Analysis of an offset modulation transmission
© Dhuness and Maharaj; licensee Springer. 2013
Received: 6 February 2012
Accepted: 22 December 2012
Published: 30 January 2013
In this article, a method called offset modulation (OM-OFDM) is proposed to control the peak-to-average power ratio (PAPR) of an orthogonal frequency division multiplexing (OFDM) signal. The theoretical bandwidth occupancy of the proposed offset modulated signal is derived. Using these bandwidth occupancy results, a closed-form theoretical bit error rate (BER) expression for an offset modulated transmission is derived and validated. Thereafter, a BER comparison between OM-OFDM and OFDM at a PAPR value of 13 dB shows that both methods offer similar BER characteristics for frequency selective fading channel conditions. The OM-OFDM method in addition is able to accurately control the PAPR of a transmission for a targeted BER. The authors have further proposed a newly applied power performance decision metric, which can be used throughout the PAPR field, in order to compare various methods. By using this power performance decision metric, the authors show that OM-OFDM offers between 4 dB–1.2 dB (60.34%–24.6%) and 4.1 dB–1.2 dB (60.8%–23.6%), net power performance gain (at a BER of 10−4) when compared to a clipped OFDM, OFDM, tone reserved (TR) OFDM and an active constellation extended (ACE) OFDM transmission in a frequency selective fading channel. Finally, by using a complementary cumulative distribution function (CCDF), the OM-OFDM method is shown to offer between 3.2 dB and 2 dB PAPR reduction (at a CCDF of 10−1) when compared to an OFDM, TR, clipped, and ACE OFDM transmission.
Orthogonal frequency division multiplexing (OFDM) has become a very popular method for high-data rate communication, primarily due to its tight spectral efficiency and its robustness to multi-path fading. This has led to it being deployed in various standards, such as digital subscriber lines, digital video broadcasting (DVB), worldwide inter-operability for microwave access IEEE 802.16d standard and recently in long-term evolution. However, it is a well-known fact that OFDM is plagued by a large peak-to-average power ratio (PAPR). This high PAPR occurs when the sinusoidal signals of the sub-carriers are added constructively. This results in an OFDM signal, which contains a number of infrequent peaks, which needs to be amplified before transmission through a channel. These high peaks necessitate the need for over-designed power amplifiers. Since these peaks are irregular, this leads to inefficient use of the power amplifiers, which ultimately leads to inefficient transmitters, as well as reduced battery life of the mobile device. Various methods [1–3] have been suggested to reduce the PAPR, such as clipping, decision-aided reconstruction (DAR) clipping, coding, partial transmission sequence, selective mapping (SLM), nonlinear companding transforms, active constellation extension, tone reservation and constant envelope OFDM phase modulation, amongst others.
Clipping is the simplest method of reducing the PAPR, by limiting the peak amplitude level of the input signal to a predetermined level. At the receiver, the clipped samples can be reconstructed by using a number of methods [1, 2, 4, 5]. Kim and Stuber  have recommended using an iterative process called DAR to reconstruct the clipped signal. A limiting factor of clipping, as well as DAR clipping, is that as the number of peak amplitudes increases, this would lead to a severe bit error rate (BER) degradation. Also, the iterative nature of the DAR technique requires increased computational complexity.
In contrast to clipping, coding can also be used to reduce the PAPR, by selecting a codeword which minimizes the PAPR. Various coding schemes have been recommended by Jiang and Wu  and Jones et al. . Davis and Jedwab  have further shown that it is possible to combine block coding (with its encoding, decoding, and error-correcting capability) and Golay contemporary sequences (with their attractive PAPR properties), in order to reduce the PAPR. Coding can be used to reduce the PAPR; however, it is not always possible to achieve a specific PAPR value. In certain cases coding gain is sacrificed for this PAPR decrease. An alternative method employed in PAPR reduction is the partial transmitted sequence (PTS) technique. In this PTS technique, the input data block is partitioned into disjointed sub-blocks. These sub-blocks are inverse fast Fourier transformed, thereafter these partial sequence sub-blocks are independently phase-rotated. The objective of this phase rotation is eventually to optimally combine these sub-blocks, to achieve a minimum PAPR. A limiting factor of PTS is that it requires high computational overhead to find an optimum phase-rotated sub-block combination and requires additional side information to be transmitted to allow the receiver to reconstruct the original signal.
