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A decision metric approach to PAPR performance analysis of an OM-OFDM transmission K. Dhuness, P. Botha and B. T. J. Maharaj Department of Electrical, Electronic and Computer Engineering University of Pretoria, South Africa Tel:+27 12 4204760, Fax: +27 12 3625000 Email: kdhuness@tuks.co.za, philip.botha@mweb.co.za, sunil.maharaj@up.ac.za TABLE I Abstract—In this paper, a novel method called offset modu- AN IDEAL PAPR REDUCTION METHOD lation (OM-OFDM) is proposed, to control the peak-to-average power ratio (PAPR) of an OFDM signal. The theoretical band- width occupancy of the proposed offset modulated signal is Requirements Methods not Complying derived. Using this bandwidth occupancy a closed form theo- to the requirements Low complexity Partial transmitted sequence retical bit error rate (BER) expression for an offset modulated Selective mapping transmission is further derived, validated and compared to DAR clipping OFDM. A BER comparison between OM-OFDM and OFDM Does not lead to an Non-linear companding at a PAPR value of 13 dB, shows that both methods offer increase in average power similar BER characteristics for additive white Gaussian noise Does not affect the coding gain Coding (AWGN) channel conditions. Furthermore, by using a newly Does not require any CE-OFDM applied decision metric, the authors show that OM-OFDM offers further bandwidth expansion Partial transmitted sequence between 64.6%-46.8% net performance gain (at a BER of 10−4 ) or the transmission of side information Selective mapping when compared to a clipped OFDM and OFDM transmission in Does not lead to a severe BER Clipping an AWGN channel. degradation as the DAR clipping number of carriers increases CE-OFDM Index Terms—PAPR, OFDM, OM-OFDM, DVB-T I. INTRODUCTION an OM-OFDM transmission is derived. Using these bandwidth Orthogonal frequency division multiplexing (OFDM), has occupancy results, in Section IV, a closed form bit error rate found wide application in many wireless standards, such as expression for an OM-OFDM transmission is derived and digital video broadcasting (DVB), worldwide inter-operability validated. In Section V, a newly applied decision metric (D) for microwave access (WiMAX) IEEE 802.16d and recently is presented. Using this metric in Section VI, OM-OFDM, in long term evolution (LTE). However, it is a well known OFDM, a classically clipped OFDM and a DAR clipped fact that OFDM is plagued by a large peak-to-average power OFDM transmission are compared. To conclude this paper in ratio (PAPR). This high PAPR necessitates the need for Section VII the beneﬁts of OM-OFDM are discussed. over designed power ampliﬁers, which ultimately reduces the battery life of the mobile devices. Various methods [1], [2] II. PROPOSED OFFSET MODULATION have been suggested to reduce the PAPR, these are: clip- Consider the complex output of a N -point inverse Fourier ping, decision aided reconstruction (DAR) clipping, coding, transform, OFDM signal, given by partial transmission sequence, selective mapping, non-linear N −1 companding transforms and constant envelope OFDM phase 1 2πtk modulation (CE-OFDM). These are by no means all the m(t) = √ Xk ej Ts , 0 ≤ t < Ts (1) N k=0 methods, but rather the more popular ones. Ideally a method is required which meets the requirements summarized in where Ts is the symbol duration and Xk represents the Table I. In this paper, the authors propose such a method complex signal, which may also be written as ak + jbk . This called offset modulation (OM-OFDM), which requires low signal may be modulated using the method shown below. implementation complexity, does not require any additional (m(t)) (m(t)) bandwidth expansion or