Sajjad Hussain - Peak to Average Power Ratio Analysis and Reduction of Cognitive Radio Signals

Peak to Average Power Ratio Analysis and Reduction of Cognitive
Radio Signals Sajjad HUSSAIN Equipe Signal, Communication et Electronique Embarquée, Supélec, IETR Ecole Doctorale Matisse, Université de Rennes-1 Directeurs de thèse: Jacques PALICOT, Yves LOUËT 21 Octobre 2009

Contexte des études OFDM: Orthogonal Frequency Division Multiplexing Principe d’un
multiplex de porteuses orthogonales. SWR: SoftWare Radio (radio logicielle) une même architecture supportant plusieurs standards => notion de multiplex de standards. CR: Cognitive Radio (radio intelligente) un système radio logicielle intelligent associé à des capteurs et des prises de décisions.

multiplex de porteuses orthogonales. SWR: SoftWare Radio (radio logicielle) une même architecture supportant plusieurs standards => notion de multiplex de standards. CR: Cognitive Radio (radio intelligente) un système radio logicielle intelligent associé à des capteurs et des prises de décisions. Caractéristiques communes multiplex de porteuses modulées

multiplex de porteuses orthogonales. SWR: SoftWare Radio (radio logicielle) une même architecture supportant plusieurs standards => notion de multiplex de standards. CR: Cognitive Radio (radio intelligente) un système radio logicielle intelligent associé à des capteurs et des prises de décisions. Caractéristiques communes multiplex de porteuses modulées Conséquence Fortes fluctuations de puissance (forts Peak to Average Power Ratio (PAPR)) des signaux pouvant générer des distorsions non linéaires dues aux amplificateurs de puissance et limiter le rendement des amplificateurs.

Objectifs des études Analyse de la distribution du PAPR des
signaux OFDM et SWR en radio fréquence. Réduction du PAPR de signaux SWR à l’aide de méthodes appropriées. Etude du compromis complexité/performance de ces méthodes. Etude de l’inﬂuence de l’accès opportuniste au spectre sur le PAPR dans le contexte de la radio intelligente.

Objectifs des études Analyse de la distribution du PAPR des
signaux OFDM et SWR en radio fréquence. Réduction du PAPR de signaux SWR à l’aide de méthodes appropriées. Etude du compromis complexité/performance de ces méthodes. Etude de l’inﬂuence de l’accès opportuniste au spectre sur le PAPR dans le contexte de la radio intelligente. En résumé Réduire le PAPR des systèmes multi-standards.

Outline 1 Multi carrier signals and non-linear ampliﬁcation Multi carrier
signals and systems High PAPR and Non-linear ampliﬁcation 2 Our contribution I: PAPR Analysis of RF signals Continuous OFDM signals SWR signals Carrier per Carrier PAPR view 3 Our contributions II: PAPR Reduction of SWR signals PAPR reduction method: TR-SOCP TR application on SWR signal MB-OFDM PAPR reduction MC-GSM PAPR reduction Bi-standard SWR PAPR reduction OOB PRC parameter effect on PAPR reduction performance 4 Our contributions III: TR Methods Comparison TR Schemes TR comparison for WLAN system TR comparison for MC-GSM system TR comparison for Bi-standard SWR TR complexity reduction 5 Our contributions IV: PAPR Reduction in CR context PAPR variations on spectrum access PAPR reduction in CR context using joint spectrum access scheme 6 Conclusions & Perspectives Conclusions Perspectives

MC signals and HPA PAPR Analysis of RF signals PAPR
Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Multi carrier signals and systems OFDM System Orthogonal Frequency Division Multiplexing (OFDM) is a multi-carrier modulation scheme. Transmission over multiple orthogonal carriers with the help of IFFT. Used in many high data rate standards like Digital Audio Broadcasting (DAB), Terrestrial Digital Video Broadcasting (DVB-T), Wireless Local Area Network (WLAN), Worldwide Interoperability for Microwave Access (WiMAX) etc. RX data RECEIVER Para. IFFT to Para. to Serial HPA LNA FFT Serial Serial to Para. Para. to Serial RF TRANSMITTER TX data Serial Serial Figure: OFDM Transceiver 1

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Multi carrier signals and systems OFDM Signal Discrete time OFDM signal s(n): s(n) = N−1 k=0 Ck e2jπ kn N , where 0 ≤ n ≤ N − 1 and N is the IFFT size. Also Ck are the mapped data values OFDM Sub-carriers OFDM Symbol Envelope Figure: OFDM symbol envelope and sub-carriers ⇒ Advantages: Immunity to selective channel fading (Inter-symbol interference reduction). High spectral efﬁciency. Simple channel equalization and transceiver implementation. ⇒ Disadvantages: High signal ﬂuctuations. Sensitive to frequency and timing offsets and phase noise. 2

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Multi carrier signals and systems SWR System ‘All digital’ reconﬁgurable architecture with all the processing performed in digital domain. Ideally, (de)modulation of one or more channels without ﬁltering and down conversion of the analog signal. LNA ADC high frequency and large band DAC Duplexer or Switch AMP DSP high frequency and large band Figure: Ideal SWR block diagram. 3

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Multi carrier signals and systems SWR Signal Arbitrary Amplitude GSM DVB-T Arbitrary Amplitude GSM UMTS WiLAN ~900 MHz ~2 GHz frequency DVB-T ~700 MHz WiMAX ~2.4 GHz SWR signal x(t) is a composite signal given by, x(t) = S i=1 Si (t), (1) where each signal Si (t) associated to a given standard of Pi carriers can be expressed as, Si (t) = Pi p=1 ri,p(t)e2iπfi,pt , where ri,p(t) represents the modulated and ﬁltered signal associated to carrier p of the standard i. A multi-standard signal can be written as, x(t) = S i=1 Pi p=1 (femi (t) ∗ mi,p(c(t))e2iπfi,pt . (2) 4

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Multi carrier signals and systems CR System ⇒ Mitola Deﬁnition: "A radio or system that senses, and is aware of, its operational environment and can dynamically and autonomously adjust its radio operating parameters accordingly." ⇒ FCC Deﬁnition: "A radio frequency transmitter/receiver that is designed to intelligently detect whether a particular segment of the radio spectrum is currently in use, and to jump into (and out of, as necessary) the temporarily-unused spectrum dynamically, without interfering with the transmissions of other authorized users." Flexible RF Flexible RF Flexible RF Flexible Baseband Network Processor (MAC+) CR Strategy (host) Flexible Antenna A/D/AA Baseband & Network Processor Board (Rutgers & Lucent) Antenna & RF Board (Georgia Tech.) A/D/A Board (Rutgers) A/D/AA A/D/AA Figure: SWR based CR block diagram. 5

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Multi carrier signals and systems SWR Signal in CR context SWR signal x(t) in the context of CR would become, x(t) = S i=1 Pi p=1 (femi (t) ∗ mi,p(c(t))e2iπfi,pt + U u=1 (fem(t) ∗ mu(c(t))e2iπfut (3) where U is the number of unlicensed carriers. Figure: Spectrum access in a multi-standard system scenario. 6

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Multi carrier signals and systems SWR Signal in CR context SWR signal x(t) in the context of CR would become, x(t) = S i=1 Pi p=1 (femi (t) ∗ mi,p(c(t))e2iπfi,pt + U u=1 (fem(t) ∗ mu(c(t))e2iπfut (3) where U is the number of unlicensed carriers. Figure: Spectrum access in a multi-standard system scenario. OFDM and SWR, both are multi-carrier signals. 6

