  M-ary Quadrature Amplitude Modulation ◦ IFFT and FFT  Signal Representation of OFDM using IDFT/DFT ◦ Orthogonality ◦ Guard Interval and Cyclic Extension ◦ Advantages and Disadvantages ◦ Background theory ◦ Selective mapping ◦ Partial transmit sequence ◦ Companding ◦ Companding with gaussian distribution ◦ Central limit theorem ◦ Reference
OFDM is the most popular one. The first OFDM scheme was proposed by Chang in 1966. Even though the concept of OFDM has been around for several years, but it has not been recognized as a great method for high speed bi-directional wireless data communication until recent years. The first applications of OFDM were in the military HF radio links. Today, the OFDM technique is in many wirelesses and wired applications, such as broadband radio access networks (BRAN), Digital Audio Broadcasting (DAB), Digital Video Broadcasting-Terrestrial (DVB-T) and Asymmetric Digital Subscriber Line (ADSL) Basic Principles of OFDM
Serial-to- Parallel Converter Signal Mapper IFFT Parallel- to-Serial Converter Guard Interval Insertion Serial Data Input x bits 0d 1d 1nd 0s 1s 1ns D/A & Low pass Filter Up- Converter Down- Converter A/D Guard Interval Removal Serial-to- Parallel Converter FFT One-tap Equalizer Signal Demapper Parallel- to-Serial Converter Serial Data Output 0 ˆdx bits 1 ˆd 1 ˆ nd 0 ˆs 1 ˆs 1 ˆns Channel )(ts Time Frequency Subchannels Fast Fourier Transform Guard Intervals Symbols
Signal Mapper (QPSK) IFFT Parallel- to-Serial Converter Guard Interval Insertion Serial-to- Parallel Converter 2d 1nd Serial Data Input    1s 2s 1ns x bits D/A & Lowpass Filter 1x 1d 2x 1nx x=[0,0,0,1,1,0,1,1,….] x1=[0,0] x2=[0,1] x3=[1,0] x4=[1,1] Q . I . . . 00 01 11 10 . I . . . 00 01 11 10 Q . . . . 00 01 11 10 I . . . . 00 01 11 10 d1=1 d2=i d3=-1 d4=-i …..
DATA CP CP CP CP CP 1 1 1 i i d é ù ê ú ê ú ê ú ê ú= ê ú ê ú ê ú ê ú-ê úë û M 0 10 20 30 40 50 60 70 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 [ ]-0.09, -0.003-0.096i, , 0.01+ 0.247i, -0.035-0.0472is = L 0 10 20 30 40 50 60 70 80 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 Signal Mapper (QPSK) IFFT Parallel- to-Serial Converter Guard Interval Insertion Serial-to- Parallel Converter 2d 1nd Serial Data Input    1s 2s 1ns x bits D/A & Lowpass Filter 1x 1d 2x 1nx 0 10 20 30 40 50 60 70 80 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2
In OFDM system design, the series and parallel converter is considered to realize the concept of parallel data transmission. Serial-to- Parallel Converter  Serial data Parallel data s bT NTbT 2 bT 00 t t
 Series ◦ In a conventional serial data system, the symbols are transmitted sequentially, with the frequency spectrum of each data symbol allowed to occupy the entire available bandwidth. ◦ When the data rate is sufficient high, several adjacent symbols may be completely distorted over frequency selective fading or multipath delay spread channel.
 Parallel ◦ The spectrum of an individual data element normally occupies only a small part of available bandwidth. ◦ Because of dividing an entire channel bandwidth into many narrow subbands, the frequency response over each individual subchannel is relatively flat. ◦ A parallel data transmission system offers possibilities for alleviating this problem encountered with serial systems.  Resistance to frequency selective fading
 The process of mapping the information bits onto the signal constellation plays a fundamental role in determining the properties of the modulation.  An OFDM signal consists of a sum of sub- carriers, each of which contains 1. M-ary Phase Shift Keying (PSK) or 2. Quadrature Amplitude Modulated (QAM) signals.
