10.IJAEST-Vol-No-6-Issue-No-2-Peak-to-Average-Power-Ratio-Reduction-Techniques-for-Long-Term-Evoluti by ISERP ISERP

Wafaa Radi* et al / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIES Vol No. 6, Issue No. 2, 230 - 236

Peak to Average Power Ratio Reduction Techniques for Long Term Evolution- Single Carrier Frequency Division Multiple Access System Hesham ElBadawy

Wafaa Radi

Network Planning dept. National Telecommunication Institute, NTI Cairo, Egypt heshamelbadawy@ieee.org

Faculty of Engineering, Ain Shams University, ASU Cairo, Egypt sramlye@netscape.net

Interleave Frequency Division Multiple Access (IFDMA) and Localized Frequency Division Multiple Access (LFDMA), compared to OFDMA system, is the lessening of the variation in the instantaneous transmit power as a result of their single carrier configuration [4]. This relieves the mobile terminal of maintaining highly efficient signal transmission by its power amplifier [5]. The current research evaluates PAPR characteristics for LTE SCFDMA system by using the Complementary Cumulative Distribution Function (CCDF) with Root Raised Cosine (RRC) pulse shaping filter. Notably, pulse shaping is necessary for a single carrier structure to band limit the transmit signal [10].

Abstractâ&#x20AC;&#x201D; As the power consumption is an essential issue for designers of mobile devices The 3rd Generation Partnership Project (3GPP) â&#x20AC;&#x201C; Long Term Evolution (LTE) employs a multicarrier communication technique on the air interface, Single Carrier Frequency Division Multiple Access (SCFDMA), in uplink scenario and Orthogonal Frequency Division Multiple Access (OFDMA) in the downlink. SCFDMA core modulation technology has a significantly lower Peak to Average Power Ratio (PAPR) compared to OFDMA. This paper studies the PAPR reduction techniques for LTE SC-FDMA system.

Salwa ElRamly Electronics & Communication

Electronics & Communication Engineering dept, Canadian International College, CIC Cairo, Egypt wafaa_radi@cic-cairo.com

Keywords-(3GPP) 3rd Generation Partnership Project, (LTE) Long Term Evolution, (SC-FDMA) Single Carrier Frequency Division Multiple Access, (OFDMA) Orthogonal FDMA and (PAPR) Peak to Average Power Ratio.

I. INTRODUCTION Wireless mobile communications are undergoing rapid progression towards fourth generation (4G). One common design approach in 4G systems is Orthogonal Frequency Division Multiple Access (OFDMA) [1]. It is a multicarrier communication technique on the air interface; it has become broadly accepted mainly because of its high resistance to frequency selective fading channels [2]. The immunity to multipath fading develops from the reality that the OFDMA signal in the frequency domain consists of several orthogonal sub-carriers [3]. Although OFDMA system has many advantages, it suffers from a major drawback: high Peak to Average Power Ratio (PAPR) of the transmit signal, where PAPR is defined as the ratio of the peak power to the average power of the transmit signal [4]. Signals with a high PAPR require extreme linear power amplifiers to avoid excessive inter-modulation distortion [5]. Excessive linearity for power amplifiers is not considered a problem in fixed applications where the device has a large volume and is connected to the mains, but for small mobile devices running on their own batteries it creates more challenges [6]. The 3rd Generation Partnership Project (3GPP) adapted its next 4G cellular system Long Term Evolution (LTE) [7]. It decided to use OFDMA in the downlink direction and to use the power efficient Single Carrier Frequency Division Multiple Access (SC-FDMA) in the uplink direction [8] [9]. SCFDMA is a unique technique for uplink wireless communication. The most important advantage of SC-FDMA schemes, such as

