Pre-Scrambling Method for PAPR Reduction in OFDM Communication Systems

By Guided by

E. Geetha Rani Shakeel Ahmed

14B81D6501 Senior Asst. Prof

Introduction to OFDMIntroduction to OFDM

Definition of OFDM

An Orthogonal Frequency Division Multiplexing (OFDM) is a Frequency Division Multiplexing scheme used as a Digital multicarrier modulation method. A large number of closely spaced orthogonal sub-carriers signals are used to carry data on several parallel data streams or channels.

It is also called as Quadrature Carrier Multiplexing.

BLOCK DIAGRAM OF OFDM

Example of OFDM

Lets we have following information bits

1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, …

Just converts the serials bits to parallel bits

C1 C2 C3 C4

1 1 -1 -1

1 1 1 -1

1 -1 -1 -1

-1 1 -1 -1

-1 1 1 -1

-1 -1 1 1

Example of OFDM cont..

Modulated signal for C1 Modulated signal for C2

Modulated signal for C3 Modulated signal for C4

Modulate each column with corresponding sub-carrier using BPSK

Example of OFDM cont..

Final OFDM Signal = Sum of all signal

)2sin()()(1

0

nttItVN

nn

Generated OFDM signal, V(t)

V(t)

Multipath Radio Channel

Inter-Symbol-Interference

Transmitted signal:

Received Signals:

Line-of-sight:

Reflected:

The symbols add up on the channel

Distortion!

Delays

Concept of an OFDM signal

Ch.1

Ch.2 Ch.3 Ch.4 Ch.5 Ch.6 Ch.7 Ch.8 Ch.9 Ch.10

Saving of bandwidth

Ch.3 Ch.5 Ch.7 Ch.9Ch.2 Ch.4 Ch.6 Ch.8 Ch.10

Ch.1

Conventional multicarrier techniques

Orthogonal multicarrier techniques

50% bandwidth saving

frequency

frequency

Disadvantages of OFDM

Peak to average power ratio (PAPR)

avgP

txPAPR

2

)(

The large amplitude variation increases in-band noise and increases the BER when the signal has to go through amplifier nonlinearities.

• Due to the large number of sub-carriers in typical OFDM systems, the amplitude of the transmitted signal has a large dynamic range, leading to in-band distortion and out-of-band radiation when the signal is passed through the nonlinear region of power amplifier.

• Although the above-mentioned problem can be avoided by operating the amplifier in its linear region, this inevitably results in a reduced power efficiency.

• The PAPR of the transmit signal is defined as

The effect of high PAPRThe effect of high PAPR

2

0

2

0

max

1/

t TT

x tPAPR

T x t dt

Bandwidth Regrowth

• If we sample x(t) by a sampling rate of 1/Ts (the sampling period Ts= T/N ), we may miss some signal peaks and get optimistic results for the PAPR.

• For better approximating the true PAPR in the discrete-time case, we usually oversample x(t) by a factor of L , i.e., the sampling rate is L/Ts .

• It was shown in that an oversampling factor L=4 is sufficient to approximate the true PAPR.

PAPR in discrete-time casePAPR in discrete-time case

• For an OFDM system with N sub-carriers, an oversampling rate of L can be achieved by inserting (L － 1)·N zeros in the middle of the modulated symbol vector to form a 1×LN data vector X, i.e.

• The PAPR computed from the L-times oversampled time-domain signal samples is given by

PAPR in discrete-time casePAPR in discrete-time case

2

0 12

max kk LN

k

xPAPR

E x

1

0 , 1 , , / 2 1 , 0, , 0, / 2 , , 1L N

X X X N X N X N

X

• The cumulative distribution function (CDF) of the PAPR is one of the most frequently used performance measures for PAPR reduction techniques. In the literature, the complementary CDF (CCDF) is commonly used instead of the CDF itself.

• The CCDF of the PAPR denotes the probability that the PAPR of a data block exceeds a given threshold.

• From the central limit theorem, the real and imaginary parts of the time domain signal samples follow Gaussian distributions, assuming each distribution with a mean of zero and a variance of 0.5 for a multicarrier signal with a large number of subcarriers.

The CCDF of the PAPR

• Hence, the amplitude of a multicarrier signal has a Rayleigh distribution, while the power distribution becomes a central chi-square distribution with two degrees of freedom.

