Performance of OFDM System with Constant Amplitude Modulation

The Orthogonal Frequency Division Multiplexing (OFDM) technique has recently received considerable attention for wireless networks. Despite its advantages, it has a major drawback of its high Peak-to-Average Power Ratio (PAPR) value which affects the system efficiency and the cost. In this paper, a proposed system is discussed to achieve 0 dB PAPR value. It depends on a proposed block, called Constant Amplitude (CA) modulation. The whole characteristic mathematical analysis is presented for the proposed system. Additionally, the complexity evolution is explained. Afterwards, many MATLAB simulation programs are executed. Time and frequency domain behaviors are presented. Furthermore, in-band distortion introduced by the proposed CA modulation is calculated in terms of Error Vector Magnitude (EVM). Moreover, the proposed system outperforms the conventional one when compared in terms of PAPR, equalization, and BER under Additive White Gaussian Noise (AWGN) channel and multipath fading channels. In addition, the impact of the proposed scheme design parameter is studied.


Introduction
Many modern broadcasting wireless systems (such as wireless local area networks, digital audio and digital video broadcasting, WiFi, WiMAX, LTE) use multicarrier modulations like OFDM [1].
One of the advantages of OFDM modulations is its resistance against multipath.Its drawback is the large PAPR value which is a measure of the modulated signal envelope dynamics.This makes the modulated signal very sensitive to the distortions introduced by the non linearity of power amplifiers.Hence, this increases the cost of the RF power amplifier which is one of the most expensive components in the radio hardware.Many strategies are introduced by the researchers to reduce the PAPR value of the OFDM signal [2][3][4][5].
In this paper, a proposed scheme is suggested to achieve 0 dB PAPR value.Therefore, it outperforms the previous techniques in terms of PAPR reduction value.It depends on a proposed block, named CA modulation, which is inserted in the conventional system to fix the OFDM signal amplitude.The mathematical model of the proposed scheme is presented.Furthermore, the complexity modification is studied.Additionally, many MATLAB simulation programs are executed to compare the performance of the proposed and the conventional OFDM systems in terms of time and frequency domains, in-band distortion, PAPR, BER for multipath fading channels, and equalization.Moreover, the impact of the proposed scheme design parameter is explained.The simulation showed that the proposed system behaved better performance than the conventional one in all measurement terms.
The paper is organized as follows; Section 2, introduces the mathematical model for the conventional OFDM system.The PAPR definition and some of the major existing methods for reducing it are defined in Sections 3 and 4, respectively.Section 5, gives a comprehensive mathematical analysis for the proposed system.Section 6, evaluates the complexity proposed by the proposed scheme.Extensive simulation results are discussed in Section 7. Finally, conclusions are extracted in section 8 followed by the relevant references.

The Transmitter
The schematic diagram of the OFDM system is shown in Figure 1.At the transmitter, the encoded data are transformed to parallel sequence of complex numbers in one of several possible mapping formats (QPSK, 16-QAM, 64-QAM, etc.).Then, the N-points Inverse Fast Fourier transform (IFFT) is applied to the resulting modulated symbols.After that, a cyclic prefix (CP) is added to the resulting signal and it is converted to a serial sequence.Afterwards, the resulting signal is analogy modulated after the conversion to analog signal.Finally, the resulting signal is transmitted through the wireless channel [2].

N
One sampled baseband OFDM symbol after the IFFT can be expressed as: where 1 j   and   x k represents the complex modulated data symbol of duration th k s T .This OFDM symbol can be written in a 1 N  column vector as [1]: where denotes the transpose of  and is the OFDM symbol number.and 1 

W
X are the complex points IFFT N N N  matrix and the complex OFDM modulated data symbol (column) th i 1  N vector, respectively.X and W can be expressed as follows: 1 e e e e e e e j k N (6) where the samples and the subcarriers are represented by the rows and the columns of the

N N
1  W matrix, respectively.They can be separated as shown by ( 5), ( 6) into the two vectors; (the complex samples vector which varies for each subcarrier) and complex subcarriers vector).In order to achieve unitary, 1  W should be scaled by   1 N [6].
After CP insertion, the samples variation is modified to . Therefore, vector should be regulated as (7).Consequently, P S and (8).respectively a

The Energy Loss
ansmitted signal has the disad-The use of a CP in the tr vantage of requiring more transmit energy.The loss of transmit energy (or loss of signal-to-noise ratio (SNR)) due to the CP is [7]: It is worth mentioned that cp S should be divided by Loss E to compensate the wa energy due to the CP rtion.