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P High PAPR and Non-linear amplification PAPR Multi-carrier signal fluctuations are very high due to multiplicity of carriers. Power fluctuations commonly termed as Peak to Average Power Ratio (PAPR). Continuous signal case: PAPR{s(t)} = max t∈[0,T] |s(t)|2 1 T T |s(t)|2dt . (4) where T is the time of integration. Discrete signal case: PAPR{s} = max k∈[0,Ns−1] |s(k)|2 1 Ns Ns−1 k=0 |s(k)|2 . (5) where Ns are the number of symbol samples. High PAPR Disadvantage! Transmitter non-linear components sensitive to high signal fluctuations, one of them is High Power Amplifier (HPA). 7

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P High PAPR and Non-linear amplification High Power Amplifier (HPA) and non-linear distortions A very important transmitter components which consumes 60-70% of terminal consumption. Consumption at HPA should be reduced in order to reduce terminal consumption. Base band processings RF Stages High Power Amplifier Seminar SCEE 22 Power supply DAC/ADC ~70% ~15% ~15% Figure: Typical 2.5 G terminal consumption budget. HPA operated at high efficiency region.⇒ Non-linear distortions. HPA operated at low efficiency region.⇒ High terminal consumption. PAPR Power efficiency Input signal Signal to be amplified peak power ηmax 1 dB compression Point (maximum output) ηmin P saturation Power Gain Pin Pout 1 dB IBO* Input signal average power Efficiency η Figure: Trade-off between HPA efficiency and non-linear distortions. 8

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P High PAPR and Non-linear ampliﬁcation HPA non-linear distortions in CR context PAPR varied on spectrum access. Measures should be taken to counter these variations. after spectrum insertion w/o taking PAPR into account Solution 1 : Large IBO >> Low PA efficiency Solution 2 : Insertion with PAPR constraint >>High PA efficiency Pout Power Amplifier efficiency Psat Pin IBO Low efficiency zone High efficiency zone Pm1 Pm2 Pout Power Amplifier efficiency Psat Pin IBO before spectrum insertion Figure: Spectrum access effect on PAPR and in turns on PA efﬁciency. 9

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P High PAPR and Non-linear ampliﬁcation HPA non-linear distortions in CR context PAPR varied on spectrum access. Measures should be taken to counter these variations. after spectrum insertion w/o taking PAPR into account Solution 1 : Large IBO >> Low PA efficiency Solution 2 : Insertion with PAPR constraint >>High PA efficiency Pout Power Amplifier efficiency Psat Pin IBO Low efficiency zone High efficiency zone Pm1 Pm2 Pout Power Amplifier efficiency Psat Pin IBO before spectrum insertion Figure: Spectrum access effect on PAPR and in turns on PA efﬁciency. Our approach: PAPR reduction. 9

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P High PAPR and Non-linear amplification PAPR reduction methods’ classification A large number of PAPR reduction techniques have been developed in literature and classified[1]. Tone Reservation Clipping Convex interior point method efficiency yes yes Methods at the transmitter treatements targets ? down compatibility ? yes no Coding Pulse shaping Signal companding no Partial Transmit Sequences Selected Mapping Treillis shaping Tone Injection bit error rate degradation ? Peak windowing no SOCP on unused carriers Active Set data rate loss ? Invertible clipping Hadamard change the amplifier ? down compatibility ? type of linearization model comparison Predistorsion Feed-back yes no LIST yes no LINC EER CALLUM linearity —————————————————————————————————————- 1 Y. Louët and J. Palicot, “A classification of methods for efficient power amplification of signals,” Annals of Telecom, vol. 63, pp. 351–368, July/August 2008. 10

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P High PAPR and Non-linear ampliﬁcation Selected method: Tone Reservation We wanted to use a method which is 1 Downward compatible (no receiver modiﬁcations). 2 No BER degradation. 3 No Side Information (SI) transmission required.

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P High PAPR and Non-linear amplification Selected method: Tone Reservation We wanted to use a method which is 1 Downward compatible (no receiver modifications). 2 No BER degradation. 3 No Side Information (SI) transmission required. Tone Reservation[2] when applied with certain constraints satisfies our demands data carriers data carriers data carriers X unused carriers unused carriers 0 …….. 0 0…0 C corrected carriers corrected carriers 0 ………….. 0 0 ……………... 0 0 ……….…….. 0 corrected carriers corrected carriers data carriers data carriers data carriers X+C Figure: Block diagram of Tone Reservation process. NL−IFFT NL−IFFT x + c CNL−1 XNL−1 C X x c X0 X1 C0 C1 DAC PA fc Figure: TR methodology based PAPR reduction. —————————————————————————————————————- 2 J. Tellado-Mourelo, “Peak to Average Power Ratio Reduction for multicarrier modulation”, PhD Thesis, Stanford University, 1999. 11

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Recap PAPR of multi-carrier signals like OFDM, SWR signal is very high. To avoid PA non-linear distortions, PAPR should be reduced. TR selected as the method to reduce PAPR.

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Recap PAPR of multi-carrier signals like OFDM, SWR signal is very high. To avoid PA non-linear distortions, PAPR should be reduced. TR selected as the method to reduce PAPR. Up next Statistical analysis of multi-carrier signal PAPR.

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Outline 1 Multi carrier signals and non-linear ampliﬁcation Multi carrier signals and systems High PAPR and Non-linear ampliﬁcation 2 Our contribution I: PAPR Analysis of RF signals Continuous OFDM signals SWR signals Carrier per Carrier PAPR view 3 Our contributions II: PAPR Reduction of SWR signals PAPR reduction method: TR-SOCP TR application on SWR signal MB-OFDM PAPR reduction MC-GSM PAPR reduction Bi-standard SWR PAPR reduction OOB PRC parameter effect on PAPR reduction performance 4 Our contributions III: TR Methods Comparison TR Schemes TR comparison for WLAN system TR comparison for MC-GSM system TR comparison for Bi-standard SWR TR complexity reduction 5 Our contributions IV: PAPR Reduction in CR context PAPR variations on spectrum access PAPR reduction in CR context using joint spectrum access scheme 6 Conclusions & Perspectives Conclusions Perspectives 13

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Continuous OFDM signals Deterministic PAPR study Deterministic PAPR upper bound: PAPR(x) ≤ N max 0≤k≤N−1 |Ck |2 E{|Ck |2} . (6) The above inequality turns to equality only if the value of all Ck ’s is maximal. In phase modulation schemes, maximum and mean power is same and hence, PAPRmax,PSK = N. (7) In M-ary QAM modulation, maxk |Ck |2 = 2( √ M − 1)2 and E{|Ck |2} = 2 3 ( √ M − 1). Thus PAPRmax would be, PAPRmax,M−QAM = 3N √ M − 1 √ M + 1 , (8) where M is the number of modulation states. The probability that PAPR reaches its maximum value is 1 MN−2 For IEEE 802.11 a/g standard, the theoretically maximum PAPR shall be observed statistically only once in 2 × 1018 million years!