The rest of this paper is organized as follows: section II demonstrates a system model of SC-FDMA and investigates the upper bound analytical analysis to characterize the PAPR of IFDMA modulated signal specifically for Binary Phase Shift Keying (BPSK) and Quadrature Phase Shift Keying (QPSK) modulation format. Section III presents the simulation model of SCFDMA; section IV shows the numerical results with physical interpretation given. First of all, the analytical results of PAPR of IFDMA with BPSK and QPSK technique by using RRC and RC pulse shaping filter are shown. then, the simulated analysis of PAPR of SCFDMA techniques (IFDMA and LFDMA) by using RRC and RC pulse shaping filter for BPSK, QPSK, 16-Quadratue Amplitude Modulation (16QAM), and 64QAM is shown. Finally, a comparative result between the analytical upper bound and the simulation results is introduced. In addition, a case study of the impact of data blocks size and number of data subcarriers on the PAPR of LTE SC-FDMA/OFDMA system is illustrated in this section. Section V, then, presents the conclusion and recommendations for future studies. II. SYSTEM MODEL Fig. 1 shows the block diagram of a basic LTE SCFDMA system. SC-FDMA is a modified structure of OFDMA system [4]. SC-FDMA can be viewed as Discrete Fourier Transform (DFT)-spread OFDMA or frequencyspread OFDMA, where time domain data symbols are transformed to frequency domain by DFT before going through OFDMA system [11].

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SC-FDMA Transmitter m (s)

S/P Converter “Symbols block”

Constellation Mapping

Sub-carrier Mapping

DFT Size- S

~ T = T S/N

N>S

S T

S: number of data symbols N: number of data subcarriers ~ T, T: symbol durations

SC-FDMA Transmitted Signal m(n)

Cyclic Prefix & Pulse shaping

IFFT Size- N

Figure 1: block diagram of LTE SC-FDMA/OFDMA Transmitter

The input to the SC-FDMA transmitter is a stream of m bits that is converted to multilevel sequences of complex number m(s), where m(s) is the data symbol, and s is the sample index. Then, the transmitter concatenates the modulation symbols into blocks through Serial to Parallel converter (S/P) block, each containing S symbols. These modulated symbols perform S-point DFT to produce a frequency domain representation [12] [13] [14] as follows: M k    ms  s 

 j πsk e S



 i   M   ,i  B . k B  ~  M i    (   k  S   ), ( 0  i  N - 1)  ,Otherwise   

The output of the DFT is then applied to a subcarrier mapping block which maps each of the S-DFT outputs to one of the N orthogonal subcarriers (N > S) that can be transmitted. The ratio between N and S is called the bandwidth expansion factor of the symbol sequence B (B=N/S) [3]. If all terminals transmit S symbols per block, the system can handle B simultaneous transmissions without co-channel interference. The outcome of the subcarrier ~ mapping is N of complex subcarrier amplitudes M ( i ) (i = 0, 1, 2…, N-1),The outputs of subcarrier mapping block are used for N-point Inverse Fast Fourier Transform (N-IFFT) which transforms the N subcarriers to a signal m( n ) in time domain, then each m( n ) is transmitted sequentially [15].

The transmitter performs two other signal processing operations prior to transmission. It inserts a set of symbols referred to as a cyclic prefix (CP) in order to provide a guard time to prevent inter-block interference (IBI) due to multipath propagation. The transmitter also performs a linear filtering operation referred to as pulse shaping in order to reduce out-of band signal energy [5]. In LTE- SC-FDMA, subcarrier mapping process is classified into two methods: localized mapping and distributed mapping. So, LTE-SC-FDMA is classified to two variations: LFDMA and IFDMA [2]. In LFDMA, the DFT outputs are mapped to a subset of successive subcarriers thus, confining them to a fraction of the system bandwidth. While in IFDMA, the DFT outputs are assigned to subcarriers over the entire bandwidth non-continuously [3]. In the time domain, the SC-FDMA modulated symbols differ based on the applied subcarrier mapping technique [11].



~ The frequency domain signal M ( i ) is then processed in the N-IFFT to get a time domain IFDMA transmitted signal, after a simple derivation the outcome is:

S 

The frequency samples after interleaved subcarrier mapping allocation are as follows:

Binary Input

~ M (i)

M (k)





 ~ mn   IFFT M i   ms  B



The time domain signal of IFDMA technique is simply a reappearance of the original input symbols m(s) with a scaling factor of 1/B. When the subcarrier allocation starts from the rth subcarrier (0 < r < B-1), then  i r   ,i  B . k  r M    B  ~    k  S   , 0  i  N - 1 M i     ,Otherwise  



~ IFFT of M ( i ) can be obtained as follows:





 ~ mn   IFFT M i   ms  e B

jπn r N



j πnr

There is an additional phase rotation of e N when the subcarrier allocation starts from the rth subcarrier instead of subcarrier zero. In case of applying a LFDMA concept, the frequency samples are expressed as: M  i  ,   i  S    ~  M i    , S  i  N     The time domain transmitted signal of LFDMA is derived as: .