Communication Channel
. The The transmitted waveform gets corrupted by noise multipath fading channel having impulse response    can be expressed as follows: where and l h l  y represent the complex fading and the wn in Figure 1, the received signal (11) where is the compl propagation dela of the th l path, and L is the number of multipaths, respectively

.
At the receiver as sho is analogy demodulated and then it is converted into a digital format.Afterwards, the CP is removed from the resulting signal and it is transformed into N parallel samples.Then, the signal is transformed in the frequency domain via the N points FFT.Thereafter, frequency domain equalization (FDE) is performed.Finally, the demapping and parallel to serial processes are performed.After removing the CP, the received symbol can be written as: ex noise vector contributed WGN w s Gaussian distributed with zero mean.H is the N N  circulant channel matrix describing th ultipath g channel.It can be diagonalized by the FFT and IFFT as follows [8]: where is diagonal matrix containing the N ulant s FFT of e circ equence of H . W is the complex N points FFT N N  matrix After the N points FFT, the resultin mbol is: . g sy

14)
The FDE complex coefficients can be de co ar C rived acrding to the minimum mean squ e (MMSE) criterion as follows [9]: where H  designates the complex conjugate transposetion of  .A major advantage of the equalization in frequency domain is the low computational complexity.The price to be paid is a reduction in the data rate caused by the insertion of the CP [10].The symbol after FDE can be expressed as: After demapping, these noise can b m e greatly miniized and the original symbol X can be recovered.

Peak-to-Average Powe Ratio r
ependently in Since OFDM signals are modulated ind each subcarrier, the combined OFDM signals are likely to have large peak powers at certain instances.The peak power is generally evaluated in terms of PAPR.
Accordingly, the PAPR of the OFDM signal which is defined as the ratio of the maximum power divided by the average power of the signal is expressed as: where denotes the expectation operation [2,11].

) of the am
The Cumulative Distribution Function (CDF plitude z of an OFDM signal sample [11] is given by: The CDF of the PAPR for an O fo FDM data block can be und in [11] as: where is the number of subcarriers.For D

N
an oversampled OF M, this last formula should be modified to: where the PAPR of an oversampled signal for N subcarriers is approximated by the distribution f N or  subcarriers without oversampling.For four times oversampled OFDM signals, 2.3   is a good approximation [12].
Therefore, CCDF of th R for an oversampled e PAP OFDM data block is:

PAPR Reduction Methods
PR have been accoding [14], peak value.A FDM syste n.The drawbacks of the DSI m m using wavelet transform is proposed.It re idea has be ibe the structure of a proposed to avoid the OFDM PAPR Many strategies for reducing the PA complished such as clipping [13], windowing [15] and tone reservation [16].Unfortunately, most of these schemes are unable to achieve a large reduction in the PAPR with a low complexity, low coding overhead and without performance degradation.
Partial Transmit Sequence (PTS) method is a well known method which can reduce the OFDM PAPR major drawback of PTS method is its high computational complexity due to the necessity of large number of Inverse Fast Fourier Transforms (IFFT) [17].
The selective mapping (SLM) scheme is one of the most effective PAPR reduction schemes in O ms.SLM scheme can achieve several decibels of PAPR reduction and hence significantly improves the transmission power efficiency [18].One of its major disadvantages is the transmission of side information bits in order to enable the receiver to recover the transmitted data blocks.The reduction of PAPR value in SLM scheme is better than obtained in PTS method but a large number of Inverse Discrete Fourier Transform (IDFT) blocks are required.This results in increased computational and hardware complexity [18].
Dummy Sequence Insertion (DSI) scheme is another method for PAPR reductio ethod is that the length of data is increased which affects the bandwidth.This degrades the transmission efficiency [19].
Additionally, in [5], an efficient technique for the OFDM syste duces the PAPR value from 8.8 dB for conventional OFDM system to 1.5 dB.While in [20], a novel multicarrier spread spectrum watermarking scheme for the application of image error concealment using multicarrier-code division multiple access with binary phase shift keying transmission in Rayleigh fading channel is proposed.This scheme can be used for PAPR reduction.Furthermore, in [21], The reduction of dynamic range or PAPR is made by using a compander in the Space Division Multiplexing/Companded Orthogonal Frequency Division Multiplexing (SDM/COFDM) system.
In [22][23][24], A constant envelope paired burst OFDM was proposed to achieve 0 dB PAPR.Its main en just adding two constant envelope OFDM signals which have been amplified using a single grossly nonlinear amplifier.The constant envelope OFDM signal can also be thought of as a phase transformation of the OFDM signal [25].In this paper, our proposed technique uses a different method to achieve the 0 dB PAPR.