 M-ary phase shift keying ◦ Consider M-ary phase-shift keying (M-PSK) for which the signal set is where is the signal energy per symbol, is the symbol duration, and is the carrier frequency. ◦ This phase of the carrier takes on one of the M possible values, namely , where 2 12 cos 2 0 , 1,2,...,s i c s s iE s t f t t T i M T M 2 1i i M 1,2,...,i M sE sT cf
An example of signal-space diagram for 8-PSK . sE 2m 3m 4m 5m 6m 7m 8m Decision boundary 2 message point sE sE d d M M 1m Decision region 1 sE
An example of signal-space diagram for 16-square QAM.
Time domain Frequency domain Example of four subcarriers within one OFDM symbol Spectra of individual subcarriers
Two different sources of interference can be identified in the OFDM system. ◦ Inter Symbol Interference (ISI) - crosstalk between signals within the same sub-channel of consecutive FFT frames, which are separated in time by the signaling interval T. ◦ Inter Carrier Interference (ICI) - crosstalk between adjacent sub channels or frequency bands of the same FFT frame.
Delay spread Environment Delay Spread Home < 50 ns Office ~ 100 ns Manufactures 200 ~ 300 ns Suburban < 10 us
If Tg < Tdely-spread Tg Symbol 1 Tg Symbol 2 Tg Symbol 3 Tg Symbol 4 Tdely-spread If Tg > Tdely-spread Tg Symbol 1 Tg Symbol 2 Tg Symbol 3 Tg Symbol 1 Tg Symbol 2 Tg Symbol 3 Tg Symbol 4 Tg Symbol 1 Tg Symbol 2 Tg Symbol 3 Tdely-spread ﹒ ﹒ ﹒ ﹒ ﹒ ﹒ ﹒ ﹒ ﹒ ﹒ ﹒ ﹒ ﹒ ﹒ ﹒ ﹒
o To eliminate ICI, the OFDM symbol is cyclically extended in the guard interval. o This ensures that delayed replicas of the OFDM symbol always have an integer number of cycles within the FFT interval, as long as the delay is smaller than the guard interval. Guard Interval (Cyclic Extension)
Effect of multipath with zero signals in the guard interval, the delayed subcarrier 2 causes ICI on subcarrier 1 and vice versa. Part of subcarrier #2 causing ICI on subcarrier #1 Guard time FFT integration time=1/carrier spacing Guard time FFT integration time=1/carrier spacing OFDM symbol time OFDM symbol time Subcarrier #1 Delayed subcarrier #2
Time and frequency representation of OFDM with guard intervals. Time Frequency T Tg 1/T Subchannels Fast Fourier Transform Guard Intervals Symbols
◦ Immunity to delay spread ◦ Resistance to frequency selective fading ◦ Simple equalization ◦ Efficient bandwidth usage
◦ The problem of synchronization  Symbol synchronization  Frequency synchronization ◦ Need FFT units at transmitter, receiver
◦ Sensitive to carrier frequency offset ◦ Problem of high peak to average power ratio (PAPR) Problem 1. Increased complexity of ADC and DAC. Problem 2. Reduced efficiency of the RF power amplifier. Solutions  Signal distortion techniques  Special forward-error-correction code  Scrambling
Various reduction techniques of peak to average power reduction (PAPR) of ofdm. o Selective mapping o Partial transmit sequence o Companding
Sistec ppt
Sistec ppt
Sistec ppt
Research Methodology
Sistec ppt
o Companding is another popular PAPR reduction scheme. Companding is a composite word formed by combining compressing and expanding. In this scheme, at the transmitter a signal with high dynamic range is applied to a compander and at the receiver a decompanding function (the inverse of companding function) is used to recover the original signal o It increases the average power while peak remains the same therefore PAPR reduced .
function [y] = compressor(x,mu,sigma) y = (1/(sigma*sqrt(2*pi)))*exp(-((x-mu).^2)./(2*sigma^2)); end  function [y] = decompressor(x,mu,sigma) y = sqrt(-1*(2*sigma^2)*(log(sigma*sqrt(2*pi).*x))) + mu; end
PAPR =
Gaussian probability distribution is perhaps the most used distribution in all of science. It is also called “bell shaped curve” or normal distribution. Unlike the binomial and Poisson distribution, the Gaussian is a continuous distribution.
