Fast Dummy Sequence Insertion method for PAPR reduction in WiMAX systems

In literature, many researches proposed a variety of methods to reduce PAPR (Peak to Average Power Ratio). Among those, DSI (Dummy Sequence Insertion) is one of the most attractive methods for WiMAX systems because it does not require side information transmitted along with user data. However, the conventional DSI methods find dummy sequence by performing an iterative procedure until achieving PAPR under a desired threshold. This causes a significant delay on finding dummy sequence and also effects to the overall performances in WiMAX systems. In this paper, the new method based on DSI is proposed by finding dummy sequence without the need of iterative procedure. The fast DSI method can reduce PAPR without either delays or required side information. The simulation results confirm that the proposed method is able to carry out PAPR performances as similar to the other methods.


I. INTRODUCTION
OFDM (Orthogonal Frequency Division Multiplexing) is a technique to provide high spectrum efficiency [1] by increasing density of subcarriers.The advantages of OFDM are robust to ISI (Inter Symbol Interference) and multipath fading.With these benefits, OFDM technique has been adopted for many standards such as DAB (Digital Audio Broadcasting) system, DVB (Digital Video Broadcasting) system, wireless LAN (IEEE 802.11x),WiMAX, etc.However, it is a nature of OFDM signal to face the problem of high PAPR (Peak to Average Power Ratio).This deficiency occurs when the peak power is much higher than the range of amplifier, resulting in a clipping of the peak signal.Hence, larger linear range of amplifier must be required to protect the clipped signal.In practice, the cost of such an amplifier is very expensive and also the energy consumption is inefficient.
In literature, many methods have been proposed to solve a problem of high PAPR.For example clipping method [2][3], this method is very simple by clipping the parts of the signals which are outside the allowed region.The disadvantage of this method is to provide the low performance of BER.In [4][5], SLM (SeLective Mapping) method multiplies the several phase sequences in OFDM data after IFFT operation and selects the sequence of the lowest PAPR to transmit.But this method necessarily requires the side information on phase rotation to transmit along with user data to the receiver.It results in lower data rate.In [6][7], PTS (Partial Transmit Sequence) method is similar to SLM method but its difference is on multiplying the phase factor after IFFT operation.For DSI (Dummy Sequence Insertion) method [8][9], it employs the dummy sequence adding to the data in order for PAPR reduction.This method is simpler than SLM and PTS methods because it does not require side information.For WiMAX system, it is more practical to apply DSI than SLM or PTS.This is because SLM and PTS require the change in air interface protocol but not for DSI.Moreover, the data frame of WiMAX affirmably supports the ease of applying DSI method.According to IEEE 802.16, the data frame of OFDM signal is allocated by 256 subcarriers which is composed of 192 data subcarriers, 1 zero DC subcarrier, 8 pilot subcarriers, and 55 guard subcarriers.Therefore, the dummy sequence can be added within the slot of 55 guard subcarriers without degradation of user data.
To obtain the suitable dummy sequence, DSI method has to perform the iterative procedure by changing the possible sequences until its PAPR is under the desired threshold.The delay due to iterations is unpredictable and it is changed from one data frame to another.This causes an unnecessary delay added in the system and also it provides the unreliability on data rate transmission.In this paper, the new approach of DSI to find suitable dummy sequence is proposed.It does not require any iterative procedures so the fast PAPR reduction can be achieved.The proposed method is also convenient to implement because the suitable dummy sequence is obtained by a close-form solution.

II. FAST DUMMY SEQUENCE INSERTION
The new approach to find the suitable dummy sequence without the use of iterative procedure is to estimate the closeform solution of dummy sequence when knowing the input data sequence.Assuming one OFDM frame having N subcarriers, then the signal after IFFT operation is given by 1 Where X(k) is the input signal sampled at kth time whose amplitude and phase are determined by modulation types.
From (1), the PAPR can be defined as ( Where E[•] is the operation of expectation.By assigning the dummy sequence into D subcarriers, then the expression in (1) can be rewritten into a matrix form as shown in (3). Where Note that X D and X N-D is the vector of dummy sequence and input signals which are allocated at the first N-D subcarriers and the last D subcarriers of OFDM frame, respectively.
As noticed in (2), the problem to find a suitable dummy sequence is established by Considering ( 4), the best PAPR is equal to 1 when for all n.Hence, the optimal problem can be rewritten as Using the inequality of and applying (3) into (5), then the summation of errors is expressed as (6) Where (•) H is the conjugate and transpose operation and 1 N×1 is the N×1 column vector whose each entry is equal to 1.
By taking ∂J(X D )/ ∂X D = 0, the optimal solution can be found by ( ) From (7), the suitable dummy sequence signals can be achieved.It is clearly seen that there is no need of either using iterative procedure or sending side information.In such a way, the fast and simple processing can be implemented for WiMAX systems.In addition, the proposed PAPR reduction is able to be applied on any available WiMAX protocols.
The solution in ( 7) is required to know only the average power of signal which can be calculated by Parseval's theorem as shown in (8).
Where (•) * is the conjugate operation.It is noticed in (8) that the average power of signal after IFFT operation is the same as average power of input signal which depends on its modulation technique.For WiMAX systems, there are four modulation types used for adaptive schemes; 2-PAM, 4-QAM, 16-QAM and 64-QAM.Then it is easy to estimate the average power of each modulation by considering its signal constellation.

