DESCRI PTI ON

The Technical Field Of The I nvention

The invention relates to a PAPR ( Peak-to- Average Power Ratio) reduction of OFDM (Orthogonal Frequency Division Multiplexing) communication systems via rotation of optimally selected information symbols.

Prior Art About The I nvention(Previous Technique)

One of the major drawbacks of the OFDM communication systems is their large PAPRs which lead to very inefficient amplification and expensive transmitters. To alleviate large PAPR problem, researchers proposed some methods. And these methods can be classified as: clipping and filtering [2-4] , coding [5, 6] , use of interleavers [7, 8] , use of partial transmit sequences [9, 10] , tone reservation [ 1 1 ] , tone injection [ 12] , selective mapping [ 13, 14] , active constellation extension [ 15, 16] , companding [ 17] I n [ 18-20] , a number of studies to decrease the complexity of SLM method is performed considering the decimation in time and decimation in frequency FFT algorithms. I n these studies, a trivial approach is followed to rotate the sub-FFT frames. An overview of recent PAPR reduction techniques can be found in [21 -23]

There are wide variety of methods to lower PAPR. Since, PTS is the first remedy to high PAPR patent applications are focus on the difference of their methods from PTS. Application [24] offers a set of interleavers. According to a judgment logic, best interleaver that fits the information signal is used in transmitter. I n [25] , a mapping is offered based on a Markovian symbol transition probability distribution with quantized probabilities. So, puncturing one or more bits on the data set can be done. I n [26] , a modified version of PTS method is presented. Patent application [27] offers a circular phase rotation in between sub-blocks of data set. I n [28-29] , two different types of tone reservation are introduced. As a result, presented patent applications are different from our method.

Aims Of The I nvention and a Brief Explanation

This invention relates to a PAPR reduction of OFDM communication systems via rotation of optimally selected information symbols. A new PAPR reduction technique is proposed in which rotations of information symbols are focused on before the calculation of OFDM signal. For this purpose, decimation in frequency FFT algorithm is inspected in details and rotation procedure is applied on information symbols such that when they enter into the FFT algorithm they produce OFDM symbols with low PAPR values. The combination of information symbols during the run of the decimation in time FFT algorithm is inspected in details and according to obtained information , phase rotation for certain set of information symbols to reduce PAPR is proposed.

Another aspect of the invention , wherein to reduce the PAPR of the OFDM signal are rotated by phase factors, and modify the information signal .

A PAPR problem will be valid for new systems in future such as 5G systems. Thanks to this invention proposed a new approach and technique, and a PAPR reduction of OFDM com munication systems via rotation of optimally selected information symbols technique solves A PAPR problem in 5G systems.

The Descriptions Of The Figures Explaining The I nvention

The figures used to better explain PAPR reduction of OFDM comm unication systems via rotation of optimally selected information symbols developed with this invention and their descriptions are as follows:

Figure 1 : Summation of two complex numbers a and b.

Figure 2: PAPR reduction via Rotation of Optimally Selected I nformation Symbols.

Figure 3: CCDF comparison of the proposed method and PTS technique.

The Detailed Explanation Of The I nvention

To better explain a PAPR reduction of OFDM comm unication systems via rotation of optimally selected information symbols developed with this invention , the details are as presented below.

This invention proposed a new approach for PAPR reduction . The proposed method focuses on rotation of the information symbols before the calculation of OFDM signal . The combinations of information symbols in OFDM signal are inspected considering the decimation in frequency FFT algorithm and this information is used during the rotation of information symbols. Sim ulation results show that our proposed method is better than PTS technique and computational complexity of the proposed method is m uch less than that of the PTS approach Furthermore, the proposed technique is open to further improvements. CCDF comparison of the proposed method and PTS technique in Figure 3. PAPR of OFDM Symbol and Decimation in Frequency FFT Algorithm : Brief information about PAPR of OFDM signal and decimation in frequency FFT algorithm is provided below. Peak-to-Average Power Ratio:

For the complex information sequence consisting of N symbols, i.e. , S[n], n = 1, the discrete OFDM signal is calculated as:

where the envelope |s[n] | is Rayleigh distributed and its probability density function is given as

The PAPR for the OFDM symbol s[n] is calculated as: And the complementary cumulative distribution function (CCDF) for PAPR is defined as where PAPR ₀ is the threshold level. CCDF is employed to compare the performance of different PAPR reduction methods. Decimation in Frequency FFT Algorithm :

Discrete Fourier transform or inverse discrete Fourier transform can be calculated using either decimation in time or decimation in frequency FFT algorithms. For the given information sequence S[n] the DFT coefficients using decimation in frequency algorithm are calculated as

Explanation of the Proposed Technique Let S _j denote a complex number and for this complex number let's define 5 _t ^* as follows

S ^* = Si X b ^ίf (6) where f is any phase value in the range—p/2 £ f < p/2. Let s = [¾ 5i ¾ 5 ₃ ] be an information sequence consisting of 4 information symbols. The 4— point DFT coefficients of s can be calculated using decimation in frequency FFT algorithm as

The above result can be generalized for the N— point Fourier transform of an information sequence as