~ mn   IFFT M i  

  B 

1- e

j πb B

    S 

mp 

S 



p 



 s-p b j 2 π   S BS  e

   

where 0 < b < B, n  B. s  b and 0 < p < S - 1 2

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From equation (7); we find that the LFDMA signal also has exact copies of input time symbols in multiple separated positions and in-between there are values which are the sum of all time input symbols in the input block with different complex-weighting. The complex pass band transmit signal of SC-FDMA X(t) for a block of data can be represented as follows:



N ~ X t   e j ωc t  m n  p t  n T n 





X t 

   











 P   Pr  V

to achieve this, the CCDF Pr

 T 

RRC filter is characterized by a roll off factor α determines the sharpness of the frequency response where 0 < α < 1.

PAPR





Contrastedly, lower PAPR allows higher efficiency, and higher PAPR signal allows lower efficiency. PAPR is defined as follows: PAPR 

Max

X(t )

  t  NT



~ NT







~  X ( t ) dt NT  As in [6], the authors derived an upper-bound of the CCDF of the instantaneous power for IFDMA with RC pulse shaping filter. Here the RRC filter is deployed and the bounds for BPSK and QPSK modulations are shown.

The baseband conventional SC modulated signal is considered as follows:  ~  X t    m n  p t  n T n





a random variable V for a given to is defined as follows:

 m n p t ~  m n p t  n T  .

V  X t 0  



n

 a

~ 0  nT 



n

where a n The paper goal is to characterize the following CCDF:



 

V δ

 



   



X (t )

   

 P

X t 

   



 P

   





n 



  e  υ δ  E  e 

 υ an     

(15)

where  is a solution of the following equation:



E a n e  υ an





E e

 υ an



 δ

(16)

n 

Here the span is limited by considering - nmax ≤ n ≤ nmax. By applying the upper bounds specifically for BPSK modulation format then (15) and (16) become: n max ~ ~ (17)  p t  nT Tansh υ p t  nT  δ n   n max





 



where δ  γ P and for BPSK γ  [17 ]. Pr  X t   Po   







The theoretical relationship between PAPR [dB] and transmit power efficiency (η) is as follows [8]: η  ηmax .

 Pr

upper bounds as follows [6]:

The impulse response of RRC filter is given as follows [10]: ~ T  α    π t     α  π t  cos  sin    ~ ~ α  α t T T      p t   ~  π T  α t     ~ 

   

 P

where P   and δ  P



where ωc is the carrier frequency of the system, p(t) is the ~ baseband pulse shaping filter, and T is the symbol duration of the transmitted symbol m(n).





   

e υ δ



~   n max n max υ p t  n T   e   n   n max



  e υ p t  n T~ 



(18)

By Applying the upper bounds specifically for QPSK modulation format then (15) and (16) become: n max  υ p t  nT~  ~   δ (20) p t  nT Tansh     n   n max   





where δ  γ P and for QPSK γ   [8].  

Pr  X ( t ) 

 e υ δ   

   



   

 P



 n max 

n max



n   n max

      

~ υ p ( t  n T )





~  υ p ( t  n T )    e    

(21)

In section IV, the numerical analysis for the PAPR will be illustrated. III.

SIMULATION MODEL

In order to check and validate the presented mathematical model in section II the present section will introduce a simulation criteria based upon the deployment of different system stages as shown in Fig. 1. The simulation process is presented in the following flow chart as shown in Fig. 2. A 104 uniformly random binary data bits were generated to acquire the CCDF of PAPR, transmission bandwidth of 5MHz was assumed when calculating PAPR [6].