The Transmitter
In this section, we descr efficient OFDM scheme problem.It is shown in Figure 2. At the transmitter, a new block named by "Constant Amplitude (CA) Modulator" is inserted after the IFFT process.It consists of three sub-blocks as shown in Figure 3. Firstly, a leading zero sample is inserted prior to each OFDM symbol via "Inserting Zero Sub-block".Secondly, extra samples are inserted between each two adjacent samples of the resulting OFDM symbol via "Inserting Samples Subblock".These extra samples are gradually increased or decreased according to the primitive samples.Finally, each sample value of the resulting signal is converted into 0 or 0.5  value via "Comparing Samples Subblock".This is based on the comparison between it and a reference ge ted signal.Therefore, 0 dB PAPR value is expected to be achieved via our proposed nera CA modulator.That is because the output of the CA modulator has a constant amplitude and the randomly amplitude peaks of the OFDM phenomenon is eliminated.
The mathematical analysis of the proposed scheme can be summarized as follows: 1) After IFFT block, the complex OFDM symbol S , expressed by (2), is separated into its real and imaginary parts as follows: where Re  and Im  donate the real and the imaginary part of  .Su quently, our proposed block (CA tor) rte e bse modula is inse d for each part.2) At th real branch, after "Inserting Zero Sub-block",  the resulting real OFDM symbol samples.It can be written as: (23) blo e re (25) where is the extra inserted samples between each two adjacent samples in

S
is the difference between these two adjacent samples.4) After "Comparing Samples Sub-block", each sample value in the Re s

S
symbol is converted into 0 or 3) After "Inserting Samples Sub-ck", th sulting real OFDM symbol It can th creas written as:   , where is the sample numb c) Produce the resulting OFDM symbol i er.
Re o

S
and update symbol as follows: and ACC can be represented as follows: At the imaginary branch, the same analysis can be oped to derive Im o S .Therefore, the final modified tra OFDM sym nsmitted o bol S can be expressed as: Finally, the CP is inserted.The resulting symbol can be d as: w due to e ex resul

The Energy Loss
The use of a CA modulator in the transmitted signal has the disadvantage of requiring more transmit energy.The loss of transmit energy due to the CA modula lowed by the CP insertion is: here It is worth mentioned that o S should be divided by Loss E to compensate the wasted energy.

The Receiver
At the receiver as shown in Figure 2, the received signal is analogy demodulated and then it is converted into a digital format.Afterwards, CP is removed and our proposed "Constant Amplitude (CA) De-modulator" is inserted to reverse the impact of the CA modulator.It consists of three sub-blocks as shown in Figure 3. Firstly, the OFDM symbol is regen tion Sub-block".Secondly, the ex removed from the resulting OFDM symbol via "Removing Residual Samples Sub-block".Finally, the leading zero sample is removed from the fo OFDM symbol via "Removing Lea block".
ts F a tio The mathematical analysis ca lo erated via "Samples Generatra inserted samples are refront of each ding Zero Sub-Then, the signal is transformed into the frequency domain via the N poin FT.Finally, the demapping and parallel to serial processes re performed without any equalization as in the conven nal system.n be summarized as folws: 1) After CP removal, the resulting symbol is: , after "Samples Generation odulator) is 3) At the real branch Sub-block", the OFDM symbol is regenerated.This is executed by the following steps: a) Generate a reference symbol with a leading zero . It can be written as follows:

The Complexity An lysis for the Propose
The exc s in the conventional OFDM receiver complexity via the CA de-modulator can be summarized as follows:  One simple adder used 1   N times per OFDM symbol, and simple comparator used N  times per OFDM symbol are needed by "Samples Generation b Su -block". Simple switches are used to eliminate the residual samples for both "Removing Residual Samples Subblock" and "Removing Leading Zero Sub-block". Therefore, the additional operational complexity is one simple adder and one simple comparator per one CA modulator.

