2. OFDM Adaptive Modulation Reduction of Peak-to-Average Power Ratio Channel estimation OFDM in frequency selective fading channel Puja Thakral Silvija Kokalj-Filipovic Youngsik Lim Sadhana Gupta

3. OUTLINE Introduction to OFDM Introduction to OFDM Adaptive Modulation Adaptive Modulation Reduction of Peak-to-Power Average Ratio Reduction of Peak-to-Power Average Ratio OFDM in Frequency Selective Fading Channel OFDM in Frequency Selective Fading Channel Channel Estimation Channel Estimation Conclusions Conclusions

4. OFDM SYSTEM

5. Baseband Transmitter

6. Baseband Ideal Receiver

7. Adaptive Modulation In OFDM,adaptive bit loading algorithms set the modulation level in each frequency band such that a predefined total number of bits are transmitted with minimum power.Adaptive Modulation independently optimizes the modulation scheme to each sub carrier so that spectral efficiency is maximized,while maintaining a target Bit Error Rate(BER). In OFDM,adaptive bit loading algorithms set the modulation level in each frequency band such that a predefined total number of bits are transmitted with minimum power.Adaptive Modulation independently optimizes the modulation scheme to each sub carrier so that spectral efficiency is maximized,while maintaining a target Bit Error Rate(BER).

8. OFDM Block Structure With Adaptive Modulation S/P IFFTFFT P/S FREQUENCY SELECTIVE CHANNEL MODULATOR 1 MODULATOR 2 MODULATOR N DEMODULATOR 1 DEMODULATOR 2 DEMODULATOR N CHANNEL ESTIMATION ADAPTIVE BIT AND POWER ALLOCATION +

9. Various Algorithms in Adaptive Modulation For a given target BER and bit-rate, the total transmit power can be minimized by optimally distributing the power and bit-rate across the sub channels. For a given target BER and bit-rate, the total transmit power can be minimized by optimally distributing the power and bit-rate across the sub channels. For a given target BER and power transmitted,the total bit-rate can be maximized. For a given target BER and power transmitted,the total bit-rate can be maximized. For a given target power and bit rate,the total BER can be minimized. For a given target power and bit rate,the total BER can be minimized.

10. ALGORITHM Compute the subchannel signal to noise ratios. Compute the subchannel signal to noise ratios. Compute the number of bits for the ith subchannel based on the formula, b`(i)=log2(1+SNR(i)) Compute the number of bits for the ith subchannel based on the formula, b`(i)=log2(1+SNR(i)) Round the value of b`(i) down to b(i). Round the value of b`(i) down to b(i). Restrict b(i) to take the values 0,1,2,4,6,8 Restrict b(i) to take the values 0,1,2,4,6,8 Compute the energy for the ith subchannel based on the number of bits initially assigned to it using the formula e(b(i))=(2^b(i)-1)/SNR Compute the energy for the ith subchannel based on the number of bits initially assigned to it using the formula e(b(i))=(2^b(i)-1)/SNR

11. RESULTS

12. FUTURE WORK Feasibility study of MIMO OFDM systems Feasibility study of MIMO OFDM systems Simulation of MIMO OFDM system with adaptive modulation and multilevel transmit power control. Simulation of MIMO OFDM system with adaptive modulation and multilevel transmit power control.

13. Peak To Average Power Ratio in OFDM Causes, Effects and Reduction Methods Silvija Kokalj-Filipovic

14. Summary Goal: reducing maximum output power to near average power by limiting the set of transmitted signals through coding Goal: reducing maximum output power to near average power by limiting the set of transmitted signals through coding Complementary Golay Sequences have peak-to-average power less then 2 Complementary Golay Sequences have peak-to-average power less then 2 Reed-Muller Coding used to produce these sequences out of information sequence Reed-Muller Coding used to produce these sequences out of information sequence

15. Stochastic Structure In accordance with CLT, when large number of modulated carriers (N) are combined into a composite time-domain signal by means of IFFT (they are assumed to be independent, since the assigned data symbols are iid ( µ 0, σ 0 )), it leads to near Gaussian pdf of amplitude, where the amplitude value exceeds certain threshold value A with probability Q(A- µ /σ), and In accordance with CLT, when large number of modulated carriers (N) are combined into a composite time-domain signal by means of IFFT (they are assumed to be independent, since the assigned data symbols are iid ( µ 0, σ 0 )), it leads to near Gaussian pdf of amplitude, where the amplitude value exceeds certain threshold value A with probability Q(A- µ /σ), and µ ~ Nµ 0 σ ~ Nσ 0 µ ~ Nµ 0 σ ~ Nσ 0

16. Since we have N independent points in the composite time signal: Since we have N independent points in the composite time signal: –For BPSK modulation we ’ ll have ~ Gaussian distribution of the amplitude –For MPSK and M-QAM modulations (which both have 2-dimensional space: I and Q component ) we have a Rayleigh distribution (square root of the sum of squares of I & Q Gaussian random variables ). –Cumulative distribution of power: F (z) = 1-e -z