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Continuous OFDM signals Deterministic PAPR study Deterministic PAPR upper bound: PAPR(x) ≤ N max 0≤k≤N−1 |Ck |2 E{|Ck |2} . (6) The above inequality turns to equality only if the value of all Ck ’s is maximal. In phase modulation schemes, maximum and mean power is same and hence, PAPRmax,PSK = N. (7) In M-ary QAM modulation, maxk |Ck |2 = 2( √ M − 1)2 and E{|Ck |2} = 2 3 ( √ M − 1). Thus PAPRmax would be, PAPRmax,M−QAM = 3N √ M − 1 √ M + 1 , (8) where M is the number of modulation states. The probability that PAPR reaches its maximum value is 1 MN−2 For IEEE 802.11 a/g standard, the theoretically maximum PAPR shall be observed statistically only once in 2 × 1018 million years! Need of statistical analysis. 14

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Continuous OFDM signals Statistical properties CCDF of PAPR for a base band OFDM signal x = [x0 , ..., xN−1] can be given by the relation: Pr PAPRd {x} > γ ≈ 1 − (1 − e−γ)N . (9) The relation (9) is only valid for an oversampling factor L = 1. For an oversampling factor L > 4, Pr PAPRc {x} > γ ≈ 1 − (1 − e−γ)τ1N , (10) where τ1 ≈ 2.8 is a constant obtained by simulations. An analytical CCDF upper bound for L > 4 is given, Pr PAPRc {x} > γ ≈ N π 3 γe−γ. (11) 2 4 6 8 10 12 10-3 10-2 10-1 100 γ (in dB) CCDF = Pr(PAPR>γ) L=1 L=8 1-(1-e-γ)N 1-(1-e-γ)2.8N N(γ π/3)0.5e-γ 15

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Continuous OFDM signals Proposed first order analysis Starting from a analytically developed PAPR distribution function we calculated mean PAPR. By definition, first statistical order is related to density function fc(γ) = d(Fc(γ))/dγ by, mc(N) = +∞ −∞ γfc(γ)dγ. (12) Using Eq. 11 calculated mean: mc,a(N) ≈ µ(lnN + ln α √ e ) = 1.07ln( 5.12 √ e N). (13) When compared to the one given by simulations: mc,s(N) ≈ lnN + ζ + lnτ1 ≈ lnN + 1.60. (14) 16

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Continuous OFDM signals Proposed Distribution Function With the help of mean, a new PAPR distribution function was calculated: Fc,a(γ) ≈ (1 − e−γ)τ2Nµ = (1 − e−γ)τ2N1.07 . (15) where τ2 = ( 5.12 √ e )1.07e−ζ. N=64 N=1024 N=256 Figure: CCDF Comparison for different N values. 17

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P SWR signals SWR and OFDM analogies Analytical equivalence: If the carrier inter spacing p is constant for all standards, SWR signal will become a multi carrier signal, x(t) = S i=1 Pi p=1 ri,p(t)e2iπ((p−1) p)t . (16) Generally speaking, this condition cannot be veriﬁed because the channel bandwidths and inter carrier spacing is different from one standard to the other. But for a mono standard SWR signal (S = 1), Si (t) = Pi p=1 ri,p(t)e2iπfi,pt , i ∈ [1, S], (17) which is equivalent to Si (t) = Pi p=1 ri,p(t)e2iπ((p−1) p)t , i ∈ [1, S]. (18) From an analytical point of view, Eq.18 is formulated in the same way as an OFDM signal. OFDM signal remains a particular case of a SWR signal 18

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P SWR signals SWR and OFDM analogies Gaussian equivalence: Validating central limit theorem, the distribution function of OFDM signals is Gaussian. SWR signal being the multi-carrier signal demonstrates the same Gaussian behavior. We ﬁnd that CCDF upper bounds given for continuous OFDM signals still hold for RF SWR signals. Figure: PAPR distribution of a SWR signal with MC-GMSK, MC-QPSK and OFDM modulation in RF. 19

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Carrier per Carrier PAPR view OFDM signal context OFDM mapped symbols C s are tabulated carrier per carrier. Rows and columns are interchangeable. Obtain the time domain signal table with the help of IFFT. Relate time domain PAPR with individual carrier PAPR. Figure: Time and frequency vision of an OFDM signal. NS j=1 N k=1 Cj,k exp ι2πjk/N = N k=1 NS j=1 Ck,j exp ι2πjk/N. (19) Interest: Expressing time domain PAPR as a function of individual carrier PAPR is very easy to compute and very informative in the context of multi-standard signals. 20

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Carrier per Carrier PAPR view Frequency PAPR upperbound PAPRNs (S(n)) ≤ ( N k=1 Pm(k) × PAPRfk ) + max k∈K (max j∈J (λ(j, k))) N k=1 Pm(k) . (20) where λ(j, k) = N p=1 Cj,p p =p Cj,p e2iπ k(p−p ) N , j ∈ J, k ∈ K. Figure: Frequency PAPR calculation for 64 carrier base band 16-QAM-OFDM signal. OFDM PAPR is upper bounded by spectral information 21

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Carrier per Carrier PAPR view SWR signal context ⇒ Application to any SWR signals: SWR signal is sliced into pieces of suitable FFT size. FFT is taken on these pieces to get ‘C’. Eq. 20 is applied on ‘C’ and upper bound is obtained. Figure: Temporal signal slicing for PAPR upper bound calculation. Figure: Frequency PAPR calculation for SWR signal. SWR PAPR is upper bounded by spectral information. This concept will be very useful in CR under spectrum access context. 22

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Recap Statistical analysis of multi-carrier signals show high PAPR feature. Publications on the presented work: 1-Sajjad Hussain, Yves Louët, “Peak to Average Power Ratio Analysis of Multi-carrier and Multi-standard signals in software radio context", IEEE ICTTA 08, Damas, Syria, April 08. 2-Yves Louët, Sajjad Hussain, “Peak to Mean Power Ratio Statistical Analysis of continuous OFDM signals", IEEE VTC 08, Singapore, May 08. 3-Sajjad Hussain, Jacques Palicot, Yves Louët, Sidkieta Zabre, “Frequency Domain Interpretation of Power Ratio Metric for Cognitive Radio Systems", Proceedings of IET Communications Journal, Volume 2, Issue 6, July 2008 Page(s):783 - 793. 23

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Recap Statistical analysis of multi-carrier signals show high PAPR feature. Up next PAPR reduction of SWR signals with the help of TR method. TR method selected to fulﬁll required needs. Publications on the presented work: 1-Sajjad Hussain, Yves Louët, “Peak to Average Power Ratio Analysis of Multi-carrier and Multi-standard signals in software radio context", IEEE ICTTA 08, Damas, Syria, April 08. 2-Yves Louët, Sajjad Hussain, “Peak to Mean Power Ratio Statistical Analysis of continuous OFDM signals", IEEE VTC 08, Singapore, May 08. 3-Sajjad Hussain, Jacques Palicot, Yves Louët, Sidkieta Zabre, “Frequency Domain Interpretation of Power Ratio Metric for Cognitive Radio Systems", Proceedings of IET Communications Journal, Volume 2, Issue 6, July 2008 Page(s):783 - 793. 23

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Outline 1 Multi carrier signals and non-linear ampliﬁcation Multi carrier signals and systems High PAPR and Non-linear ampliﬁcation 2 Our contribution I: PAPR Analysis of RF signals Continuous OFDM signals SWR signals Carrier per Carrier PAPR view 3 Our contributions II: PAPR Reduction of SWR signals PAPR reduction method: TR-SOCP TR application on SWR signal MB-OFDM PAPR reduction MC-GSM PAPR reduction Bi-standard SWR PAPR reduction OOB PRC parameter effect on PAPR reduction performance 4 Our contributions III: TR Methods Comparison TR Schemes TR comparison for WLAN system TR comparison for MC-GSM system TR comparison for Bi-standard SWR TR complexity reduction 5 Our contributions IV: PAPR Reduction in CR context PAPR variations on spectrum access PAPR reduction in CR context using joint spectrum access scheme 6 Conclusions & Perspectives Conclusions Perspectives