In SLM, the input data block is mapped onto different candidate data blocks, all representing the same information as the original data block. These subsequent mapped data blocks are inverse fast Fourier transformed and the data transmission with the lowest PAPR is then selected for transmission . Just as in the case of PTS, this method requires high computational overhead, as well as the transmission of side information. Wang and Ouyang  have proposed a method of reducing the computational complexity, while Breiling et al.  have suggested a method which does not require the transmission of side information. Despite all these methods, both PTS and SLM still require relatively high computational overhead and in some cases the transmission of side information.
Another method employed in PAPR reduction involves using a nonlinear companding transform. The idea behind nonlinear companding transforms originates from speech processing. Similar to speech signals, OFDM signals contain peaks which occur infrequently, thus similar companding techniques used in speech processing may be applied to improve the PAPR of an OFDM transmission. Wang et al.  have proposed using a nonlinear transform, which enlarges the small signals while compressing the large signals. Later Huang et al.  proposed a companding method based on μ law companding, which combined clipping and Wang companding, in order to reduce the PAPR of OFDM signals. Jiang and Zhu  have also proposed an alternative companding technique, which uses the statistical distribution of an OFDM transmitted signal to reduce the PAPR. These companding methods increase the average power of the signal and require larger linear amplifiers.
A further PAPR reduction method is active constellation extension (ACE) . In ACE, the outer region of a constellation is intelligently extended outwards in order to reduce the PAPR. Extending the outer constellation points leads to an average power increase. Furthermore, extending the constellation intelligently requires the use of an iterative clipping process. The iterative nature of this process increases the computational complexity. Also the optimum choice of clipping parameters may prove difficult as well.
Another method used in PAPR reduction is tone reservation (TR) . In TR, the transmitter does not send data on a specified set of sub-carriers. The values of these sub-carriers (which are determined by using an iterative clipping process) are chosen in order to reduce the PAPR of a transmission. Similar to the ACE method, the iterative nature of the TR process increases the computational complexity and the optimum choice of the clipping parameter may prove difficult. Furthermore, the reservation of sub-carriers compromises throughput.
An ideal PAPR reduction method
Methods not complyingto the requirements
SLM, DAR clipping
Does not lead to an increase in average power
Does not affect the coding gain
Does not require any further bandwidth expansion or the transmission of side information
Does not lead to a severe BER degradation as thenumber of carriers increases
In this article, the authors propose a method called offset modulation (OM-OFDM), which meets a number of the requirements summarized in Table 1. The proposed offset modulation method is developed in Section 2. Thereafter, in Section 3, a closed-form bandwidth occupancy expression of an OM-OFDM transmission is derived. Using these bandwidth occupancy results, in Section 4, a closed-form BER expression for an OM-OFDM transmission is derived and validated. In Section 5, a newly applied power performance decision metric is presented which can be used throughout the PAPR field, in order to compare various methods. Thereafter, in Section 6, OFDM, OM-OFDM, clipped OFDM, ACE, and TR methods are compared by using a BER performance analysis, the newly applied power performance decision metric, and a complementary cumulative distribution function (CCDF). In Section 7, conclusions are drawn.
The contribution of this article is the introduction of a method called offset modulation which is used to control the PAPR of an OFDM transmission for a targeted BER. Both the theoretical bandwidth occupancy and BER expressions for an OM-OFDM transmission are derived. A further contribution is the introduction of a newly applied decision metric, which can be used throughout the PAPR field to compare various methods.