Using the above expression, 4 of the DFT coefficients of an 8 point sequence are calculated as in the form

s[n] = (So + S ₄ ) ^* + (S ₂ + s ₆ y + (S ₁ + S ₅ ) ^* + (s ₃ + s ₇ y (9) and the other 4 coefficients are calculated using s[n] = (S ₀ - S ₄ ) ^* + (S ₂ - S ₆ Y + (S ₁ - S ₅ Y + (S ₃ - S ₇ ) ^* . (10)

I t is obvious from (9) and ( 10) that even indexed information symbols are paired, they are summed and subtracted and the results are multiplied by some exponential terms, i.e. , they are rotated, then the rotated terms are summed, and similar operation has been performed on odd indexed information symbols. Finally, both partial sums are added to each other and resulting DFT coefficient is calculated. Addition of two complex numbers results in a complex number with large absolute value if the phases of the added complex numbers are not much different from each other. This is illustrated in Figure 1 for the complex numbers a and b. I n (9) , let's denote the summation of the terms involving even indexed pairs by S _even and the summation of the terms involving odd indexed pairs by S _odd . Then (9) can be written as

I f s[n] is a large number it can be decreased by rotating S _even or S _odd or rotating both of them with different amounts. For this purpose, all of the even indexed pairs or some of the even indexed pairs can be rotated which results in a rotation of S _even and vice versa for the odd indexed pairs. I n other words, some information symbol pairs appearing in (9) and ( 10) can be selected for phase rotation aiming lower PAPR. This is the main motivation for PAPR reduction. I n other words, either even indexed pairs or odd indexed pairs or both can be rotated before I DFT calculation such that after I DFT calculation the resulting signal owns lower PAPR. That is, instead of trivially determining the information symbols to be rotated for lower PAPR, an intelligent approach is introduced for the determination of information symbols to be rotated for lower PAPR.

Proposed Algorithm : The proposed algorithm is explained in details as follows. Let S[n] denote the information symbol sequence, and n denote the set of index values from 0 up to N— 1. Let a, b and c be the disjoint subsets of n such that n = a U b U c. Define S[n] as

Then S[n] can be written as the sum of 3 pairwise disjoint information sub-blocks 5 ^a [n], 5 ^fc [n], and S ^c [n], i.e. ,

S[n] = 5 ^a [h] U S ^b [n] U 5 ^c [n], (13)

Let ep be the set consisting of the even index pairs (2k 2k + N / 2) k = 0, 1, ··· , iV/2— 1 and op be the set consisting of the odd index pairs (2k + 1 2k + 1 + N / 2). And let ep _s be a subset of ep and op _s be a subset of op. And o _s is the set of elements appearing in the pairs in op _s , e _s is set of elements appearing in the pairs in ep _s , i _rem is set of elements not appearing in o _s and e _s i.e., n e _s u o _s u i _g . This means that

S[n] = S ^es [n] U 5° ^s [n] U S ^lrem [n ]. (14)

To reduce the PAPR of the OFDM signal s[n] = IDFT(S[n]) the 5 ^es [n] and 5° ^s [n] are rotated by some phase factors, and modify the information signal as,

where the phase values and <p ₂ are determined using

I n ( 16) , a number of phase values for f ₁ and <p ₂ are tried and the phase pair resulting in minimum PAPR is chosen. The operation of the proposed approach is depicted in Figure 2.

I n Figure 2:

Pseudo-code Algorithm for the Proposed Technique:

The proposed technique can be described using the following pseudo-code algorithm below. • Denoting of the information symbol sequence by S[n] which is the digital signal, and denoting of the set of index values from n = 0, ··· , N— 1 by n,

• Setting of the consist of the even index pair vector ep = (2k 2k + N / 2) and Setting of the consist of the odd index pair vector op = (2k + 1 2k + 1 + N/2), k = 0, 1, , N/2— 1,

• Randomly generating subsets of ep and op and denoting them by ep _s and op _s ,

• Using the index vectors ep _s and op _s determine the information symbols to be rotated in s[n] ,

• Choosing of two phase values for rotation,

• Rotating of the information symbols as in S[n] = e ⁷ ^ ¹ x S ^es [n] + e^ ² x S° ^s [n] + S ^lrem [n] ,

• Calculating and recording the PAPR together with the rotation phases used,

• I f still available, choosing a new pair of rotation phases and going to step f otherwise going to i,

• Checking the recorded PAPRs and deciding on the minimum one, and determining the phases to be used for the rotation of the information symbols.

Example: S = [S ₀ S-, S ₂ S ₃ S ₄ S ₅ S ₆ S ₇ ] is the information sequence, then op = {(o 4), (2 6)} ep = {(1 5), (3, 7)}

op _s = {( 2, 6)} ep _s = {( 1, 5)} (17) o _s = { 2, 6} e _s = {1, 5} where the subsets op _s and ep _s can be chosen in a different manner. Then the information signal is modified as

And 5 = IDFT(S ), f ₁ and <p ₂ are searched such that PAPR is minimum . The complexity of the method in ( 16) is in the order of 2 X 0(JV ² ). (18)

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