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Baseband Modulator m(s) 0 < s < S-1 DFT M(k) 0 < k < S-1 N(1:B:N) = M(k)

Subcarrier Generator (N < S) (N/S =B)

IFDMA If LFDMA N(1:N) = M(k) IFFT

Calculate Average = Mean (abs(x(t))^2)

2.5

X‟(t)

alpha_ RC = 0.01 alpha _RC = 0.2 alpha _RC = 0.4 alpha _RC= 0.6 alpha _RRC= 0.01 alpha _RRC= 0.2 alpha _RRC= 0.4 alpha _RRC= 0.6

6 x 10-1 -1

5 x 10

4 x 10-1

TABLE 1: LTE SCFDMA SIMULATION PARAMETERS Simulation Case 1 Case 2 Case 3 Case 4 Parameters

Modulated data blocks

BPSK/ QPSK/ 16QAM/ 64QAM

-1

16QAM 64, 128, 256, 512, 1024

1024

32,64, 128,256, 512

N/S

5MHz

RC/RRC

RRC

None

0.5

0.01, 0.2, 0.4

---

----

Pulse Shaping Filter type

16QAM

256

Bandwidth Fs

BPSK/ QPSK

1024

-1

3 x 10

(a)

A- Analytical results The derived CCDF‟s of IFDMA upper bound PAPR (18) and (21) with RRC and RC pulse shaping filter are plotted in Fig. 3 as functions of the coefficient Po of BPSK and QPSK modulation formats.

5.5

B- Simulation results Table 1 shows all the cases simulation parameters that are used in this section:

RESULTS AND ANALYSIS

Po (dB)

Figure 3: The upper bonds of instantaneous power for IFDMA with (a) BPSK modulation and (b) QPSK modulation. Different values of α are used.

Figure 2: Simulation flow chart for LTE SC-FDMA system

4.5

The analytical parameters used are n max= 8 , T = 1, and t0 = T/2 [6]. The conclusion is the IFDMA technique with RRC pulse shaping method has lower PAPR than the case of RC pulse shaping method.

End

(b)

Plot CCDF of PAPR

3.5

Po (dB)

PAPR= Peak /Average

Pr [ PAPR > Po ]

-3

Calculate Peak = Max(abs(x(t))^2)

2 x 10

alpha _RC = 0.01 alpha _RC= 0.2 alpha _RC= 0.4 alpha _RC= 0.6 alpha_RRC= 0.01 alpha _RRC= 0.2 alpha _RRC= 0.4 alpha _RRC= 0.6

-1

10 -2

Pulse shaping filter RC/RRC X(t)

IV.

Pr [ PAPR > P o ]

Binary Data Generator (S bits)

the PAPR simulation for various subcarrier mapping schemes of SC-FDMA system (IFDMA and LFDMA) using the two types of pulse shaping filters; RC and RRC is shown in Fig. 4. All simulation parameters are summarized in (Table 1: case 1) 4

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10-1

10-2

6 Po (dB )

C- Comparison of analytical and simulation results Fig. 5 and 6 show a comparison between the derived upper bound of the instantaneous power of IFDMA - RRC in (18) and (21) with the IFDMA CCDF - RRC obtained from the simulation results. The previous analytical parameters are used, whereas the simulation parameters used are listed in (Table 1: case 2). The upper bound PAPR is valid compared to the simulation results and the bound is rather tight in the tail region of the distribution which is the research‟s main concern.

10-1 IFDMA_RC IFDMA_RRC LFDMA_RC LFDMA_RRC

Pr [ PAPR > P o ]

(a) BPSK

-2

Fig. 4 presents a comparison between the simulation results obtained by using RRC and RC pulse shaping filters for different data modulations BPSK, QPSK, 16QAM and 64QAM. The conclusion is that for different data modulation formats the IFDMA scheme with RRC pulse shaping filter has lowest PAPR values, but in LFDMA technique it has a very similar level of PAPR due to the complex weighting in LFDMA signal equation (7) which limits the effect of the deployed pulse shaping filter.