2 Proposed offset modulation
During a CE-OFDM transmission, as depicted in Figure 4, a frequency-domain equalizer (FDE) is used to mitigate the effects of a channel. The FDE extracts CSI from the prefix [pilot and guard intervals (GI)], which are inserted between successive CE-OFDM blocks. During the FDE process either a zero-forcing or minimum mean-squared error equalizer can be used. The CE-OFDM equalization process requires additional overhead (pilot and GI) and an increase in computational complexity when compared to an OM-OFDM transmission. A comparison between Figures 1 and 4 demonstrates the structural difference between an OM-OFDM and CE-OFDM transmission, in particular the placement of the equalizer. The only similarity that OM-OFDM and CE-OFDM share is that both methods involve a form of phase modulation. Other than that, the two methods are significantly different. The OM-OFDM transmission in addition contains a dominant component. By subtracting from the dominant frequency component at the transmitter (Figure 2), and re-instating the subtracted term at the receiver (Figure 3), the PAPR may be controlled. This is not the case in an OFDM and CE-OFDM transmission. As the dominant component becomes prominent, the PAPR of the signal decreases. However, because in reality some energy restrictions are imposed on a transmitter, the other components can contain less energy, leading to a BER trade-off.
3 Bandwidth occupancy of offset modulation
This frequency spectrum in Figure 5 is different from that of a conventional phase-modulated signal. The squaring of the Bessel functions limits the bandwidth occupancy of the signal. 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) frequency components. This depiction in Figure 5 may serve as a simplistic OM-OFDM bandwidth occupancy description. The dominant frequency component is given by , provided Ψos>>Φ2(t)−Φ1(t). In such a case, the dominant frequency component can be shown to be dependent on the Ψos term. This expression also provides some insight into an OM-OFDM transmission, namely the bandwidth expansion is dependent on the ς term. The higher the ς term, the lower the phase β, thus indicating less bandwidth expansion. Ideally, an attempt might be made to choose ς as high as possible. However, as the ς term increases, the signal would lose resolution and this would lead to an increase in the BER. Thus far it has been shown that the dominant frequency component of an OM-OFDM transmission can be predicted by . By subtracting (where γ is the dominant frequency component control factor) from the dominant frequency component at the transmitter (Figure 2) and re-instating the subtracted term at the receiver (Figure 3), the PAPR may be controlled. The receiver gains knowledge of the subtracted term by examining the PAPR of the incoming signal, from which the Ψos, ς and γ terms can be extracted by using a simple look-up table. It might be argued that after a transmission through a multi-path fading channel, the received and transmitted PAPR might differ. However, for an n-tap channel, each path affects both the root mean square and peak value of the received signal equally, therefore the PAPR from each path is equivalent to the originally sent PAPR.
In the following section, the manner in which the dominant frequency component is varied and the resultant BER characteristics are presented.
4 BER characteristics of offset modulation
Selection of a φ term, based on γ and α
0. 1≤α<0. 2
0. 2≤α<0. 3
Various QAM constellation BER expressions
ξ a v
For the choice of Ψos, ς, and γ terms, both Equation (36) and Table 2 (provided ) offer guidelines for these parameters. An attempt might be made to reduce the noise component (Equation 36) by increasing the Ψos term. Ideally, a Ψos value as close as possible to the limits () should be used.
Parameters for an 8-PSK OM-OFDM system ( α =0 . 027)
Parameters for an 64-QAM OM-OFDM system ( α =0 . 27)
In the next section, a power performance decision metric is presented, which will be later used to highlight the benefits of using an OM-OFDM transmission.
5 Decision metric
In Equation (46), E w is the wasted energy per bit due to inefficient power amplifier utilization. In order to determine E t , the power added efficiency (PAE) of the amplifier which is to be used is required. In the next section, this metric is applied and the benefits of using an OM-OFDM transmission are presented.