The important thing to note about a normal distribution is the curve is concentrated in the center and decreases on either side A bell curve graph depends on two factors, the mean and the standard deviation
C.L.T. tells us that under a wide range of circumstances the probability distribution that describes the sum of random variables tends towards a Gaussian distribution as the number of terms in the sum tends to infinite.
Sum of 12 uniform random numbers minus 6 is distributed as if it came from a Gaussian pdf with m = 0 and s = 1
N Orthogonal carrier SNR(dB) Sigma (σ) Mu(µ) PAPR Average power 1000 4 0-10 1 0 2.09 0.4955 10000 4 0-10 1 0 2.05 0.50246 100000 4 0-10 1 0 2.1095 0.49941 1000 8 0-10 1 0 2.02 0.49425 Performance Analysis Table1:Comparison of various parameter used in OFDM
1 2 0 0.5 1 1.5 2 2.5 Simple OFDM,OFDM compander PAPR Simulated PAPR for OFDM with and without Compander RESULTS PAPR with and without companding
0 1 2 3 4 5 6 7 8 9 10 10 -5 10 -4 10 -3 10 -2 10 -1 Eb/No, dB BitErrorRate Simulated BER for OFDM with different Codes under AWGN Channel Simple OFDM OFDM compander BER with and without companding
[1] Richard van Nee, Ramjee Prasad, OFDM wireless multimedia communication, Artech House Boston London, 2012. [2] Ahmad R. S. Bahai and Burton R. Saltzberg, Multi-carrier digital communications - Theory and applications of OFDM, Kluwer Academic / Plenum Publishers New York, Boston, Dordrecht, London, Moscow, 2011. [3] Ramjee Prasad, “OFDM based wireless broadband multimedia communication,” Letter Notes on ISCOM’99, Kaohsiung, Taiwan, Nov. 7-10, 2010. [4] L. Hanzo, W. Webb and T. Keller, Single- and multi-carrier quadrature amplitude modulation – Principles and applications for personal communications, WLANs and broadcasting, John Wiley & Sons, Ltd, 2013. [5] Mark Engels, Wireless Ofdm Systems: How to Make Them Work? Kluwer Academic Publishers. [6] Lajos Hanzo, William Webb, Thomas Keller, Single and Multicarrier Modulation: Principles and Applications, 2nd edition, IEEE Computer Society. [7] Zou, W.Y.; Yiyan Wu, “ COFDM: An overview ” Broadcasting, IEEE Transactions on, Vol. 41, Issue 1, pp. 1 –8, Mar. 2011. [8] Emmanuel C. Ifeachor & Barrie W. Jervis, Digital signal processing – A practical approach, Addision- Wesley, 2012. [9] Blahut, R. E., Fast Algorithms for digital processing. Reading, Ma: Addison-Wesley, 2011. [10] Simon Haykin, Communication Systems, John Wiley & Sons, Inc., 3rd edition, 2012. [11] Roger L. Peterson, Rodger E. Ziemer, David E. Borth, Introduction to spread spectrum communications, Prentice Hall International Editions, 2010
THANKS

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Sistec ppt

  • 1. DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING PRESENTED BY :- HEMANT CHOUBEY SISTEC-E RATIBAD DEPARTMENT OF ELECTRONICS AND COMMUNICATION www.sistec.ac.in EFFICIENT PAPR REDUCTION IN OFDM SYSTEM BASED ON A COMPANDING TECHNIQUE WITH GAUSSIAN DISTRIBUTION
  • 2. Literature survey 1 .S. H. Han and J. H. Lee, “An overview of peak-to-average power ratio reduction techniques for multicarrier transmission,” IEEE Wireless Commun., vol. 12, pp. 56– 65, Apr. 2005. 2. T. Jiang and Y.Wu, “An overview: Peak-to-average power ratio reduction techniques for OFDM signals,” IEEE Trans. Broadcast., vol. 54, no. 2, pp. 257–268, Jun. 2008. 3. C. P. Li, S. H. Wang, and C. L. Wang, “Novel low-complexity SLM schemes for PAPR reduction in OFDM systems,” IEEE Trans. Signal Process., vol. 58, no. 5, pp. 2916–2921, May 2010.