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P PAPR reduction method: TR-SOCP TR-SOCP Formulation In TR, problem of minimizing the PAPR can be formulated as[3], minimize β subject to xk + qrow k,L C ≤ β, 0 ≤ k ≤ NL − 1 (21) Second Order Cone Programming (SOCP) is used in TR-SOCP to optimize the peak reducing carriers (C). 2 4 6 8 10 12 10-3 10-2 10-1 100 γ (dB) CCDF = Pr(PAPR>γ) Original PAPR PAPR Reduced without power constraint Figure: OFDM PAPR reduction using TR-SOCP method without any constraints on carriers. (N = 64) -40 -20 0 20 40 -80 -70 -60 -50 -40 -30 -20 -10 0 Frequency (MHz) Power Spectral Density (dB) After TR Before TR Figure: Power spectrum density before and after PAPR reduction without constraints on carriers. (N = 64) —————————————————————————————————————- 3 S. Zabre, J. Palicot, Y. Louët and C. Lereau, “SOCP approach for OFDM Peak to Average Power Ratio reduction in the signal adding context,” IEEE ISSPIT, pp. 834–839, August 2006. 25

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P PAPR reduction method: TR-SOCP TR-SOCP Formulation In TR, problem of minimizing the PAPR can be formulated as[3], minimize β subject to xk + qrow k,L C ≤ β, 0 ≤ k ≤ NL − 1 (21) Second Order Cone Programming (SOCP) is used in TR-SOCP to optimize the peak reducing carriers (C). 2 4 6 8 10 12 10-3 10-2 10-1 100 γ (dB) CCDF = Pr(PAPR>γ) Original PAPR PAPR Reduced without power constraint Figure: OFDM PAPR reduction using TR-SOCP method without any constraints on carriers. (N = 64) -40 -20 0 20 40 -80 -70 -60 -50 -40 -30 -20 -10 0 Frequency (MHz) Power Spectral Density (dB) After TR Before TR Figure: Power spectrum density before and after PAPR reduction without constraints on carriers. (N = 64) High PAPR reduction but at the cost of spectral regrowth —————————————————————————————————————- 3 S. Zabre, J. Palicot, Y. Louët and C. Lereau, “SOCP approach for OFDM Peak to Average Power Ratio reduction in the signal adding context,” IEEE ISSPIT, pp. 834–839, August 2006. 25

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P PAPR reduction method: TR-SOCP Constrained TR-SOCP ⇒ Mean power constraint: ∆E = 10 log10 E{|x + c|2} E{|x|2} ≤ γ(dB). (22) where γ is a constant related to power ampliﬁer characteristics. ⇒ Mask constraint: |Ck | ≤ δk , k ∈ R, (23) where R is the index set of all the reserved carriers and δk are the instantaneous values of the transmission mask. 2 4 6 8 10 12 10-3 10-2 10-1 100 γ (in dB) CCDF = Pr(PAPR>γ) Original PAPR PAPR Reduced without power constraint PAPR Reduced with ∆ E=0.1 dB PAPR Reduced with ∆ E=0.3 dB Figure: OFDM PAPR reduction using TR-SOCP method with mean power constraints on carriers. (N = 64) -40 -30 -20 -10 0 10 20 30 40 50 -80 -70 -60 -50 -40 -30 -20 -10 0 Frequency (MHz) Power Spectral Density (dB) No mean power constraints Original spectrum ∆ E=0.1 dB ∆ E=0.3 dB Figure: Power spectrum density before and after PAPR reduction with mean power constraints on carriers. (N = 64) 26

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P MB-OFDM PAPR reduction MB-OFDM signal MB-OFDM signal, x(t) = 1 √ N B b=1 N−1 k=0 Xb k ej2πfk,bt , 0 ≤ t ≤ TS . (24) Here B is the number of bands over which the OFDM signal is transmitted while fk,b is the frequency of the kth data sample on bth band. 3 carriers 3 carriers 3 carriers 3 carriers OFDM symbol#1 OFDM symbol#2 X=64 X=64 Inter band distance Figure: Schematic diagram of PAPR reduction in MB-OFDM context. 100 120 140 160 180 200 220 -80 -70 -60 -50 -40 -30 -20 -10 0 Frequency (MHz) Power Spectral Density (dB) After global PRC optimization Original spectrum After individual PRC optimization OFDM Symbol#2 OFDM Symbol#1 Figure: MB-OFDM Spectrum. 27

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P MB-OFDM PAPR reduction PAPR reduction gain vs Complexity Global and individual optimization: 2 4 6 8 10 12 10-3 10-2 10-1 100 γ (in dB) CCDF = Pr(PAPR>γ) Original PAPR PAPR after global PRC optimization PAPR after individual PRC optimization Figure: MB-OFDM PAPR reduction with PRC=12. Global Optimization Individual Optimization PAPR Gain at 10−2 ≈ 3 dB ≈ 1.5 dB Computational Complexity O(9 × 214) O(9 × 211) Table: Performance vs Complexity comparison for MB-OFDM system using R = 12 28

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P MC-GSM PAPR reduction 1 free GSM channel as PRC GSM Base Station (BS) transmitting 4 GSM channels per sector. Channels are separated by 800 kHz. 1 free GSM channel used for PAPR reduction under C/I constraint of −13 dB to avoid inter-channel interference. 50 60 70 80 90 100 110 120 130 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9 9.1 Symbol No. PAPR (dB) Instantaneous Original PAPR Instantaneous Reduced PAPR Mean Original PAPR Mean Reduced PAPR Figure: PAPR reduction of 4 GSM channels using 1 free GSM channels as PRC. C/I PRCs Figure: Spectrum after TR-SOCP application (1 PRC). Mean PAPR gain of 0.45 dB 29

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P MC-GSM PAPR reduction 3 free GSM channels as PRC Same scenario as previous but 3 free GSM channels as PRC under same C/I constraint. 0 20 40 60 80 100 7 7.5 8 8.5 9 9.5 Symbol No. PAPR (dB) Instantaneous Original PAPR Instantaneous Reduced PAPR Mean Original PAPR Mean Reduced PAPR Figure: PAPR reduction of 4 GSM channels using 3 free GSM channels as PRC. C/I C/I PRCs PRCs PRCs Figure: Spectrum after TR-SOCP application (3 PRC). Mean PAPR gain of 1.2 dB 30

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Bi-standard SWR PAPR reduction SWR PRC position and simulation parameters Hypothetical SWR system containing two standards A and B. In-band carriers Data + Pilots In-band unused carriers In-band carriers Inter-standard out-of-band carriers Spectrum mask A Spectrum mask B OOB PRC %age of in-band Standard A PRC: 12/64 = 18.75% %age of in-band Standard B PRC: 56/256 = 21.87% Inter carrier spacing Standard A(δfA): 0.3125 MHz Inter carrier spacing Standard B(δfB): 0.078125 MHz Channel bandwidth (A & B): 20 MHz %age of out-of-band PRC: 15.63% Mapping scheme (A & B): 4-QAM Power gap ∆ P: 25 dB Table: Simulation model parameters. 31

