A Tree Structure PTS Technique for PAPR Reduction in OFDM Systems

High peak-to-average power ratio (PAPR) of the transmitted signals is the major problem in orthogonal frequency division multiplexing (OFDM) system. The partial transmit sequence (PTS) technique can reduce PAPR in OFDM system. However, the severe computational complexity in conventional PTS (C-PTS) is the major drawback. In this paper, we propose the tree PTS (T-PTS) to find codewords of a linear code as weighing factors by executing the PTS method in the tree structure of this code. The combination of PTS and tree structure not only reduce the computational complexity but also provide error correction capability for the weighting factors. Simulation results show that the T-PTS achieves good PAPR reduction with lower complexity, compared to conventional PTS.


Introduction
Orthogonal frequency-division multiplexing (OFDM) is a multi-carrier modulation (MCM) technology for high data-rate transmission in wireless channels and is adopted in a number of communication systems, such as DAB [1], ADSL [2], and WiMAX [3].One of the major problems in OFDM system is the high Peak-to-Average Power Ratio (PAPR) of transmitted signals, which means that a complicated power amplifier is needed at the transmitter.Therefore, the subject of finding a computationally efficient algorithm to decrease the PAPR in OFDM systems is an active research.There are many proposed methods to reduce PAPR of OFDM signals, such as clipping and filtering [4], coding techniques [5] and partial transmit sequence (PTS) [6].
The C-PTS technique partitions the input data into disjoint subblocks, forms the partial transmit sequences by taking the Fourier transform of these subblocks, and generates a number of OFDM candidates by linear combination of these PTS with different weighting factors.However, the computation complexity of exhaustive search in C-PTS increases exponentially with the number of subblocks and C-PTS is thus not easily implemented for a large number of subblocks.In [7] the authors proposed an iterative algorithm to reduce PAPR with low complexity, however its PAPR performance is relatively unsatisfied.Thus, the issue of low complexity PTS techniques with good PAPR performance is an active area of research and has widely attracted the attention of researchers, such as [8,9,10].
In this paper, we present a novel low complexity PTS algorithm by combining the C-PTS and tree diagrams, called T-PTS.More precisely, a linear code with good error correction and low complexity tree diagram, consisting of all weighting vectors, is used to generate all possible transmitted OFDM candidates.The advantage of T-PTS method not only reduces the search complexity but also provides error control capability for side information.This paper is organized as follows.Section II introduces PAPR of OFDM systems and the PTS method.Section III describes our proposed low complexity T-PTS algorithm.Section IV shows the simulation results and Section V gives a conclusion.

PAPR Definition and PTS Technique
In an OFDM system of N subcarriers, we denote X=(X 0 ,X 1 ,...,X N-1 ) as the input data block of length N where each symbol is modulated with one of orthogonal subcarriers f k , k={0, 1,..., N-1}.In the continuous time domain, an OFDM baseband signal x(t) of N subcarriers can be expressed as the PAPR of a transmitted signal is defined as after that, these PTS signal are independently rotated by the phase weighting factor b m and combined together to generate many different candidates: were b m =e j(2 πw/W ) , w=0,1,2,...,W-1 and W is the number of the varying phases.

Proposed Method and Computational Complexity
In the C-PTS method, we know decided to calculate the Complexity of weighting factor by dividing into sub-blocks M and W is an interference amount related to the exponential, then reducing computational complexity of C-PTS is an important topic.So in [10] proposed a method to reducing the computational complexity of C-PTS.In this proposed then the interference amounts W=2, must be have full weighting factor for equivalent to using a coding for G[M-1, M-1, 1] matrix.Example: M=8, W=2 is the optional weighting factor of 2 8-1 =128, and the choose matrix of G[7,7,1] is a same.Therefore if we make a matrix G [n, k, d], n=M-1, we can ensure that this codewords has the 2 k weighting factor and error correction capability.In the computational complexity has from the 2 (M-1) (M-1) reduced to 2 k (M-1).So, then one of G matrix having the error correction capability in accordance with the codeword a certain regular arrangement, we can get his needed computational complexity from the 2 k (M-1) reduction to 2 k d and in the changing symbols have need an added.But this is a computational complexity is very high.