A. Channel Model
The channel model for fixed wireless communication is considered here.The SUI (Stanford University Interim) [10] channel models are adopted in simulation.SUI channel models consist of low delay spread, moderate delay spread and high delay spread.In this paper, the SUI-3 channel is selected which its definition is shown in the Table I.

B. Amplifier Model
As mentioned on high PAPR for OFDM signal, the serious problem is occurred when implementing a practical amplifier on such a system.To realize this effect, the amplifier model is necessary to be included in simulation.This paper adopts the concept of solid state power amplifier [11] which is expressed in (9).Where Where, ρ is the amplitude of input signal, A is the saturated output level, and β is the parameter to decide the non-linear level.In simulation, A is set to 8 and β is set to 5 for all simulations.

IV. SIMULATION RESULTS
The simulation is undertaken by focusing on WiMAX data frame which employs OFDM format with 256 subcarriers.The detail of WiMAX data frame is described by IEEE 802.16e in which the guard band interval is allocated by 55 subcarriers.As a result, the DSI method is able to add the dummy sequence into these subcarriers with the maximum of D = 55.In this paper, the results of proposed DSI method are compared with the other DSI methods presented in literatures.We select two methods from [12] referred here as method 1 and method 2 because they offer the best performance in PAPR reduction.Method 1 obtains the dummy sequence from changing bit by bit while method 2 gains the dummy sequence from input information.Both methods require the iterative procedure to get the suitable sequence for each OFDM block.In simulations, the length of dummy sequence is set to 8, D = 8, and the threshold level is 15 dB for both methods.
Fig. 1 presents the complimentary cumulative distribution function of PAPR for proposed DSI method in comparing with method 1 and method 2. As seen in Fig. 1, all PAPR reduction methods provide lower PAPR than the system using no PAPR reduction method, for all modulation types.The proposed DSI method with D = 8 has its capability of reducing PAPR as similar to other DSI methods presented in literatures but its advantageous is no iterative processing required to find the suitable dummy sequence.The authors did more simulations on Bit Error Rate (BER) but still the results provide the same performance when using proposed method, method1 and method 2. Hence, for saving space in this paper, the BER performance is not presented here.Also noticed in Figure 1, the results of proposed method with D = 8 and 55 are compared.The better performance is achieved when more subcarriers are assigned by dummy sequence.In addition, the performance of D = 55 implies the best PAPR reduction in WiMAX systems because of the maximum limit of guard interval in WiMAX data frame.
The number of iterations required for finding the dummy sequence in each OFDM frame, D = 8, is presented in Table II.As expected, method 1 requires the most number of iterations because this method tries bit by bit until getting the desired solution.For method 2, it utilizes the input information so that the number of iterations is much less than method 1 but still higher than proposed method.The results in Table II show the undesirable delays caused by method 1 and method 2 whereas the proposed method does not cause any delay.These delays are unpredictable and cause the system with unreliable transmission rate.Therefore, the choice of using proposed method seems to be more practical Fig. 2 and 3 show BER performance for proposed DSI, DSI method 1, DSI method 2 and no PAPR reduction for 2-PAM and 16-QAM respectively.Only two modulation types are shown because the rest types provide the similar trend.As seen in Fig. 2 and 3, BER performance of proposed technique is similar to the other methods.However, BER performance of all PAPR reduction techniques is better than no PAPR reduction when modulation types is changed from 2-PAM to 16-QAM.The effect of high PAPR is more pronounced for more number of constellations, M-QAM.This is because the high order of modulation increases high peak power then it causes the signal clipped by amplifier.

V. CONCLUSION
In this paper, the new method for PAPR reduction based on DSI method is proposed.This method does not require the iterative procedure to find the suitable dummy sequence.Therefore, the proposed method is able to offer the faster PAPR reduction in comparing with the other DSI methods in literatures.Also the simulation results confirm that the proposed method provides the similar performances as other DSI methods.Without delay and no required side information, the proposed method is practically interesting to be applied on WiMAX systems.Moreover the proposed method is more increase BER performance of system than DSI methods in literatures.

Fig. 1 .
Fig.1.The complimentary cumulative distribution functions of PAPR for proposed DSI method, method 1 and method 2.

TABLE II NUMBER
OF ITERATIONS REQUIRED FOR FINDING THE DUMMY SEQUENCE IN EACH OFDM FRAME, D=8