6 Results and discussion
A 64-QAM Gray-coded 8k mode of the DVB-T2  standard was used to compare OFDM, ACE OFDM, tone reserved (TR) OFDM, OM-OFDM, and a classically clipped OFDM transmissions. The clipping method was chosen since, to the best of the authors knowledge this method in conjunction with the OM-OFDM method are the only methods currently in the PAPR field, which allows for the accurate control of the PAPR of an OFDM transmission. The ACE and TR methods were selected since the DVB-T2 standard has recommended that these methods be used to reduce the PAPR of an OFDM transmission.
When classically clipping a signal at various clipping rates (CRs), both in-band and out-of-band distortions are introduced. In order to minimize the in-band distortion, the classically clipped OFDM signal was over-sampled by a factor of 4. To limit the out-of-band distortion, the clipped OFDM signal was filtered before transmission with a 7th-order Butterworth band-pass filter, with a 9 dB ripple in the pass-band and a 42 dB stop attenuation.
The ACE method made use of the projection onto convex sets (POCS) [35, 36] approach. This iterative filtering and clipping ACE process involved using an oversampled signal (oversampled by a factor of 4), which is clipped with a clipping threshold of 7.8 dB and thereafter filtered with a 14th-order Butterworth band-pass filter, with a 9 dB ripple in the pass-band and a 42 dB stop attenuation. The outer constellation points of this clipped and filtered signal, which lie within a certain region which does not affect the BER, are left unaltered, hence the constellation is said to be extended. The remaining constellation points are returned to their original position (before the clipping and filtering process). The outer constellation points have a maximum constellation extension limit (L) and this limit for this particular case is L=1.4 (as recommended in the DVB-T2 standard). This iterative POCS approach was terminated after 30 iterations, since this proved to be a convergence point. The clipping threshold and filter parameters were determined after an exhaustive search.
Similarly, the POCS approach was used in the TR method. Each sub-carrier in the TR method is limited to ten times the average power of the data carriers (as recommended in the DVB-T2 standard). The TR signal is oversampled by a factor of 4, with a clipping threshold of 7.8 dB. This iterative POCS approach used for the TR method was terminated after 60 iterations, since this proved to be a convergence point. Furthermore, in all the BER results which follow, a 64-QAM Gray-coded 8k mode of the DVB-T2 standard was used to transmit OM-OFDM, OFDM, and clipped OFDM data through a 5-tap typical-urban frequency selective fading channel. For an OM-OFDM, OFDM, and clipped OFDM transmission, CSI is extracted from the pilot symbols and used during the equalization process to mitigate the effects of fading. The pilot symbol placement, as well as TR sub-carrier (used in TR), can be found in the DVB-T2 standard. Similarly, the 5-tap typical-urban area model was obtained from Patzold  (which originates from the COST 207 models). Identical throughput and bandwidth occupancies were used to ensure a fair comparison between the various methods. The OM-OFDM method as well as the other methods conform to both throughput and the spectrum mask properties imposed by DVB-T2 standard. Perfect carrier and timing synchronization is assumed. The parameters used for the OM-OFDM transmission are given in Table 5.
6.1 A BER performance analysis
OM-OFDM, OFDM, and clipped OFDM data were sent through a 5-tap typical-urban area by using the parameters previously mentioned.
When a signal is clipped, information about the signal is permanently removed. Methods like DAR clipping , as previously discussed, have been recommended to be used to reconstruct the clipped method, i.e., restore missing information about the signal. However, this DAR method does not work well under frequency selective fading conditions. This permanent removal of information about the signal during clipping results in the subsequent BER plateau effect. A combination of the removal of information about the signal and the channel effects, results in the subsequent clipping BER characteristics. OM-OFDM on the other hand does not remove information about the transmission, hence no BER plateau effect. However, the resultant BER characteristics are primarily dependent on the channel, hence, the various difference between an OM-OFDM and clipped transmission.