Proposed Method
First, we know that they meet the linear block code characteristic can be draw the tree structure.So we can be find the information bits [v 1 , v 2 ,..., v k ] and parity check bits [p 1 , p 2 ,..., p n-k ] of G matrix, and will the same bits position After finishing the matrix G is a generator matrix.From this generator matrix, we can draw into a tree structure.In the branch case of information bit is 0 or 1, parity check bits use not alteration.Example: From (6), if P 1 =[1011] and now information is v 1 =0, v 2 =1, v 3 =1, and v 4 =0 then we can find in this branch bit is 1.Shown the Fig. 2, we can from this tree structure to get 2 k codewords for used as weighting factors.But this still a high computational complexity.Therefore, we propose to a suboptimal for reducing the computational complexity methods.
We use references [11], if information bits are concentrated on one side of generator matrix, and make soon expansion of the tree structure of the last branch, such a tree structure is relatively not good.So, if We can reset some of information bits moving backwards, then the relativity of the slow growth branch.View of this we adjusted the generator matrix in accordance with the references [11], maybe also make the reducing computational complexity.First, we know a generator matrix G and find the dual codes G ⊥ of matrix [n, r, dc], then r=n-k.Find the dual codes, we started for performing matrix G a row computation to make over a certain amount of information bits after the dc, next the 1 of the last row had generator matrix the minimum hamming distance d, while the previous row is the 1 number of   .Accordance with this method until the upper limit is 1, put the remaining information bits to fill.After the complete this procedure the matrix we define as G DLP .For the Example we after finishing (6) a result as , 0000111 0011001 0101010 1001011 Next, we also draw out the G DLP of tree PTS (T-PTS).Shown the Fig. 3, we can see that a G DLP matrix their information bits it will slowly increase the selection number.

Computational complexity
Like the C-PTS method of computational complexity, we propose a method of reducing the computation.In the tree structure representation of every stage it corresponds to every subblocks can be represented as a selectable weighting factor.In each strata, if there is a change we will as a computing element.So when we can get all codeword on this T-PTS.In the process of the moment weighting factor has changes will only the computational this subblocks and find the PAPR [9].So we set a generator matrix [n, k, d], and information bits is [v 1 , v 2 ,..., v k ], then a generator matrix of T-PTS the computational complexity result as Our proposed method wherein knows the generator matrix G [n, k, d] and dual code G ⊥ , Worth noting that when the i=k+1 then (v i -v i-1 )=d; i=k, . Accordance with this method until the upper limit is 1, and then i=dc the (v i -v i-1 )=2.For the Example: we set generator matrix G [23,12,7] and dual code G ⊥ [23,11,8] form (8), find the generator matrix in the sequence of its complexity as SC=2 0 +2 1 +2 2 +2 3 +2 4 +2 5 +2 6 +2 7 +2 8 +2 9 +2 10 +2 11 +2 12 *12.However, we proposed method of its complexity as SC=2 0 +2 1 +2 2 +2 3 +2 4 +2 5 +2 6 +2 7 *2+2 8 +2 9 +2 10 *2+2 11 *4+2 12 * 7. From the process, we can draw a lot of computational complexity in the generator matrix, through the moving information bit is reducing the computational complexity.

Simulation
We examine the PAPR performance of a QPSK OFDM system with 256 subcarriers on proposed method, we are using a different subblock, and accordance number of different linear block code.Shows the Tab. 1, we can examine the computational complexity of linear code has been reduced from 2 (M-1) (M-1) to 2 k (M-1).And using the proposed method of the G [15,5,7] can reduce the computational complexity from 480 to 166, in G[15,7,5] can reduce the complexity from 1920 to 468.
. 1, conventional PTS (C-PTS) technique, the input data block X is partitioned into M disjoint subblocks.they has three methods of partition are adjacent partition, interleaved partition and random partition, our proposed method uses random partition to subblocks.So we expressed as sequences X(m) , are then passed into M IFFTs and transformed into the time domain signals called partial transmit sequences as