• The CDF of the instantaneous power of a signal sample is given by

• The CCDF of the PAPR of a data block with Nyquist rate sampling is derived as

• This expression assumes that the N time domain signal samples are mutually independent and uncorrelated.

The CCDF of the PAPR

1 exp .F z z

1

1

1 1 exp .

N

N

P PAPR z P PAPR z

F z

z

• Distortion

o Clipping

o Peak Windowing and Peak Cancellation

o Companding

• Distortion less-Based on Scrambling

o Selected Mapping (SLM)

o Partial Transmit Sequence (PTS)

• Others

o Active Constellation Extension (ACE)

o Tone Reservation (TR)

PAPR Reduction Methods

• By distorting the OFDM signal amplitude, a kind of self-interference introduced that degrades the BER.

• Nonlinear distortion increases out-of-band radiation.

• Clipping causes significant In-band distortion and Out-of-band radiation in the signal spectrum and results in BER performance degradation.

Clipping

CompandingCompanding

CompandingCompanding

Peak Windowing Symbol (QPSK) of sub-carrier i at time k

Other symbol-alphabets can be used as well (BPSK, m-QAM)

Baseband signal is generated by DSP

)(2exp)()( ,,, kTtfijxkTtwts kikiBB

Re

Imxi,k

Window function Sub-carrier

Limitations of Distortion Techniques

• The Nonlinear distortion techniques introduces a kind of self-interference and increases the level of the out-of-band radiation.

Selected mapping (SLM)

• SLM method generates M independent data sequences from the same sequence whose length is N and chooses the sequence to have the lowest PAPR among these.

• A first cluster does not give the phase change. We give

Selected mapping (SLM)

1. A set of U markedly different, distinct, pseudo-random but fixed vectors P(u) = [P0

(u) ,…, PN-1(u) ], with

must be defined.

2. The subcarrier vector A is multiplied subcarrier-wise with each

one of the U vectors P(u), then resulting to component

3. Then all U alternative subcarrier vectors are transformed into time domain to get and finally that transmit sequence with the lowest PAPR is chosen.

For implementation, the SLM technique needs U IDFT operations, and the number of required side information bits is

, denotes the smallest integer that exceed y.

Selected mapping (SLM)

( )( ) ( ), [0, 2 ),u

nju un nP e 0 , 1n N u U

0 ,n N

( ) ( ){ }u uIDFTa A ( )ua a

( ) ( ) ,u un n nA A P 1 .u U

2log U y

N = 256, L = 4, 16-QAM,

PAPR reduction performance of SLMPAPR reduction performance of SLM

( ) { 1, 1, , }.unP j j

Partial Transmit Sequence (PTS)

Partial Transmit Sequence (PTS)

Partial transmit sequence (PTS)

Partial transmit sequence (PTS)

In general, the selection of the phase factors is limited to a set with afinite number of elements to reduce the search complexity.

The set of allowed phase factors is written as , where W is the number of allowed phase factors.

In addition, we can set without any loss of performance.

Hence, sets of phase factors are searched to find the optimumset of phase factors.

PTS needs M IDFT operations for each data block, and the numberof required side information bits is .

Partial transmit sequence (PTS)

2 / | 0,1, ,j n WP e n 1W

(1) 1b

1MW

12log MW

N = 256, L = 4, 16-QAM, exhausted research for .

W=2 means [+1,-1], W=4 means [+1, -1, +1j, -1j].

PAPR reduction performance of PTSPAPR reduction performance of PTS

1MW

Example of OFDM

Lets we have following information bits

1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, …

Just converts the serials bits to parallel bits

C1 C2 C3 C4

1 1 -1 -1

1 1 1 -1

1 -1 -1 -1

-1 1 -1 -1

-1 1 1 -1

-1 -1 1 1

Ranking of PAPR

Block diagram of Pre-Scrambling Method

Results

For a spectrum of 1000 sets of randomly generated data in time domain when the number of sub carriers is 16. The maximum PAPR of 1000 random data is 9.5 dB

Theoretical Peak value of the data without PAPR reduction method is 12 dB

The Peak Value decreases to 8 dB by pre-scrambling method

The Pre- Scrambling method has 0.5 dB performance gain over conventional PTS and considering the data which has high PAPR value (Worst Case)

PTS requires several IFFT operations which lead to problem of real time transmission because of transmission delay. But this problem is solved in Pre- Scrambling Method