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Bi-standard SWR PAPR reduction PAPR reduction performance PAPR reduction using in-band and out-of-band PRC. 4 6 8 10 12 10-2 10-1 100 γ (in dB) CCDF = Pr(PAPR>γ) Original PAPR Using in-band PRC only Using in & out of band PRC Figure: PAPR reduction using in band and out-of-band PRC. -50 -40 -30 -20 -10 0 10 20 30 40 50 -60 -50 -40 -30 -20 -10 0 10 Frequency (MHz) Power Spectral Density (dB) Spectrum Mask Standard B Standard A symbol Standard B symbol Free band PRC Spectrum Mask Standard A Figure: Each standard’s spectrum mask is respected on PAPR reduction. OOB PRC don’t reduce much PAPR compared to in-band PRC Vary different PRC parameters to see the inﬂuence on PAPR performance 32

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P OOB PRC parameter effect on PAPR reduction performance PRC Position effects Variations in positions lead to variations in PAPR reduction performance. 4 6 8 10 12 10-2 10-1 100 γ (in dB) CCDF = Pr(PAPR>γ) Original PRCs near Stnd. A PRCs in the centre between A & B PRCs near Stend. B Figure: Out-of-band PRC’s position effects on PAPR reduction. -60 -40 -20 0 20 40 60 -60 -50 -40 -30 -20 -10 0 10 Frequency (MHz) PowerSpectral Density (dB) PRCs positioned near Standard A Standard A spectrum mask Standard A symbol PRCs positioned near Standard B Standard B spectrum mask Standard B symbol PRCs positioned between Standard A & B Figure: Spectrum of out-of-band PRC’s position effects. Near the PRC to the data carriers, more the PAPR reduction gain and vice versa 33

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P OOB PRC parameter effect on PAPR reduction performance PRC Position effects Variations in positions lead to variations in PAPR reduction performance. 4 6 8 10 12 10-2 10-1 100 γ (in dB) CCDF = Pr(PAPR>γ) Original PRCs near Stnd. A PRCs in the centre between A & B PRCs near Stend. B Figure: Out-of-band PRC’s position effects on PAPR reduction. -60 -40 -20 0 20 40 60 -60 -50 -40 -30 -20 -10 0 10 Frequency (MHz) PowerSpectral Density (dB) PRCs positioned near Standard A Standard A spectrum mask Standard A symbol PRCs positioned near Standard B Standard B spectrum mask Standard B symbol PRCs positioned between Standard A & B Figure: Spectrum of out-of-band PRC’s position effects. Near the PRC to the data carriers, more the PAPR reduction gain and vice versa Attention: Mask constraints!!! 33

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P OOB PRC parameter effect on PAPR reduction performance PRC Mean power effects Variations in mean power lead to variations in PAPR reduction performance. 4 6 8 10 12 10-2 10-1 100 γ (in dB) CCDF = Pr(PAPR>γ) Original With ∆ E=0.2dB With ∆ E=0.4dB With ∆ E=0.8dB Figure: Out-of-band PRC’s mean power effects on PAPR reduction. -60 -40 -20 0 20 40 60 -70 -60 -50 -40 -30 -20 -10 0 10 Frequency (MHz) Power Spectral Density (dB) Standard A symbol Standard A spectrum mask Standard B spectrum mask Standard B symbol ∆ E=0.4 dB ∆ E=0.2 dB ∆ E=0.8 dB Figure: Spectrum of out-of-band PRC’s mean power effects. More the PRC mean power, more the PAPR reduction gain and vice versa 34

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P OOB PRC parameter effect on PAPR reduction performance PRC Mean power effects Variations in mean power lead to variations in PAPR reduction performance. 4 6 8 10 12 10-2 10-1 100 γ (in dB) CCDF = Pr(PAPR>γ) Original With ∆ E=0.2dB With ∆ E=0.4dB With ∆ E=0.8dB Figure: Out-of-band PRC’s mean power effects on PAPR reduction. -60 -40 -20 0 20 40 60 -70 -60 -50 -40 -30 -20 -10 0 10 Frequency (MHz) Power Spectral Density (dB) Standard A symbol Standard A spectrum mask Standard B spectrum mask Standard B symbol ∆ E=0.4 dB ∆ E=0.2 dB ∆ E=0.8 dB Figure: Spectrum of out-of-band PRC’s mean power effects. More the PRC mean power, more the PAPR reduction gain and vice versa Attention: PA mean power constraints!!! 34

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P OOB PRC parameter effect on PAPR reduction performance PRC Bandwidth effects Variations in bandwidth lead to variations in PAPR reduction performance. 5 6 7 8 9 10 11 10-2 10-1 100 γ (in dB) CCDF = Pr(PAPR>γ) Original With 20 PRCs With 50 PRCs With 80 PRCs Figure: Out-of-band PRC’s bandwidth effects on PAPR reduction. -60 -40 -20 0 20 40 60 -60 -50 -40 -30 -20 -10 0 10 Frequency (MHz) Power Spectral Density (dB) Symbol Standard B Symbol Standard A Standard A spectrum mask Standard B spectrum mask PRC=20 PRC=80 PRC=50 Figure: Spectrum of out-of-band PRC’s bandwidth effects. More the bandwidth reserved for PRC, more the PAPR reduction gain and vice versa 35

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P OOB PRC parameter effect on PAPR reduction performance PRC Bandwidth effects Variations in bandwidth lead to variations in PAPR reduction performance. 5 6 7 8 9 10 11 10-2 10-1 100 γ (in dB) CCDF = Pr(PAPR>γ) Original With 20 PRCs With 50 PRCs With 80 PRCs Figure: Out-of-band PRC’s bandwidth effects on PAPR reduction. -60 -40 -20 0 20 40 60 -60 -50 -40 -30 -20 -10 0 10 Frequency (MHz) Power Spectral Density (dB) Symbol Standard B Symbol Standard A Standard A spectrum mask Standard B spectrum mask PRC=20 PRC=80 PRC=50 Figure: Spectrum of out-of-band PRC’s bandwidth effects. More the bandwidth reserved for PRC, more the PAPR reduction gain and vice versa Attention: Spectrum availability??? 35

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P OOB PRC parameter effect on PAPR reduction performance BER veriﬁcation 0 2 4 6 8 10 12 10-4 10-3 10-2 10-1 Eb/No (in dB) Bit Error Rate Conventional BER After TR-SOCP Figure: BER analysis before and after PAPR reduction for Standard A. 0 2 4 6 8 10 12 10-4 10-3 10-2 10-1 Eb/No (in dB) Bit Error Rate Conventional BER After TR-SOCP Figure: BER analysis before and after PAPR reduction for Standard B. BER is not degraded on TR-SOCP implementation. 36

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Recap PAPR of SWR signal is reduced with the help of TR-SOCP in different scenarios. PRC parameter variations inﬂuence a lot on the PAPR reduction performance and should be selected very carefully in order to respect in-band and out-of-band interference. Publications on the presented work: 1-Sajjad Hussain, Yves Louët, “PAPR reduction of Software Radio signals using PRC method", IEEE Sarnoff Symposium, NJ USA, March 09. 2-Sajjad Hussain, Yves Louët, “Peak to Average Power Ratio Reduction for Multi-band OFDM System using Tone Reservation", URSI General Assembly 08, Chicago USA, Aug 08. 3-Sajjad Hussain, Yves Louët, Jacques Palicot, “Peak Power Control of Software Radio signals ", International Journal of Digital Multimedia Broadcasting, under preparation. 37