The Overall Additional Complexity Computation
The overall transmitter additional complexity is four simple adders, two simple subtrac comparators.That is because each transmitter contains two CA modulators.Further, the overall receiver additional complexity is two simple adders and two simple comparators.Therefore, the proposed scheme requires additional six simple ad ur simple compa tors.Noteworthy co is ui tegrator, and grossly look up table "memory storage" at the iver, a huge complexity ea up table, two low-pass filters, arc-tan function generator, e tiveness heme.WiMAX system has OFDM systems are studied.The upper part of Figure 4, compares 50 real part samples for ventional syste system produces a constant ampli-very low compared to the previous constant envelope technique in [23][24][25] which req res oversampling, in transmitter.According to the rece is added.It requires a band-pass filter (which is ar consuming), two complex multipliers, a grossly look phase unwrapper, matched filters, and hard decisions.Additionally, the frequency domain equalizer is needed contrary to our proposed scheme.

The Complexity Reduction Analysis for the Proposed Scheme
The equalization process is removed in the proposed scheme.That is because of the presence of the "Samples Generation Sub-block".Therefore, the receiver complexity is extremely reduced.Additionally, hermitian OFDM can be used.Hence, only real outputs are occurred.Therefore, only one CA modulator/ de-modulator is used instead of two.Then, the overall additional complexity is reduced by a factor of 2.

Simulation Setup
Monte Carlo MATLAB simulation experiments hav been carried out to study the performance and the effecof the proposed sc been used as an example of the conventional OFDM system [26].The WiMAX and the CA modulation block parameters used for these simulations are illustrated in Table 1.Both AWGN and multipath channels are considered.For the multipath channel, we consider ITU Pedestrian A and ITU Vehicular A channels [27] with GN.The de AW lay profiles of the two channels are described in Table 2.

Time and Frequency Domains Behaviors
In this subsection, the characteristics of both conventional and proposed both systems output.On the contrary to the con m, our proposed tude signal.Therefore, 0 dB PAPR value is expected to be achieved.
The lower part of Figure 4, compares the frequency domain for both systems output.It is clear that the frequency domain of the proposed system concentrates the power in the DC component and the side bands.Therefore, it suffers from the severe frequency selectivity channels.Step Output values 0, 0.5 

In-Band Distortion Calculation
Error vector gure of merit adopted by tion standards for evaluating in-band distortions introduced munic concept.
magnitude (EVM) is a popular fi various communica in a com ation system.
Figure 5, illustrates the EVM Denote by k X -called th nal, its distorted version, and the erro al (vector).so as [26, e reference sig k Y r sign 28]: nd compared.104 data blocks are generated to calculate the CCDFs of the PAPR.To have a precise PAPR value the oversampling factor should take into chosen to be 4 [11].
In Figure 6, plots of the CCDFs of the PAPR for both systems are shown.It is clear that the conventional Wi-MAX system has PAPR values in the range ~6.5 -11.5 dB, while the proposed system has 0 dB PAPR va .That is because of the con tant amplitude achieved by the pr ck "CA modulator".This means that there are no peaks in the transmitted signal.processes.It can be observed that the proposed system provides a significant BER performance improvement over the conventional system.

For AWGN Channel
The performance of the proposed system is better than that of the conventional system over all b o E N ity ratio) (the energy per bit to noise power spectral dens values.At BER = 10 -2 , the performance gain is about 6.6 dB for the proposed system when compared to that of the conventional system.This is attributed to the use of only positive or negative levels in our proposed CA demodulator, while the zero level is very rarely to be happened due to the OFDM nature.Therefore, the effect of the In-phase noise can be completely removed.However, pact of Out-of-phase noise can't be eliminated.the im That is because it changes the signal polarity.It is worth mentioned that our proposed system performance is superior to the best case of the previous constant envelope OFDM system [25] by 2 dB gain.

For ITU Pedestrian-A Multipath Fading
Channel The performance of the proposed system is also better than that of the conventional system over all b o E N values.At BER = 10 -2 , the performance gain is about 8.4 dB for the proposed system when compared to that of the formance gain is due to the onsequently, BER performance enhancement can be achieved but, the price to be paid is a reduction in the system transmission throughput.