Also similarly to the previous case, for the ACE and TR methods the resultant fixed average PAPR is 12 dB and 12.7 dB, respectively. The BER performance of the ACE and TR methods are not presented, since it resembles that of an OFDM transmission.
6.2 A decision metric performance analysis
This decision metric result might appear to be misleading, since in Figure 12 at a BER of 10−4, a 2.2 dB net gain is not expected, as proposed by the decision metric. This 2.2 dB net power performance gain is attributed to the fact that the PAE curve of a typical amplifier is exponentially shaped, depicted in Figure 14, instead of linear. Hence, there is an exponential relationship between PAPR (dB) and PAE, instead of a linear relationship. Thus as the PAPR decreases, this leads to an exponential increase in efficiency; this relationship is valid within a certain PAPR range. It is this association which leads to the 2.2 dB net power performance gain.
In order to further validate the results another standard OTS AN10858  RF power amplifier manufactured by a different supplier was used. A second degree polynomial was used to describe the PAE of this particular amplifier.
A decision metric performance improvement obtained when using OM-OFDM at a BER of 10 −4
2.8 dB (47.6%)
2.2 dB (39.8%)
4.0 dB (60.4%)
4.1 dB (60.8%)
1.2 dB (23.6%)
1.2 dB (23.6%)
2.7 dB (45.3%)
2.0 dB (36.8%)
From these comparisons, it is noted that OM-OFDM offers between 4 dB–1.2 dB (60.34%–24.6%) and 4.1 dB–1.2 dB (60.8%–23.6%) performance improvement for an AN10858 and an FPD2000AS RF power amplifier, respectively, when compared to an ACE, TR, OFDM, and a clipped OFDM transmission.
A CCDF performance analysis
At these optimum operating points, OM-OFDM is shown to offer a 2 dB, 2.27 dB, 2.75 dB, and 3.19 dB PAPR reduction (at a CCDF of 10−1) when compared to an ACE, clipped OFDM, TR, and OFDM transmission, respectively. From these comparisons, it is noted that OM-OFDM offers a significant PAPR reduction when compared to the various methods.
The authors have proposed a method called offset modulation to control the PAPR of an OFDM transmission. The theoretical bandwidth occupancy of the proposed offset modulation signal was derived. Using these bandwidth occupancy results, a closed-form theoretical BER expression for an offset modulation transmission is derived. This mathematically derived BER expression has been shown to agree with the simulated results, thus validating the derivation. A BER comparison between OM-OFDM and OFDM at a PAPR value of 13 dB shows that both methods offer similar BER characteristics for frequency selective fading channel conditions. The authors have further introduced a newly applied power performance decision metric, which can be used throughout the PAPR field to compare various methods. This decision metric is used to investigate whether the proposed OM-OFDM transmission has an optimum solution and whether a net gain exists for such a solution. When using this decision metric, OM-OFDM is shown to offer between 4 dB–1.2 dB (60.34%–24.6%) and 4.1 dB–1.2 dB (60.8%–23.6%) net power performance gain (at a BER of 10−4) for an AN10858 and an FPD2000AS RF power amplifier, respectively, when compared to a clipped OFDM, OFDM, TR, and ACE transmission, in a frequency selective fading channel. Finally, by using a CCDF, the OM-OFDM method is shown to offer between 3.2 and 2 dB PAPR reduction (at a CCDF of 10−1) when compared to an OFDM, TR, clipped, and ACE OFDM transmission.
The proposed offset method is shown to offer a performance improvement when compared to both simple (clipping), as well as more well-established (ACE and TR) PAPR reduction methods. These performance gains combined with the fact that OM-OFDM requires low-implementation complexity and does not lead to a severe BER degradation as the number of carriers increase. It also does not require any additional bandwidth expansion or the transmission of any side information to reconstruct the original message signal. These aspects make it a good alternative approach to current methods already in the field.
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