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Recap PAPR of SWR signal is reduced with the help of TR-SOCP in different scenarios. PRC parameter variations inﬂuence a lot on the PAPR reduction performance and should be selected very carefully in order to respect in-band and out-of-band interference. Up next TR schemes comparison to provide Performance vs Complexity trade-off. Publications on the presented work: 1-Sajjad Hussain, Yves Louët, “PAPR reduction of Software Radio signals using PRC method", IEEE Sarnoff Symposium, NJ USA, March 09. 2-Sajjad Hussain, Yves Louët, “Peak to Average Power Ratio Reduction for Multi-band OFDM System using Tone Reservation", URSI General Assembly 08, Chicago USA, Aug 08. 3-Sajjad Hussain, Yves Louët, Jacques Palicot, “Peak Power Control of Software Radio signals ", International Journal of Digital Multimedia Broadcasting, under preparation. 37

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P TR Schemes TR-Gradient method At each step, the algorithm updates the PRC vector C by adding to it the result of DFT on the positions of PRC of the vector consisting of the difference between the samples of unclipped and clipped signal[4]. Set a threshold A, the PRC set K, an initial peak canceling signal C(1) p , and parameter µ. The set K is the index set of R unused carriers. Let xn be the original data signal with n = 0, 1, . . . NL − 1, c(l) n = p∈K C(l) p e−2jπp n NL , (25) ˆ y(l) n =        y(l) n if y(l) n ≤ A Aej arg y(l) n if y(l) n > A , (26) and ∆(l) n = y(l) n − ˆ y(l) n , where y(l) n = xn + c(l) n is the PAPR reduced signal at l-th iteration. Then, for p ∈ K, the update on step l + 1 of the algorithm is C(l+1) p = C(l) p + µ NL−1 n=0 ∆(l) n e−2jπp n NL . (27) —————————————————————————————————————- 4 S. Litsyn, Peak Power Control in Multicarrier Communications, Cambridge University Press, 2007. 39

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P TR Schemes TR-Geometric[5] Adding signal, an =      0 , |xn| ≤ A A |xn| − 1 xnejθn , |xn| > A , (28) where A is the magnitude threshold, θn is defined as θn ∆ = 2π∆f n NL Ts, 0 ≤ n ≤ NL − 1 and ∆f is defined as ∆f ∆ = fr − fc, where fc and fr are the carrier frequencies of the OFDM signal and adding signal respectively. CALCULATION GENERATOR ADDING SIGNAL yn A ∆f an xn ˜ an cn β(opt) Figure: Geometric method for PAPR reduction. Adding signal an is filtered by FFT/IFFT based filter to put PRC on unused carriers. Filtered adding signal ˜ an is scaled by β to further reduce PAPR. —————————————————————————————————————- 5 D. Guel, Y. Louët, and J. Palicot, “A Geometric Method for PAPR Reduction in a Signal Adding Context for OFDM Signals,” in Proc. 15th International Conference on Digital Signal Processing, pp. 347–350, 1–4 July 2007. 40

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P TR comparison for WLAN system PAPR reduction performance System Parameters Method Speciﬁc Parameters %age of PRC: 18.75% µ (TR-Gradient): 5 Mapping scheme: 64-QAM P (TR-Gradient): 4 Oversampling factor: 4 ∆fTs (TR-Geometric): 1/8 Table: Simulation model parameters. 0.05 0.1 0.15 0.2 0.25 0.5 1 1.5 2 2.5 3 3.5 4 ∆ E (in dB) ∆ PAPR (in dB) TR-Geom. Method TR-Grad. Method TR-SOCP Method Figure: Mean PAPR reduction performance as a function of ∆E for the three different implementation schemes for TR methods. TR-SOCP outperforms the other two TR methods in PAPR reduction performance 41

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P TR comparison for WLAN system Performance vs Complexity 2 4 6 8 10 12 10−3 10−2 10−1 100 λ (in dB) CCDF = Pr(PAPR>λ) Orignal OFDM TR−Grad. Method TR−Geom. Method TR−SOCP Method Figure: CCDF for the three implementation schemes for TR methods for a ﬁx ∆E=0.25 dB. TR-Geometric Method TR-Gradient Method TR-SOCP Method Generalized Complexities Comparison O(NL log2 NL) O(NLRP) O(NLR2) IEEE 802.11a/g Speciﬁc Complexities Comparison O(211) O(6 × 211) O(18 × 211) NL: IFFT size=256; R: PRC number=12; P: Iterations=4 Performance vs complexity comparison trade-off 42

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P TR comparison for WLAN system Interference analysis 0 2 4 6 8 10 12 10−4 10−3 10−2 10−1 Eb/N0 (in dB) Bit Error Rate Conventional BER TR−Grad. Method TR−Geom. Method TR−SOCP Method Figure: BER vs Eb/N0 for the three implementation schemes of TR methods. -40 -30 -20 -10 0 10 20 30 40 -40 -35 -30 -25 -20 -15 -10 -5 0 Frequency (MHz) Power Spectral Density (dB) Spectrum Mask TR-SOCP Method TR-Gradient Method TR-Geometric Method Figure: PSD of the three implementation schemes of TR methods. No in-band and out-of-band interference on TR implementation. 43

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P TR comparison for MC-GSM system PAPR reduction comparison Same MC-GSM system as discussed earlier with 3 free GSM channels as PRC. 50 100 150 8.8 9 9.2 9.4 9.6 9.8 10 10.2 10.4 Symbol No. PAPR (dB) instantaneous PAPR before TR-Geo instantaneous PAPR after TR-Geo mean PAPR before TR-Geo mean PAPR after TR-Geo Figure: PAPR ‘reduction’ of MC-GSM signal using TR-Geometric method. 50 60 70 80 90 100 8.8 9 9.2 9.4 9.6 9.8 10 10.2 10.4 Symbol No. PAPR (dB) instantaneous PAPR before TR-Grad instantaneous PAPR after TR-Grad mean PAPR before TR-Grad mean PAPR after TR-Grad Figure: PAPR ‘reduction’ of MC-GSM signal with TR-Gradient method. Instead of decreasing, PAPR is increased. PRC position very far from data carriers leads to peak regrowths in case of sub-optimal solutions. Peak Regrowth 44

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P TR comparison for Bi-standard SWR PAPR reduction performance vs Complexity Bi-standard SWR system same as before. 4 6 8 10 12 10-2 10-1 100 γ (in dB) CCDF = Pr(PAPR>γ) TR-Gradient TR-Geometric Original TR-SOCP Figure: CCDF for the three implementation schemes for Tone Reservation methods for a ﬁx ∆E=0.14 dB. TR-Geometric TR-Gradient TR-SOCP Generalized Complexities Comparison O(NL log2 NL) O(NLRP) O(NLR2) SWR Signal Speciﬁc Complexities Comparison O(3 × 214) O(58 × 214) O(830 × 214) NL: IFFT size=1024 × 4=4096; R: =56; P: Iterations=4 Table: Computational complexity comparison of the TR schemes. Performance vs Complexity trade-off validated in SWR case. 45