For ITU Vehicular-A Multipath Fading
Channel The performance of the proposed system outperforms the conventional system for conventional system.
The improvement in the per multipath fading channel effect.Hence, our CA demodulator outperforms the equalization process in the conventional system for multipath noise impact removal.In addition, extra samples are inserted in the proposed system.Therefore, the length of the CP is increased.C .At BER = 10 -2 , the performance ga for the proposed system when compared to that of the conventional system.While the conventional system behaves better than the proposed system for 20.5 dB

Impact of Equalization
In this subsection, the effect of the equalization process for the conventional and the proposed OFDM systems are studied as shown in Figure 8.Both Zero Forcing (ZF) and MMSE equalization process are compared unde ), it behaves as an equalnoise removal.Therefore, r Vehicular-A channel.It is clear that the equalization processes enhances the performance of the conventional system, while it degrades the proposed system performance.That is because besides, the original function of the CA de-modulator in the proposed system (which is to regenerate the OFDM samples izer for the In-phase channel the proposed system does not need any equalization processes.In addition, due to the perfect channel estimation used, both ZF and MMSE equalization have the same performance.

Impact of ins N
The main parameter which affects the proposed scheme is ins N value.Its effect on the system accuracy, In-band distortion, output symbol length, complexity, and the transmission throughput are studied.

The System Accuracy
Under no channel conditions, Figure 9  That is because for higher ins N values, the less step size T , the CA de-modulator can ER performanc performance is achieved.Howeve pr hen more precisely follow the original symbol.
Figure 10 displays the B e of the proposed OFDM system under Vehicular-A multipath fading channel environment.It is clear that for higher ins N values, better r, the ice to be paid is the system throughput or the system speed degradation.

In-Band Distortion
Under no channel conditions, the EVM values are calculated for different ins N values as displayed in Table 3.It is clear that for higher ins N values, lower EVM values are obtained.Hence, better performance is achieved.

The System Comple
serial manner used to perform the proposed CA modulation, the higher N value ins ocessing time to produce the output.Therefore, ins N values do not affect the system complexity but it affects the system speed.However, if the OFDM symbol length   s T , the re is kept fixed, the sampling rate is increased.Hence quired bandwidth is enlarged.Moreover, the IFFT length is decreased.Consequently, the subcarrier spacing is increased.However, there is no degradation in the transmission throughput.

Conclusion
OFDM is a method of transmitting data simultaneously over multiple equally-spaced carrier frequencies, using Fourier transform processing for modulation and de osed scheme in this paper (which uses the suggested A modulation block) has achieved 0 dB PAPR value.Consequently, the power amplifier of the transmitter can modulation.High PAPR value is the most serious OFDM drawbacks.On the contrary to traditional techniques, the rop p C operate at the optimum (saturation) point.Hence, its efficiency and battery life are maximized.The mathematical model for the proposed system has been discussed.Furthermore, Extensive simulation programs have been executed to study the behavior of the proposed system compared with the traditional one.The proposed system has outperformed the traditional one in terms of BER under AWGN and multipath fading channels.At BER = 10 -2 , 6.6 dB, 8.4 dB, and 19 dB performance gains have been achieved for the proposed system over the conventional one under AWGN, ITU Pedestrian-A, and ITU Vehicular-A multipath fading channel, respectively.Additionally, the proposed system has outperformed the previous constant envelope system in terms of hardware complexity and BER perf e.Moreover, CA modu-14 tion parameters.In addition, the e ired proposed scheme.Finally, the impact of has been studied.For highe alues, the s curacy has be increased b h a cost of sy oughput degradation.
is executed by the followi steps: ate a reference symbol called accumulated stepped

Figure 4 .
Figure 4. Time and frequency domains for both systems.

Figure 6 .Figure 7 .
Figure 6.The CCDFs of the PAPR for the conventional and the proposed OFDM systems.BER Vs E b /N o is due to the huge excess in the propos m symbol length.Therefore, the proposed system is a frequency selectivity is se-.Under using a g coding or channel adaptive modulation scheme, this limitation can be overcome.Due to the long proposed system symbol length, the performance is the best under Vehicular-A channel then under Pedestrian-A channel and finally under AWGN channel for low ffected by the Doppler spreading in the multipath fading channel.This is more evident in the Vehicular-A channel mulation results where the si vere ood channel reversed for high b o E N values.

Figure 8 .
Figure 8.The Equalization effect for both the conventional and the proposed OFDM systems.
OFDM symbol length time is increased which affects the system speed.
there is no effect on t dwidth, the IFFT length, and increased pling rate, the required ban the subcarrier spacing.However, the transmission throughput is decreased to H. Y. Sakran, M. Shokair and A. A. Elazm, "Combined for PAPR Reduction in i: ormanc lation has introduced EVM = .85%for In-band distortion under the given simula qualization process has not requ for the