17. Definition of PAPR (PMEPR) PAPR & PAR: Peak-To-Average Power Ratio PAPR & PAR: Peak-To-Average Power Ratio PMEPR: Peak-To-Mean Envelope Power Ratio PMEPR: Peak-To-Mean Envelope Power Ratio Crest factor of x(t): square root of PAR Crest factor of x(t): square root of PAR Definition: PAR = (||x|| ∞ ) 2 / E[(||x|| 2 ) 2 ] Definition: PAR = (||x|| ∞ ) 2 / E[(||x|| 2 ) 2 ]

18. Crest Factor - notation The crest factor of u(t): square root of PMEPR where is the maximum absolute value of u(t) and is the rms of u(t):

19. Effects of PAPR The power amplifiers at the transmitter need to have a large linear range of operation. The power amplifiers at the transmitter need to have a large linear range of operation. nonlinear distortions and peak amplitude limiting introduced by the High Power amplifier (HPA) will produce inter-modulation between the different carriers and introduce additional interference into the system. nonlinear distortions and peak amplitude limiting introduced by the High Power amplifier (HPA) will produce inter-modulation between the different carriers and introduce additional interference into the system. additional interference leads to an increase in the Bit Error Rate (BER) of the system. additional interference leads to an increase in the Bit Error Rate (BER) of the system. one way to avoid non-linear distortion is by forcing the amplifier to work in its linear region. Unfortunately such solution is not power efficient and thus not suitable for wireless communication. one way to avoid non-linear distortion is by forcing the amplifier to work in its linear region. Unfortunately such solution is not power efficient and thus not suitable for wireless communication. –The Analog to Digital converters and Digital to Analog converters need to have a wide dynamic range and this increases complexity. if clipped, it leads to in-band distortion (additional noise) and ACI (out-of-band radiation) if clipped, it leads to in-band distortion (additional noise) and ACI (out-of-band radiation)

20. Classification of PAR reduction methods BLOCK CODING (Golay sequences) BLOCK CODING (Golay sequences) CLIP EFFECT TRANSFORMATION CLIP EFFECT TRANSFORMATION PROBABILISTIC TECHNIQUES: PROBABILISTIC TECHNIQUES: –Selective Mapping (SLM) and Partial Transmit Sequences (PTS) –Tone Reduction (TR) and Tone Injection (TI)

21. Representation of OFDM signal In the bandpass with = the multi-carrier (multitone) signal can be represented as In the bandpass with = the multi-carrier (multitone) signal can be represented as where corresponds to initial phase of the tones, i.e. the effect of modulating data. where corresponds to initial phase of the tones, i.e. the effect of modulating data.

22. Representation of OFDM signal assuming t is the frequency and 1/T is the sampling period of sequence is the discrete complex sequence of information data (phase-mapped). Crest factor depends on the maximum absolute value of the multicarrier signal, and that one depends on the “amplitude spectrum” of the complex sequence Choosing to be complementary Golay sequence crest factor of less than 6dB (PAPR of 3 dB) can be obtained Observation: OFDM has somewhat inverted logic – we are looking for flat PSD in time domain, while autocorrelation is taken in frequency domain

23. Proof: Aperiodic Aperiodic correlation C x (z) C x (z) of some sequence The Fourier transform S x (f) S x (f) of sequence Definition: Two sequences and of the length N form a complementary pair if –Golay –Golay complementary sequences have that property. where Ts is the sampling period of sequence

24. N carrier OFDM; H-PSK modulation N carrier OFDM; H-PSK modulation Information-bearing sequence is Information-bearing sequence is in fact an OFDM codeword and is the primitive H-root of unity (j in QPSK case) in fact an OFDM codeword and is the primitive H-root of unity (j in QPSK case) Instantaneous Envelope Power Instantaneous Envelope Power For complementary sequences:

25. Theory behind Reed-Muller codes An rth order Reed-Muller code R(r,m) is the set of all binary strings (vectors) of length n= 2 m associated with the Boolean polynomials p(x1, x2, …, xm) of degree at most r. An rth order Reed-Muller code R(r,m) is the set of all binary strings (vectors) of length n= 2 m associated with the Boolean polynomials p(x1, x2, …, xm) of degree at most r. A Boolean polynomial is a linear combination of Boolean monomials with coefficients in F2. A Boolean monomial p in the variables x1, x2, …, xm is the expression of the form: A Boolean polynomial is a linear combination of Boolean monomials with coefficients in F2. A Boolean monomial p in the variables x1, x2, …, xm is the expression of the form: P = x 1 r 1 x 2 r 2 …, x m r m where r i {0,1,2..} and 1 ≤ i ≤ m. P = x 1 r 1 x 2 r 2 …, x m r m where r i {0,1,2..} and 1 ≤ i ≤ m. Degree of a monomial is deduced from it reduced form (after rules x i x j = x j x i and x i 2 = x i are applied), and it is equal to the number of variables. This rule extends to polynomials Degree of a monomial is deduced from it reduced form (after rules x i x j = x j x i and x i 2 = x i are applied), and it is equal to the number of variables. This rule extends to polynomials Ex. of a polynomial of degree 3: Ex. of a polynomial of degree 3: –q = x1+ x2+x1 x2+ x1 x2 x3 How to associate Boolean monomial in m variables to a vector with 2 m entries: How to associate Boolean monomial in m variables to a vector with 2 m entries: –a vector associated with monomial of degree 0 (1) is a string of length 2 m where each entry is 1. –a vector associated with monomial x1 is 2 m-1 ones followed by 2 m-1 zeros. –a vector associated with monomial x2 is 2 m-2 ones followed by 2 m-2 zeros, then another 2 m-2 ones followed by 2 m-2 zeros. –a vector associated with monomial xi is a pattern of 2 m-i ones followed by 2 m-i zeros, repeated until 2 m values are defined.

26. Example of RM generator matrix m = 5: RM(1,5) has six rows m = 5: RM(1,5) has six rows X0: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X0: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X1: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X1: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X2: 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 X2: 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 X3: 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 X3: 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 X4: 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 X4: 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 X5: 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 X5: 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

27. Relationship between Reed-Muller codes and Complementary Golay Sequences In the binary case, Golay pairs and sets occur in the first-order Reed-Muller code RM(1,m) within the second-order Reed-Muller code (cosets). In the binary case, Golay pairs and sets occur in the first-order Reed-Muller code RM(1,m) within the second-order Reed-Muller code (cosets). Each coset has assigned coset representative of the form: Each coset has assigned coset representative of the form: where is any permutation of the sequence of generator matrix rows – see graph with rows as hypercube vertices where is any permutation of the sequence of generator matrix rows – see graph with rows as hypercube vertices : number of elements in the Galois field : number of elements in the Galois field

28. Simulation

30. Conclusions and Further Work Result: complete elimination of clipping noise Result: complete elimination of clipping noise Drawback: serious overhead (low bandwidth utilization – 17/32) Drawback: serious overhead (low bandwidth utilization – 17/32) Further work: Further work: –implementation of Tone Reservation Algorithm and Comparison with Golay Sequences –Extension of the method to Golay sequences that do not form complementary pairs but have satisfying PAR (coset representatives of different forms)

31. Conclusions and Further Work Result: complete elimination of clipping noise Result: complete elimination of clipping noise Drawback: serious overhead (low bandwidth utilization – 17/32) Drawback: serious overhead (low bandwidth utilization – 17/32) Further work: Further work: –implementation of Tone Reservation Algorithm and Comparison with Golay Sequences –Extension of the method to Golay sequences that do not form complementary pairs but have satisfying PAR (coset representatives of different forms)

32. Cyclic prefix of OFDM in frequency selective fading channel

33.  Signal distortion in frequency selective fading channel  What is the cyclic prefix ?  How is the interference eliminated with cyclic prefix?  How is its performance without the cyclic prefix. Problem Description

34. Transmission over frequency selective fading channel(*) Pulse Shaping  Tx +  (t) h(n) Channel  ch Receive Filter  Rx t=nTs +  (n) H 0 +H 1 z -1 +  (n) (*) Z. Wang, G.B. Giannakis, Wireless Multicarrier Communications. IEEE 2000 Signal Processing Magazine

35. (**) Frequency selective Flat fading channel(Naftali Chayat in IEEE P802.11-97/96) Black : Average, Gray : a realization of the channel  Channel response Dispersive in time, Static over block interval Selective in frequency Channel Model (**)

36. N+L N Memory from the past block H U What is H 0 and H 1 ?

37. How is IBI deleted ? T cp H 0 +H 1 z -1 + R cp

38. Cyclic prefix effect on OFDM S/PMapping + OFDM............ IFFT...... FFT Input bits Demapping...... P/S...... Output bits No IBI plus simpler equalizer

39. Simulation configuration Simulation configuration – Perfect channel estimation, QPSK, Fixed sub-channel power – Zero Forcing equalization – 64 sub-carriers Simulation Results Simulation Results

43. L = 7 14 22 14 7 0 7 21 43 57 64 Subcarrier numbers 1 to 64 802.11a Pilot subcarrier placement -21-7 0 7 21 Subcarrier numbers-31 to 32 Pilot subcarrier placement used

50. Conclusions and future work: Low pass filtering interpolation shows best performance among evaluated interpolation methods as reported in literature, especially for larger values of Trms. Future work: Evaluation of performance of differential modulation Evaluation with Doppler frequency shift Primary Reference: Channel Estimation Techniques based on Pilot Arrangement in OFDM Systems Coleri, et al, IEEE Transactions on Broadcasting, p223-229 September 2002