the transmission of side information to Φ1 (t) = and Φ2 (t) = . (2) ς ς reconstruct the original message signal. It also does not lead to Here, and , refer to the real and imaginary parts of the an average power increase, nor does it lead to a severe bit error OFDM message signal, ς refers to a constant division term. rate (BER) degradation as the number of carriers increases, Whereas, Φ1 (t) and Φ2 (t) represent the equivalent real and thus meeting the highest number of requirements in Table I, imaginary OFDM mapping. These, Φ1 (t) and Φ2 (t) terms may when compared to the other methods. The proposed offset now be combined into a unique co-sinusoid, given by modulation method is developed in Section II. Thereafter, in Section III, a closed form bandwidth occupancy expression of cos(2πfc t + Φ1 (t) + Ψos ) − cos(2πfc t + Φ2 (t)). (3) Alternatively, Eq (3) may also be written as is a severe BER degradation and a spectrally untidy signal. OM-OFDM, on the other hand, deals with constellations Φ2 (t) − Φ1 (t) − Ψos 2 sin · containing both real and imaginary components. The real and 2 imaginary components are combined in a unique manner; the Φ1 (t) + Ψos + Φ2 (t) Ψos and ς terms ensure that the receiver can successfully detect sin 2πfc t + (4) 2 the originally transmitted signal. This process produces a where, Ψos refers to an offset term. In this type of modu- spectrally efﬁcient signal illustrated in Fig. 4, when compared lation the parameters (Ψos , ς) are chosen such that Ψos >> to a classical OFDM transmission. Hence the only similarity Φ2 (t)−Φ1 (t), when Ψos is sufﬁciently large and Φ2 (t), Φ1 (t) that OM-OFDM and CE-OFDM share, is that at one point they are sufﬁciently small. This implies that the Ψos term will both employ a form of phase modulation. Other than that the dominate the expression, hence the name offset modulation two methods are completely different, leading to a completely (OM-OFDM) is proposed to describe this operation. A block novel method. The transmission may appear to be a phase diagram, showing the possible processes involved during an modulated signal, therefore losing its attractive OFDM prop- OM-OFDM transmission is shown in Fig. 1. Thus far the erties. However, the OM-OFDM systems transmitter receiver structure (Fig. 1) maintains the fundamental OFDM building blocks. Thus the OM-OFDM equalization process is identical Input Up OM Message IFFT Sample Modulator to that employed in OFDM. Channel state information (CSI) is extracted from the pilot symbols and used during the equalization process to mitigate the effects of fading. Thus, Channel OM-OFDM still maintains the ease of equalization. However, the OM-OFDM transmission contains a dominant component (Fig. 4) given by 2J0 (β)2 sin(2πfc t − Ψ2 ) (discussed in Sec- os Output Down OM Message Equalizer FFT Sample Demodulator tion IV). By subtracting −γ2J0 (β) sin(2πfc t − Ψ2 ), 0 ≤ 2 os γ < 1 (where γ is the dominant frequency component control factor) from the dominant frequency component at the Fig. 1. Transmitter Receiver Structure transmitter (Fig. 2), and re-instating the subtracted term at the receiver (Fig. 3), the PAPR may be controlled. This is not Input Re(t) + S/P S cos[.] + + S cos[.] - -1 cos(2pft) + + Output 1.5 V YOS S S 13 dB OM−OFDM sin[.] sin(2pft) + - 13 dB OFDM - S Im(t) sin[.] + 2 2 gJ0(b) sin(2pft-0.5Y OS) 1 Dominant OM−OFDM Amplitude (V) Component OFDM Fig. 2. OM Modulator Structure 0.5 Input + S LPF arccos[.] + x 0.5 0.5 + + Re(t) S S + - Output 0.5 YOS V P/S 0 8.2 8.4 8.6 8.8 9 9.2 cos[2pft] - Im(t) S Bandwidth (Hz) 7 cos[.] x 10 + 2 2 LPF arccos[.] Fig. 4. An averaged normalized bandwidth occupancy comparison between x=2 gJ2(b) sin(2pft-0.5YOS) 0 OM-OFDM and OFDM with identical