  • 3.  The Basic Principles of OFDM ◦ FFT-based OFDM System ◦ Serial and Parallel Concepts ◦ Modulation/Mapping  M-ary Phase Shift Keying  M-ary Quadrature Amplitude Modulation ◦ IFFT and FFT  Signal Representation of OFDM using IDFT/DFT ◦ Orthogonality ◦ Guard Interval and Cyclic Extension ◦ Advantages and Disadvantages ◦ Background theory ◦ Selective mapping ◦ Partial transmit sequence ◦ Companding ◦ Companding with gaussian distribution ◦ Central limit theorem ◦ Reference
  • 4. OFDM is the most popular one. The first OFDM scheme was proposed by Chang in 1966. Even though the concept of OFDM has been around for several years, but it has not been recognized as a great method for high speed bi-directional wireless data communication until recent years. The first applications of OFDM were in the military HF radio links. Today, the OFDM technique is in many wirelesses and wired applications, such as broadband radio access networks (BRAN), Digital Audio Broadcasting (DAB), Digital Video Broadcasting-Terrestrial (DVB-T) and Asymmetric Digital Subscriber Line (ADSL) Basic Principles of OFDM
  • 5. Serial-to- Parallel Converter Signal Mapper IFFT Parallel- to-Serial Converter Guard Interval Insertion Serial Data Input x bits 0d 1d 1nd 0s 1s 1ns D/A & Low pass Filter Up- Converter Down- Converter A/D Guard Interval Removal Serial-to- Parallel Converter FFT One-tap Equalizer Signal Demapper Parallel- to-Serial Converter Serial Data Output 0 ˆdx bits 1 ˆd 1 ˆ nd 0 ˆs 1 ˆs 1 ˆns Channel )(ts Time Frequency Subchannels Fast Fourier Transform Guard Intervals Symbols
  • 6. Signal Mapper (QPSK) IFFT Parallel- to-Serial Converter Guard Interval Insertion Serial-to- Parallel Converter 2d 1nd Serial Data Input    1s 2s 1ns x bits D/A & Lowpass Filter 1x 1d 2x 1nx x=[0,0,0,1,1,0,1,1,….] x1=[0,0] x2=[0,1] x3=[1,0] x4=[1,1] Q . I . . . 00 01 11 10 . I . . . 00 01 11 10 Q . . . . 00 01 11 10 I . . . . 00 01 11 10 d1=1 d2=i d3=-1 d4=-i …..
  • 7. DATA CP CP CP CP CP 1 1 1 i i d é ù ê ú ê ú ê ú ê ú= ê ú ê ú ê ú ê ú-ê úë û M 0 10 20 30 40 50 60 70 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 [ ]-0.09, -0.003-0.096i, , 0.01+ 0.247i, -0.035-0.0472is = L 0 10 20 30 40 50 60 70 80 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 Signal Mapper (QPSK) IFFT Parallel- to-Serial Converter Guard Interval Insertion Serial-to- Parallel Converter 2d 1nd Serial Data Input    1s 2s 1ns x bits D/A & Lowpass Filter 1x 1d 2x 1nx 0 10 20 30 40 50 60 70 80 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2
  • 8. In OFDM system design, the series and parallel converter is considered to realize the concept of parallel data transmission. Serial-to- Parallel Converter  Serial data Parallel data s bT NTbT 2 bT 00 t t
  • 9.  Series ◦ In a conventional serial data system, the symbols are transmitted sequentially, with the frequency spectrum of each data symbol allowed to occupy the entire available bandwidth. ◦ When the data rate is sufficient high, several adjacent symbols may be completely distorted over frequency selective fading or multipath delay spread channel.