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P TR comparison for Bi-standard SWR In-band interference analysis 0 2 4 6 8 10 12 10-4 10-3 10-2 10-1 EbNo (in dB) Bit Error Rate Conventional BER After TR-SOCP After TR-Gradient After TR-Geometric Figure: BER vs Eb/N0 for the three implementation schemes of TR methods for Standard A. 0 2 4 6 8 10 12 10-4 10-3 10-2 10-1 EbNo (in dB) Bit Error Rate Conventional BER After TR-SOCP After TR-Gradient After TR-Geometric Figure: BER vs Eb/N0 for the three implementation schemes of TR methods for Standard B. No BER degradation at any standard’s receiver. 46

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P TR comparison for Bi-standard SWR Out-of-band interference -60 -40 -20 0 20 40 60 -60 -50 -40 -30 -20 -10 0 10 Frequency (MHz) Power Spectral Density (dB) Standar A spectrum mask Standard A symbol Standar B spectrum mask Standard B symbol Figure: Power spectral density of SWR signal after implementation of TR-SOCP. -60 -40 -20 0 20 40 60 -60 -50 -40 -30 -20 -10 0 10 Frequency (MHz) Power Spectral Density (dB) Standard A spectrum mask Standard B symbol Standard B spectrum mask Standard A symbol Figure: Power spectral density of SWR signal after implementation of TR-Gradient. -60 -40 -20 0 20 40 60 -60 -50 -40 -30 -20 -10 0 10 Frequency (MHz) Power Spectral Density (dB) Standard B symbol Standard A symbol Standard B spectrum mask Standard A spectrum mask Figure: Power spectral density of SWR signal after implementation of TR-Geometric. Standard masks are respected on TR implementation. 47

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P TR complexity reduction Truncated IFFT Algorithm[4] Major share of complexity attributed to FFT/IFFT calculations. Figure: Radix-2 decimation in frequency butterﬂy diagram for 16 point IFFT. Truncated IFFT algorithm calculates maximal IFFT element with less complexity (O(2N) whereas normal IFFT complexity is O(Nlog2(N))). —————————————————————————————————————- 4 S. Litsyn, Peak Power Control in Multicarrier Communications, Cambridge University Press, 2007. 48

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P TR complexity reduction Truncated IFFT Algorithm[4] Major share of complexity attributed to FFT/IFFT calculations. Figure: Radix-2 decimation in frequency butterﬂy diagram for 16 point IFFT. Truncated IFFT algorithm calculates maximal IFFT element with less complexity (O(2N) whereas normal IFFT complexity is O(Nlog2(N))). Not always correct output —————————————————————————————————————- 4 S. Litsyn, Peak Power Control in Multicarrier Communications, Cambridge University Press, 2007. 48

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P TR complexity reduction Performance vs Complexity using only Truncated IFFT Figure: PAPR reduction using Tone Reservation with true and Truncated IDFT algorithm. No substantial PAPR reduction gain with Truncated IFFT only. 49

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P TR complexity reduction Combination of True and Truncated IFFT Let α be the factor of utilization of Truncated IDFT algorithm and β = 1 − α be the factor of utilization of classical IDFT inside ‘Fourier Transform’ block such that 0 ≤ α ≤ 1. Complexity gain g, g = N.Nitr .log2(N) 2αN.Nitr + βN.Nitr .log2(N) = log2(N) 2α + (1 − α)log2(N) . Figure: Variation of g with α for constant N. Figure: PAPR reduction using Tone Reservation with a mix of true and Truncated IDFT algorithm. α = 0.75 Complexity vs performance trade-off 50

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Recap Performance vs Complexity trade-off provided with the help of different TR schemes in SWR context. Publications on the presented work: 1-Sajjad Hussain, Desire Guel, Yves Louët, Jacques Palicot, “Performance comparison of PRC based PAPR reduction schemes for WiLAN systems", IEEE European Wireless, Aalborg Denmark, May 09. 2-Sajjad Hussain, Yves Louët, “Tone Reservation’s complexity reduction using fast calculation of maximal IDFT element", IEEE/ACM IWCMC 08, Crete, Greece, August 08. 51

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Recap Performance vs Complexity trade-off provided with the help of different TR schemes in SWR context. Up next PAPR analysis and reduction in SWR based CR system context. Publications on the presented work: 1-Sajjad Hussain, Desire Guel, Yves Louët, Jacques Palicot, “Performance comparison of PRC based PAPR reduction schemes for WiLAN systems", IEEE European Wireless, Aalborg Denmark, May 09. 2-Sajjad Hussain, Yves Louët, “Tone Reservation’s complexity reduction using fast calculation of maximal IDFT element", IEEE/ACM IWCMC 08, Crete, Greece, August 08. 51

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P PAPR variations on spectrum access PAPR variations in CR context 2 4 6 8 10 12 10-3 10-2 10-1 100 γ (dB) CCDF = Pr(PAPR>γ) before SA after SA Figure: CCDF before and after spectrum access with random primary and secondary data. 0 20 40 60 80 100 4 6 8 10 12 14 Symbol No. PAPR (dB) instantaneous PAPR before SA instantaneous PAPR after SA mean PAPR before SA mean PAPR after SA Figure: Instantaneous PAPR values before and after spectrum access with random primary data. Observations: 1 Mean PAPR increases after spectrum access. 2 Instantaneous PAPR increases on several occasions after spectrum access. In CR context, PAPR is varied in random fashion when spectrum is accessed by secondary users and should be controlled to avoid PA non-linear distortions 53

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P PAPR variations on spectrum access Carrier per carrier vision and PAPR upper bound in CR context Applying carrier per carrier vision, temporal PAPR can be upper bounded as PAPRNs (S(n)) ≤ PAPRp + δ. (29) Here PAPRp is the PAPR contribution because of primary user’s carriers i-e, PAPRp ≈ maxk∈K (maxj∈J (| p∈P Cj,pei2πkp/N |2)) N k=1 Pm(k) . (30) δ is the amount of variation in the initial PAPR, PAPRp, because of dynamic spectrum access. The factor δ can be written as, δ = δs + δm, (31) where δs ≈ maxk∈K (maxj∈J (| s∈S Cj,sei2πks/N |2)) N k=1 Pm(k) = s∈S Pm(s) p∈P Pm(p) .PAPRs. (32) δm ≈ 1 N k=1 Pm(k) [max k∈K (max j∈J (2| p∈P Cj,pei2πkp/N |.| s∈S Cj,sei2πks/N |))]. (33) Here δm is the contribution because of the mutual correlation of the primary and secondary user carriers. 54

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P PAPR variations on spectrum access PAPR upper bound on spectrum access Validation of upper bound results for SWR signal. 4 6 8 10 12 10-3 10-2 10-1 100 γ (dB) Pr(PAPR>γ) PAPR temp PAPR UB before Spec. Access PAPR UB after Spec. Access Figure: PAPR Upper bound is modiﬁed after spectrum access. 55

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P PAPR reduction in CR context using joint spectrum access scheme Joint spectrum access scheme Major part of free spectrum is used to transmit secondary data. A minor part of accessed spectrum is used as PRC to reduce PAPR. In our case we use 90% of the free spectrum for secondary data transmission while the rest of 10% is used for PAPR reduction. Free B.W Standard A Standard B f PRC Carriers for secondary data f Figure: Joint spectrum access methodology for PAPR reduction. 5 6 7 8 9 10 10-2 10-1 100 γ (dB) CCDF = Pr(PAPR>γ) original after spectrum access after TR-SOCP Figure: PAPR reduction using joint spectrum access methodology. 56

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Conclusions Conclusions PAPR analysis of continuous OFDM, SWR signal was performed. 58