throughput when using a 64-QAM 8k mode of the DVB - T standard [4]. Fig. 3. OM Demodulator Structure the case in a classical OFDM and CE-OFDM transmission. proposed method may appear to be similar, if not identical, As the dominant component becomes prominent, the PAPR of to constant envelope OFDM phase modulation (CE-OFDM), the signal decreases. However, because in reality some energy which has been well documented [3]. However, the resultant restrictions are imposed on a transmitter, the other components CE-OFDM signal is spectrally untidy and is ideally suited for can contain less energy leading to a BER trade-off. constellations without imaginary components (BPSK). In cases where imaginary components exist (e.g. as in 64-QAM), this constellation is uniquely mapped onto a different constellation III. BANDWIDTH OCCUPANCY OF OFFSET MODULATION without imaginary components (e.g. 64-QAM to 64-PAM mapping). Such a mapping process results in a severe BER In this section the bandwidth occupancy of an OM-OFDM degradation. Hence CE-OFDM has the ideally required 3 dB transmission will be investigated by considering a discrete PAPR (which is permanently ﬁxed), but the price paid for this complex OFDM signal given by Eq (5). This is an extension nTs of Eq (1), (t = N ), giving components of interest. In most cases the adapted phase N −1 deviation (β1 and β2 ) of the signal is not known beforehand; 1 2πnk however, a reasonably good approximation can be made, based mn = √ Xk ej N N k=0 on N −1 1 = √ Xk ejwn k . (5) α1 ≈ E[max(| (m(t))|)] N k=0 α2 ≈ E[max(| (m(t))|)] In the above expression, wn , is an arbitrary chosen variable α1 used to simplify the analysis, Eq (5) may also be written as β1 ≈ ς N −1 α2 1 β2 ≈ . (11) mn = √ (ak + jbk )(cos(wn k) + j sin(wn k)) (6) ς N k=0 it can then be shown that Here, α1 and α2 , refer to the real and imaginary phase devi- N −1 ations of the OFDM signal respectively, and E [ ] is the ex- [mn ] Φ1n = ≈ β1 cos(wn k) − β2 sin(wn k) pected value. Typically, there is no interest in all the frequency ς components, but rather in the more dominant components. k=0 N −1 Hence, the bandwidth can be deﬁned by considering only [mn ] Φ2n = ≈ β2 cos(wn k) + β1 sin(wn k). (7) those sidebands which contain signiﬁcant power. Suppose, for ς k=0 explanation purposes, the ﬁrst two components (2x = 2) are Here, Φ1n and Φ2n are the equivalent real and imaginary of interest and β = β1 = β2 . Then by inspection of Eq (10), discrete OFDM mapping, whereas β1 and β2 are constants for this particular case, the frequency spectrum is shown in deﬁned as the adapted real and imaginary phase deviation of an Fig. 5. This frequency spectrum is different from that of a OM-OFDM signal respectively. After incorporating this into the unique co-sinusoidal (Eq (3)), the following expression is obtained N −1 un ≈ ej(2πfc n+Ψos + β1 cos(wn k)−β2 sin(wn k)) Amplitude (V) 2 k=0 |2J0(b) sin(0.5(-Y os ))| |-2J1 (b)J 0(b)sin(0.25( p-2Yos))-2J 0(b)J 1(b) sin(0.25(- p-2Yos))| N −1 − ej(2πfc n+ k=0 β2 cos(wn k)+β1 sin(wn k)) . (8) 2 |-2J1(b) sin(0.5(-Yos ))| In the above expression, un is the discrete signal which is to be transmitted. With the aid of Bessel functions [5], the Fourier series can be written as ∞ fc-2f d fc-fd fc fc +f d fc +2f d j(β sin(wn k)) j(lwn k) e = Jl (β)e Frequency (Hz) l=−∞ ∞ Fig. 5. Theoretical derived (Eq (10)) frequency spectrum of an OM-OFDM j(β cos(wn k)) j(mwn k+ mπ ) signal. e = Jm (β)e 2 . (9) m=−∞ Here, Jl (β) and Jm (β) are Bessel functions of the ﬁrst kind of conventional phase modulated signal. The squaring of the order l and m respectively with argument β. After substituting Bessel functions limits the bandwidth occupancy of the signal. Eq (9) into Eq (8), and if l = m then If β is sufﬁciently small (β = 0.02), it can be seen that a large percentage of the power is constrained within these (2x = 2) 2x 2x−y π(2x − 2z − y) − 2Ψos frequency components. The dominant frequency component is un ≈ 2 sin · 4 given by 2J0 (β)2 sin(2πfc t− Ψ2 ), provided Ψos >> Φ2 (t)− os y=0 z=0 |−x+z| Φ1 (t). By subtracting −γ2J0 (β)2 sin(2πfc t − Ψ2 ), 0 ≤ os |−x + z + 1 | 2 γ < 1 (where γ is the dominant frequency component J|−x+z| (β1 ) · −x + z + 1 2 control factor) from the dominant frequency component at 1 |x−y−z| the transmitter (Fig. 2) and re-instating the subtracted term |x − y − z + 2 | at the receiver (Fig. 3), the PAPR may be controlled. The J|x−y−z| (β2 ) · x−y−z+ 1 2 receiver has knowledge of the subtracted term by examining Ψos the PAPR of the incoming signal, from which the Ψos , ς and sin 2π(fc + yfd ) − yπ + . (10) γ terms can be extracted by using a simple look-up table 2 (similar to Table III). In the next section, the manner in which In Eq (10), fd is an integer multiple of the modulation the dominant frequency component is varied and the resultant frequency and 2x refers to an even number of frequency BER characteristics are presented. TABLE III IV. BIT ERROR RATE CHARACTERISTICS OF OFFSET PARAMETERS FOR A 64 - QAM OM - OFDM SYSTEM (α = 0.27) MODULATION PAPR Ψos ς γ ϕ It can be shown by using [6], that the noise variance at the 7 dB 1.596 44000/16384 0.86 0.2 output of the various branches of the demodulator (Fig. 3) can 8 dB 1.596 44000/16384 0.9 0.251 be written as 9 dB 1.596 44000/16384 0.925 0.34 10 dB 1.596 44000/16384 0.943 0.44 2 No 2 No 11 dB 1.596 44000/16384 0.962 0.53 σx ≈ and σy ≈ (12) 12 dB 1.596 44000/16384 0.97 0.67 2 4 sin2 −ϕ2 13 dB 1.596 44000/16384 1 1 where by inspection, ϕ is a constant term and may be approximated by Table II. 0 10 7 dB OM−OFDM 7 dB Theoretical TABLE II 8 dB OM−OFDM SELECTION OF A ϕ TERM , BASED ON γ AND α 8 dB Theoretical −1 9 dB OM−OFDM 10 Average Bit Error Rate (BER) 9 dB Theoretical 10 dB OM−OFDM 10 dB Theoretical 0 < α < 0.1 0.1 ≤ α < 0.2 0.2 ≤ α < 0.3 11 dB OM−OFDM −2 11 dB Theoretical 10 12 dB OM−OFDM 12 dB Theoretical β sin(Ψos ) ϕ≈ 4(1−γ) 0 ≤ γ < 0.99 0 ≤ γ < 0.97 0 ≤ γ < 0.96 13 dB OM−OFDM 13 dB Theoretical −3 β sin(Ψos ) 10 ϕ≈ 5(1−γ) 0.99 ≤ γ < 1 0.97 ≤ γ < 1 0.96 ≤ γ < 1 −4 10 Here, γ is the dominant frequency component control factor 0 10 20 30 40 50 Average SNR per bit (Eb/No)(dB) and the, α and β terms originate from Eq (11). Based on this an approximate theoretical BER for an OM-OFDM transmission Fig. 6. Theoretically predicted (Eq (13)) and simulated bit error rate through an AWGN channel, can be derived and written as comparison. √ k · (M − 2) + ℘ · k(M − 2 M + 2) BER ≈ √ M · k2 ℘ · (2 M − M − 1) V. DETERMINING AN OPTIMUM SOLUTION FOR OFFSET + (13) MODULATION M · k2 where Liang [7] et al. have proposed a decision metric (D), to deal with the relationship between ampliﬁer efﬁciency, kξb ℘ = erfc and ampliﬁer distortion, signal bandwidth occupation, throughput ξav No and power consumption. The authors have adapted this metric to incorporate PAPR, to investigate whether the proposed OM- 4k sin2 (− ϕ )ξb = erfc 2 . (14) OFDM transmission, has an optimum solution and whether a ξav No net gain exists for such a solution. The decision metric is given by ξb Here, No refers to the signal-to-noise ratio (SNR) per bit, Et ξav is deﬁned as the energy per symbol, M denotes the M- No ary levels, M = 2k , when k is even and erfc denotes the D = Rb . (15) W error function. It should be noted that the theoretically derived expression does not accept a γ = 1; if such a term arises, then Here, Rb is the data rate and W refers to the bandwidth occu- ϕ = 1. This simpliﬁes Eq (13) into a BER expression for an