  • 10.  Parallel ◦ The spectrum of an individual data element normally occupies only a small part of available bandwidth. ◦ Because of dividing an entire channel bandwidth into many narrow subbands, the frequency response over each individual subchannel is relatively flat. ◦ A parallel data transmission system offers possibilities for alleviating this problem encountered with serial systems.  Resistance to frequency selective fading
  • 11.  The process of mapping the information bits onto the signal constellation plays a fundamental role in determining the properties of the modulation.  An OFDM signal consists of a sum of sub- carriers, each of which contains 1. M-ary Phase Shift Keying (PSK) or 2. Quadrature Amplitude Modulated (QAM) signals.
  • 12.  M-ary phase shift keying ◦ Consider M-ary phase-shift keying (M-PSK) for which the signal set is where is the signal energy per symbol, is the symbol duration, and is the carrier frequency. ◦ This phase of the carrier takes on one of the M possible values, namely , where 2 12 cos 2 0 , 1,2,...,s i c s s iE s t f t t T i M T M 2 1i i M 1,2,...,i M sE sT cf
  • 13. An example of signal-space diagram for 8-PSK . sE 2m 3m 4m 5m 6m 7m 8m Decision boundary 2 message point sE sE d d M M 1m Decision region 1 sE
  • 14. An example of signal-space diagram for 16-square QAM.
  • 15. Time domain Frequency domain Example of four subcarriers within one OFDM symbol Spectra of individual subcarriers
  • 16. Two different sources of interference can be identified in the OFDM system. ◦ Inter Symbol Interference (ISI) - crosstalk between signals within the same sub-channel of consecutive FFT frames, which are separated in time by the signaling interval T. ◦ Inter Carrier Interference (ICI) - crosstalk between adjacent sub channels or frequency bands of the same FFT frame.
  • 17. Delay spread Environment Delay Spread Home < 50 ns Office ~ 100 ns Manufactures 200 ~ 300 ns Suburban < 10 us
  • 18. If Tg < Tdely-spread Tg Symbol 1 Tg Symbol 2 Tg Symbol 3 Tg Symbol 4 Tdely-spread If Tg > Tdely-spread Tg Symbol 1 Tg Symbol 2 Tg Symbol 3 Tg Symbol 1 Tg Symbol 2 Tg Symbol 3 Tg Symbol 4 Tg Symbol 1 Tg Symbol 2 Tg Symbol 3 Tdely-spread ﹒ ﹒ ﹒ ﹒ ﹒ ﹒ ﹒ ﹒ ﹒ ﹒ ﹒ ﹒ ﹒ ﹒ ﹒ ﹒
  • 19. o To eliminate ICI, the OFDM symbol is cyclically extended in the guard interval. o This ensures that delayed replicas of the OFDM symbol always have an integer number of cycles within the FFT interval, as long as the delay is smaller than the guard interval. Guard Interval (Cyclic Extension)
  • 20. Effect of multipath with zero signals in the guard interval, the delayed subcarrier 2 causes ICI on subcarrier 1 and vice versa. Part of subcarrier #2 causing ICI on subcarrier #1 Guard time FFT integration time=1/carrier spacing Guard time FFT integration time=1/carrier spacing OFDM symbol time OFDM symbol time Subcarrier #1 Delayed subcarrier #2
  • 21. Time and frequency representation of OFDM with guard intervals. Time Frequency T Tg 1/T Subchannels Fast Fourier Transform Guard Intervals Symbols
  • 22. ◦ Immunity to delay spread ◦ Resistance to frequency selective fading ◦ Simple equalization ◦ Efficient bandwidth usage
  • 23. ◦ The problem of synchronization  Symbol synchronization  Frequency synchronization ◦ Need FFT units at transmitter, receiver
  • 24. ◦ Sensitive to carrier frequency offset ◦ Problem of high peak to average power ratio (PAPR) Problem 1. Increased complexity of ADC and DAC. Problem 2. Reduced efficiency of the RF power amplifier. Solutions  Signal distortion techniques  Special forward-error-correction code  Scrambling
  • 25. Various reduction techniques of peak to average power reduction (PAPR) of ofdm. o Selective mapping o Partial transmit sequence o Companding
  • 31. o Companding is another popular PAPR reduction scheme. Companding is a composite word formed by combining compressing and expanding. In this scheme, at the transmitter a signal with high dynamic range is applied to a compander and at the receiver a decompanding function (the inverse of companding function) is used to recover the original signal o It increases the average power while peak remains the same therefore PAPR reduced .