5 Po (dB)

(b) QPSK

IFDMA_RC

Pr [ PAPR > Po ]

Pr [ PAPR > P o ]

IFDMA _ RC IFDMA_RRC LFDMA_RC LFDMA_RRC

Upper bound alpha = 0.01 alpha = 0.2 alpha = 0.4 Simulation alpha = 0.01 alpha = 0.2 alpha = 0.4

-1

-2

-3

LFDMA_RC

-1

-2

4.5

5.5

6 Po (dB)

6.5

7.5

-1

5 Po (dB) 6

Figure 5: CCDF of instantaneous power for IFDMA with BPSK modulation and different values of α. Dotted lines are upper bonds results and solid lines are the simulation results

IFDMA_RC IFDMA_RRC LFDMA_RC LFDMA_RRC

Upper bound alpha = 0.01 alpha = 0.2 alpha = 0.4 Simulation alpha = 0.01 alpha = 0.2 alpha = 0.4

-1

Pr [ PAPR > Po ]

Pr [ PAPR > P o ]

LFDMA_RRC

Pr [ PAPR > Po ]

IFDMA_RRC

10-2

-3

-2

10-4

10-3

6.5

7.5 Po (dB)

5 Po (dB)

Figure 6: CCDF of instantaneous power for IFDMA with QPSK modulation and different values of α. Dotted lines are upper bonds results and solid lines are the simulation results.

8.5

(d) 64QAM Figure 4: PAPR for SC-FDMA subcarrier mapping schemes; IFDMA and LFDMA with RRC/RC pulse shaping filter for a) QPSK b) 16QAM C) 64QAM

D- Case study Firstly, Fig. 7 shows the impact of data block size on PAPR of SC-FDMA/OFDMA systems provided that 16QAM data modulation for is considered, see (Table 1 case 3). It has been noticed that as S increases, PAPR of OFDMA and LFDMA increases; however, for IFDMA it decreases. For 5

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10-1

10-2 2

Po (dB)

In this paper, the validation that IFDMA has the lowest PAPR than LFDMA and OFDMA is presented. Also mathematical analysis to characterize the PAPR of IFDMA modulated signal is proposed by using two type of pulse shaping filter, RC and RRC. Also a numerical analysis for the PAPR of IFDMA and LFDMA with RC/RRC is introduced. The analysis investigates that RRC pulse shaping filter is effective in reducing PAPR in IFDMA than RC pulse shaping filter. For OFDMA/ SC-FDMA system, the case study shows that the S is the major factor characterizing the CCDF of peak power; it has an impact in reducing the PAPR in IFDMA systems, especially when S increases. The recommendation for future studies is presenting the mutual performance evaluation of discussed techniques performing over Adaptive wide gaussian noise channels and state some significant considerations resulting from this. REFERENCES

[1]

[2]

Secondly, the PAPR of the IFDMA/LFDMA and OFDMA systems for different N is shown in Fig 8. All parameters are listed in Table 1: case 4.

[4]

[3]

Pr [ PAPR > Po ]

Figure 7: PAPR for OFDMA/SC-FDMA (IFDMA and LFDMA) with different S (S = 32, 64, 128, 256, 512) for 16QAM data modulation.

IFDMA N = 64 N = 128 N = 256 N = 512 N = 1024 LFDMA N = 64 N = 128 N = 256 N = 1024 N = 512 OFDMA N = 64 N = 128 N = 256 N = 512 N = 1024

-1

10-2

Po (dB)

CONCLUSION

IFDMA S = 32 S = 64 S = 128 S = 256 S = 512 LFDMA S = 32 S = 64 S = 128 S = 256 S = 512 OFDMA S = 32 S = 64 S = 128 S = 256 S = 512

resulting in zero amplitude for the remaining subcarriers, so the PAPR has almost no change.

Pr [ PAPR > Po ]

OFDMA, this results because of the growth in the envelope variation of OFDMA signal due to the increasing in the number of data symbols per block. For LFDMA, as mentioned before, the time domain signal of LFDMA has complex weighting values which are the sum of all time input symbols in the input block, so as S increases, the PAPR for LFDMA signal increases. On contrary, the case of IFDMA the time domain signal is a simple repetition of the input signal, so the peak power of the transmitted signal has a very small variation when data block size increases, but at the same time the average power increases, so the resultant PAPR goes down.

[5] [6]

[7] [8] [9] [10]

Figure 8: PAPR for OFDMA/SC-FDMA (IFDMA and LFDMA) with different N (N= 64, 128, 256, 512, 1024) for 16QAM data modulation.

It is obvious that N has almost no impact on the distribution of the PAPR for both OFDMA/SC-FDMA system, whereas in the subcarrier mapping process the processed input data is assigned to assigned subcarriers. It is allocated over the entire bandwidth continuously or non-continuously according to the type of subcarrier mapping approach,

[11]

[12]

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