pancy. Typically during fair comparisons, identical throughput AWGN transmission. Also, Table II assists in the choice of and bandwidth occupancies are used, thus Rb remains constant W Ψos and γ terms to minimize the BER degradation. In order Et and the metric simpliﬁes to D ∝ No . In Eq (15), No is the to validate the theoretically derived expressions, by means of noise power spectral density for a speciﬁc BER and Et is a simulation (the 8k mode of the DVB-T standard [4]), 64- the total energy per bit. Unlike traditional approaches, which QAM Gray-coded OM-OFDM data were transmitted through only take into account the received energy per bit (Eb ) and an AWGN channel. The parameters used for the 64-QAM OM- often ignore the total energy consumption (e.g. dc power OFDM transmission are given in Table III. From Fig. 6, it consumption of the ampliﬁer). Here, Et incorporates the total can be seen that the theoretically predicted results (Eq (13)) energy per bit and can be written as and the simulated results correlate fairly well, thus validating the theoretically derived expression. Et = Eb + Ew . (16) In Eq (16), Ew is the wasted energy per bit due to inefﬁcient discussed in Section I. When using the same DVB-T standard, power ampliﬁer utilization. In the next section, this metric is OM-OFDM allows the PAPR of the signal to be varied, applied and the beneﬁts of using an OM-OFDM transmission while still maintaining identical throughput and bandwidth are presented. occupancy as an OFDM transmission. Hence a direct com- parison between OFDM and OM-OFDM can be made when VI. R ESULTS AND D ISCUSSION both methods offer the same PAPR (13 dB) as shown in In all the results which follow, a 64-QAM Gray-coded Fig. 7. From this OM-OFDM and OFDM comparison, it is 8k mode of the DVB-T standard was used to transmit OM- noted that both methods offered similar BER characteristics OFDM, OFDM, clipped OFDM and DAR clipped OFDM at a PAPR of 13 dB. Also a BER comparison between a data through an AWGN channel. Identical throughput and clipped OFDM signal and a DAR clipped OFDM signal, bandwidth occupancies were used to ensure a fair compari- indicates that for high PAPR (12 dB) values, both methods son between the various methods. Perfect carrier and timing offer similar BER characteristics. However, for lower PAPR synchronization is assumed. The parameters used for the OM- (8 dB) values the DAR clipped technique, performs better OFDM transmission is given in Table III. When classically than the traditional clipping method. At these lower PAPR clipping a signal, both in-band and out-of-band distortion is values both the clipped and DAR clipped transmissions, BER introduced. In order to minimize the in-band distortion both plateaued. For clipping and DAR clipping these BER plateaus the clipped OFDM signal and DAR clipped OFDM signal occur when PAPR ≤ 11dB and PAPR ≤ 10dB respectively were over-sampled by a factor of 2, when compared to both for this particular case. OM-OFDM on the other hand does OFDM and OM-OFDM. To limit the out-of-band distortion not suffer from this BER plateau effect. both clipped OFDM signal and DAR clipped OFDM signal B. A decision metric comparison between OM-OFDM, were ﬁltered before transmission with a 14th order Butterworth OFDM, a clipped OFDM signal and a DAR clipped OFDM bandpass ﬁlter, with a 9 dB ripple in the pass-band and a transmission 42 dB stop attenuation. The DAR process also involved two iterations, before obtaining a BER value. In order to facilitate a direct comparison between OM- OFDM, OFDM, clipped OFDM and DAR clipped OFDM, A. A BER comparison between OM-OFDM, OFDM, a clipped the decision metric discussed in Section V was employed. OFDM signal and a DAR