  • 32. function [y] = compressor(x,mu,sigma) y = (1/(sigma*sqrt(2*pi)))*exp(-((x-mu).^2)./(2*sigma^2)); end  function [y] = decompressor(x,mu,sigma) y = sqrt(-1*(2*sigma^2)*(log(sigma*sqrt(2*pi).*x))) + mu; end
  • 34. Gaussian probability distribution is perhaps the most used distribution in all of science. It is also called “bell shaped curve” or normal distribution. Unlike the binomial and Poisson distribution, the Gaussian is a continuous distribution.
  • 35. The important thing to note about a normal distribution is the curve is concentrated in the center and decreases on either side A bell curve graph depends on two factors, the mean and the standard deviation
  • 36. C.L.T. tells us that under a wide range of circumstances the probability distribution that describes the sum of random variables tends towards a Gaussian distribution as the number of terms in the sum tends to infinite.
  • 37. Sum of 12 uniform random numbers minus 6 is distributed as if it came from a Gaussian pdf with m = 0 and s = 1
  • 38. N Orthogonal carrier SNR(dB) Sigma (σ) Mu(µ) PAPR Average power 1000 4 0-10 1 0 2.09 0.4955 10000 4 0-10 1 0 2.05 0.50246 100000 4 0-10 1 0 2.1095 0.49941 1000 8 0-10 1 0 2.02 0.49425 Performance Analysis Table1:Comparison of various parameter used in OFDM
  • 39. 1 2 0 0.5 1 1.5 2 2.5 Simple OFDM,OFDM compander PAPR Simulated PAPR for OFDM with and without Compander RESULTS PAPR with and without companding
  • 40. 0 1 2 3 4 5 6 7 8 9 10 10 -5 10 -4 10 -3 10 -2 10 -1 Eb/No, dB BitErrorRate Simulated BER for OFDM with different Codes under AWGN Channel Simple OFDM OFDM compander BER with and without companding
  • 41. [1] Richard van Nee, Ramjee Prasad, OFDM wireless multimedia communication, Artech House Boston London, 2012. [2] Ahmad R. S. Bahai and Burton R. Saltzberg, Multi-carrier digital communications - Theory and applications of OFDM, Kluwer Academic / Plenum Publishers New York, Boston, Dordrecht, London, Moscow, 2011. [3] Ramjee Prasad, “OFDM based wireless broadband multimedia communication,” Letter Notes on ISCOM’99, Kaohsiung, Taiwan, Nov. 7-10, 2010. [4] L. Hanzo, W. Webb and T. Keller, Single- and multi-carrier quadrature amplitude modulation – Principles and applications for personal communications, WLANs and broadcasting, John Wiley & Sons, Ltd, 2013. [5] Mark Engels, Wireless Ofdm Systems: How to Make Them Work? Kluwer Academic Publishers. [6] Lajos Hanzo, William Webb, Thomas Keller, Single and Multicarrier Modulation: Principles and Applications, 2nd edition, IEEE Computer Society. [7] Zou, W.Y.; Yiyan Wu, “ COFDM: An overview ” Broadcasting, IEEE Transactions on, Vol. 41, Issue 1, pp. 1 –8, Mar. 2011. [8] Emmanuel C. Ifeachor & Barrie W. Jervis, Digital signal processing – A practical approach, Addision- Wesley, 2012. [9] Blahut, R. E., Fast Algorithms for digital processing. Reading, Ma: Addison-Wesley, 2011. [10] Simon Haykin, Communication Systems, John Wiley & Sons, Inc., 3rd edition, 2012. [11] Roger L. Peterson, Rodger E. Ziemer, David E. Borth, Introduction to spread spectrum communications, Prentice Hall International Editions, 2010