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Conclusions Conclusions PAPR analysis of continuous OFDM, SWR signal was performed. PAPR reduction of SWR signal in several scenarios was performed using TR method. Mono-standard case: MB-OFDM, MC-GSM Multi-standard case: Two hypothetical standards 58

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Conclusions Conclusions PAPR analysis of continuous OFDM, SWR signal was performed. PAPR reduction of SWR signal in several scenarios was performed using TR method. Mono-standard case: MB-OFDM, MC-GSM Multi-standard case: Two hypothetical standards Comparison of different TR schemes was performed to provide complexity vs performance trade-off. 58

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Conclusions Conclusions PAPR analysis of continuous OFDM, SWR signal was performed. PAPR reduction of SWR signal in several scenarios was performed using TR method. Mono-standard case: MB-OFDM, MC-GSM Multi-standard case: Two hypothetical standards Comparison of different TR schemes was performed to provide complexity vs performance trade-off. TR complexity reduction using Truncated IFFT algorithm was proposed. 58

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Conclusions Conclusions PAPR analysis of continuous OFDM, SWR signal was performed. PAPR reduction of SWR signal in several scenarios was performed using TR method. Mono-standard case: MB-OFDM, MC-GSM Multi-standard case: Two hypothetical standards Comparison of different TR schemes was performed to provide complexity vs performance trade-off. TR complexity reduction using Truncated IFFT algorithm was proposed. PAPR variations analysis in CR context due to spectrum access was performed. 58

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Conclusions Conclusions PAPR analysis of continuous OFDM, SWR signal was performed. PAPR reduction of SWR signal in several scenarios was performed using TR method. Mono-standard case: MB-OFDM, MC-GSM Multi-standard case: Two hypothetical standards Comparison of different TR schemes was performed to provide complexity vs performance trade-off. TR complexity reduction using Truncated IFFT algorithm was proposed. PAPR variations analysis in CR context due to spectrum access was performed. A joint spectrum access scheme was introduced to reduce PAPR of SWR signal in CR context. 58

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Perspectives Perspectives For MC-GSM scenario, more PAPR reduction efﬁcient and less complex algorithms might be explored along with a complete link budget study when all the neighboring cells use TR for PAPR reduction. 59

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Perspectives Perspectives For MC-GSM scenario, more PAPR reduction efﬁcient and less complex algorithms might be explored along with a complete link budget study when all the neighboring cells use TR for PAPR reduction. SOCP implementation using frequency domain PAPR interpretation instead of classical time domain PAPR deﬁnition might be studied to reduce complexity. 59

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Perspectives Perspectives For MC-GSM scenario, more PAPR reduction efﬁcient and less complex algorithms might be explored along with a complete link budget study when all the neighboring cells use TR for PAPR reduction. SOCP implementation using frequency domain PAPR interpretation instead of classical time domain PAPR deﬁnition might be studied to reduce complexity. Truncated IFFT algorithm should be improved by proposing new branch selection criteria and the probability of false maximal detection should be statistically studied. 59

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Perspectives Perspectives For MC-GSM scenario, more PAPR reduction efﬁcient and less complex algorithms might be explored along with a complete link budget study when all the neighboring cells use TR for PAPR reduction. SOCP implementation using frequency domain PAPR interpretation instead of classical time domain PAPR deﬁnition might be studied to reduce complexity. Truncated IFFT algorithm should be improved by proposing new branch selection criteria and the probability of false maximal detection should be statistically studied. SWR signal under study could compromise of actual WLAN, WiMAX, LTE/LTE-A standards. 59

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Personal Publications Journal Publications Sajjad Hussain, Jacques Palicot, Yves Louët, Sidkieta Zabre, “Frequency Domain Interpretation of Power Ratio Metric for Cognitive Radio Systems", Proceedings of IET Communications Journal, Volume 2, Issue 6, July 2008 Page(s):783 - 793. Sajjad Hussain, Yves Louët, Jacques Palicot, “Peak Power Control of Software Radio signals", International Journal of Digital Multimedia Broadcasting, under preparation. Book Chapters Jacques Palicot, Yves Louët, Sajjad Hussain, “Power Ampliﬁcation issues related to Dynamic Spectrum Access in the Cognitive Radio Systems", in the book “Cognitive Radio Systems", ISBN 978-953-7619-25-1. Conference Publications Sajjad Hussain, Desire Guel, Yves Louët, Jacques Palicot, “Performance comparison of PRC based PAPR reduction schemes for WiLAN systems", IEEE European Wireless, Aalborg Denmark, May 09. Sajjad Hussain, Yves Louët, Jacques Palicot, “PAPR variations on dynamic spectrum access in Cognitive Radio systems", IEEE Wireless VITAE, Aalborg Denmark, May 09. 60

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Personal Publications Conference Publications (cont...) Sajjad Hussain, Yves Louët, “PAPR reduction of Software Radio signals using PRC method", IEEE Sarnoff Symposium, NJ USA, March 09. Sajjad Hussain, Yves Louët, “Peak to Average Power Ratio Reduction for Multi-band OFDM System using Tone Reservation", URSI General Assembly 08, Chicago USA, Aug 08. Sajjad Hussain, Yves Louët, “Tone Reservation’s complexity reduction using fast calculation of maximal IDFT element", IEEE/ACM IWCMC 08, Crete, Greece, August 08. Yves Louët, Sajjad Hussain, “Peak to Mean Power Ratio Statistical Analysis of continuous OFDM signals", IEEE VTC 08, Singapore, May 08. Sajjad Hussain, Yves Louët, “Peak to Average Power Ratio Analysis of Multi-carrier and Multi-standard signals in software radio context", IEEE ICTTA 08, Damas, Syria, April 08. 61

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Thanks ! Questions ? 62

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P PRC insertion in SWR signal SWR signal is transformed to frequency domain. … … One SWR symbol FFT t f Standard A data carriers Standard B data carriers SWR symbol spectrum PRC are carefully inserted in order not to cause spectral regrowth. SWR symbol with reduced PAPR IFFT f Standard A data carriers Standard B data carriers SWR symbol spectrum with possible PRC positions … … t * PRC 63

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P SWR transceiver Different standards are transmitted over their respective frequencies and demodulated independently. Standard A base-band signal generator Standard B base-band signal generator Bi-standard SWR signal Figure: A simple bi-standard SWR transmitter. Bi-standard modified SWR signal Filter Filter Standard A demodulation Standard B demodulation Filter Filter Figure: A simple bi-standard SWR receiver. 64

Reduction of SWR signals TR Methods Comparison PAPR Reduction in CR context C & P Peak regrowth in TR-Goemetric Back Peak regrowth occurs as the PRC move away from data carriers. 20 21 22 23 24 25 25 −0.015 −0.005 0.005 0.015 Time−Domain ( η −Second) Radio Frequency Signal OFDM signal x(t) Adding signal a(t) Resulting signal y(t) Reduction Peaks Figure: Peak reduction: OFDM, adding and resulting signal at ∆f/BW = 0.25. 20 21 22 23 24 25 25 −5 3 11 18 18 x 10−3 Time−Domain ( η −Second) Radio Frequency Signal OFDM signal x(t) Adding signal a(t) Resulting signal y(t) Peaks regrowth Figure: Peak regrowth: OFDM, adding and resulting signal at ∆f/BW = 4. 65

Sajjad Hussain - Peak to Average Power Ratio An...

Sajjad Hussain - Peak to Average Power Ratio Analysis and Reduction of Cognitive Radio Signals

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