clipped OFDM transmission By using this metric and employing two standard off-the- Offset modulated, OFDM, clipped OFDM data and DAR shelf (OTS) RF power ampliﬁers, an FPD2000AS [9] and clipped OFDM data were sent through an AWGN channel by a AN10858 [8] power ampliﬁer, a 10th and 2nd degree using the parameters previously mentioned. A BER compar- polynomial was used to describe the power added efﬁciency ison, between the various methods is shown in Fig. 7. The for these particular ampliﬁers, respectively. The results, when using the decision metric for these two ampliﬁers is shown in 0 Fig. 8 and Fig. 9. In both these comparisons it should be noted 10 8 dB Clipped 8 dB DAR Clipped 8 dB OM−OFDM 41 12 dB Clipped Clipped OFDM −1 12 dB DAR Clipped DAR Clipped OFDM 10 Average Bit Error Rate (BER) 12 dB OM−OFDM Optimum DAR Clipped and Clipped 40 OM−OFDM OFDM operating point 13 dB OM−OFDM OFDM 13 dB OFDM 39 (Et/No)/(Rb/W) (dB) −2 10 OFDM 38 −3 10 37 36 −4 10 Optimum OM−OFDM operating point 0 5 10 15 20 25 30 35 40 Average SNR per bit (Eb/No)(dB) 35 7 8 9 10 11 12 13 PAPR (dB) Fig. 7. A bit error rate comparison between an OM-OFDM, OFDM, clipped OFDM and DAR clipped OFDM signal. Fig. 8. System performance, at a BER of 10−4 for an FPD2000AS RF power ampliﬁer. averaged PAPR of an OFDM transmission when using the 8k mode of the DVB-T standard according to simulations is that both the clipped OFDM and DAR clipped OFDM results 13 dB. This PAPR value has also independently been veriﬁed have been abridged due to the fact that the clipped OFDM by [8]. This PAPR is ﬁxed for an OFDM transmission and BER plateaued, thus it was unable to produce the speciﬁc may only be changed by adopting one or all of the methods BER. When using these standard OTS power ampliﬁers, the 36 conditions. The authors have further proposed a newly applied 35.5 Clipped OFDM decision metric, to investigate whether the proposed OM- DAR Clipped OFDM OFDM transmission, has an optimum solution and whether 35 OM−OFDM OFDM a net gain exists for such a solution. OM-OFDM has been 34.5 shown by using this metric, to offer between 4.5 dB - 2.7 (Et/No)/(Rb/W) (dB) 34 dB (64.6%-46.8%) net performance gain (at a BER of 10−4 ) 33.5 when compared to a DAR clipped OFDM, a clipped OFDM 33 and OFDM transmission. This performance gain, combined 32.5 with the fact that OM-OFDM requires low implementation 32 complexity and does not lead to an average power increase. It 31.5 also does not require any additional bandwidth expansion or 31 the transmission of any side information to reconstruct the original message signal. Furthermore it does not lead to a 30.5 7 8 9 10 PAPR (dB) 11 12 13 severe BER degradation as the number of carriers increase. These aspects make it a good alternative approach to current methods already in the ﬁeld. Future work on OM-OFDM will Fig. 9. System performance, at a BER of 10−4 for an AN10858 RF power ampliﬁer. focus on other channel conditions. R EFERENCES optimum operating point for an OM-OFDM transmission is [1] S. H. Han and J. H. Lee, “An overview of peak-to-average power ratio reduction techniques for multicarrier transmission,” IEEE Wireless at a PAPR of 10 dB (where a minimum decision metric Communications Magazine, vol. 12, no. 2, pp. 56–65, April 2005. occurs) and for a DAR clipped and classically clipped OFDM [2] T. Jiang and Y. Wu, “An overview: Peak-to-average power ratio reduction transmission is shown to be at a PAPR of 12 dB. At this techniques for OFDM signals,” IEEE Transactions on Broadcasting, vol. 54, no. 2, pp. 257–268, June 2008. optimum operating point, when using the FPD2000AS RF [3] S. C. Thompson, “Constant Envelope Phase Modulation,” PhD Thesis, power ampliﬁer, OM-OFDM offers a 2.88 dB (48%), 4.46 dB University of California, San Diego, 2005. (64.2%) and 4.51 dB (64.6%) net performance gain (at a BER [4] ETS 300 744, “Digital Video Broadcasting (DVB); Framing structures, channel coding and modulation for digital Terrestrial television (DVB- of 10−4 ) when compared to OFDM, a DAR clipped OFDM T),” European Telecommunication Standard Doc. 300, March 1997. signal and a clipped OFDM signal respectively. Similarly [5] R. E. Zeimer and W. H. Tranter, Principles of communications: systems, when using the AN10858 RF power ampliﬁer, OM-OFDM modulation, and noise, 3rd ed. Washington D.C, 1990. [6] J. G. Proakis and M. Salehi, Communication systems engineering, 2nd ed. is shown to offer a 2.74 dB (46.8%), 3.43 dB (54.6%) and Prentice-Hall, 2002. 3.48 dB (55.1%) net performance gain (at a BER of 10−4 ) [7] C. Liang, J. Jong, W. E. Stark, and J. R. East, “Nonlinear Ampliﬁer when compared to OFDM, a DAR clipped OFDM signal Effects in Communication Systems,” IEEE Transactions on Microwave Theory and Techniques, vol. 47, no. 8, pp. 257–268, August 1999. and a clipped OFDM signal respectively. At the optimum [8] N. Semiconductors. (2010) AN10858.pdf. [Online]. Available: http: operating point of an OM-OFDM transmission (10 dB), the //www.nxp.com/documents/application note/ FPD2000AS and AN10858 RF power ampliﬁer, produces a [9] R. M. Devices. (2009) FPD2000ASDS.pdf. [Online]. Available: http://www.rfmd.com/CS/Documents/ decision metric result of 36.04 dB and 31.20 dB respectively. This comparison indicates that the AN10858 ampliﬁer offers a 4.84 dB improvement over the FPD2000AS ampliﬁer, thus making it a better ampliﬁer for this particular application. This result was intuitively expected since the AN10858 RF Kahesh Dhuness received his B.Eng and M.Eng in Electrical and Elec- tronic Engineering from the University of Johannesburg in 2004 and 2006, power ampliﬁer has being speciﬁcally designed for this current respectively. After which he was employed as a Systems Engineer at SAAB application (8k mode of the DVB - T standard). Grintek. In 2008, he joined the Department of Electrical, Electronic and Computer Engineering at the University of Pretoria. Mr Dhuness is currently VII. CONCLUSION a PhD candidate, his research work is supported by the SENTECH Chair in Broadband Wireless Multimedia Communication, at the University of Pretoria. The authors have proposed a novel method called offset modulation to control the PAPR of an OFDM transmission. The theoretical bandwidth occupancy of the proposed offset modulation signal was derived. This derivation proved that Sunil Maharaj received his BSc Eng and MSc Eng in Electronic Engineering OM-OFDM is spectrally more efﬁcient than CE-OFDM. Using from University of Natal (Durban). He received the MSc in Operational this bandwidth occupancy results, a closed form theoretical bit Telecommunications with merit from University of Coventry and a PhD in error rate expression for an offset modulation transmission is Wireless Communications from University of Pretoria. Professor Maharaj previously worked as a Microwave Design Engineer at EMLAB Pty Ltd further derived. This mathematically derived BER expression and then at the Eastern Cape Technikon. He currently holds the position of has been shown to agree with the simulated results, thus SENTECH Chair in Broadband Wireless Multimedia Communications in the validating the derivation. A BER comparison between OM- Department of Electrical, Electronic and Computer Engineering at University of Pretoria. His research interests are in MIMO Channel Modeling, OFDM- OFDM and OFDM at a PAPR value of 13 dB, shows that both MIMO Systems and Cognitive Radio. methods offer similar BER characteristics for AWGN channel