1 PTS with Non-uniform Phase Factors for PAPR Reduction in OFDM Systems 指導教授 : 蔡育仁 博士 學生姓名 : 黃信智 To appear in IEEE Communications Letters, Jan. 2008

2 Outline Introduction PTS Algorithm PTS with Non-uniform Phase Set Simulation Results Conclusion References

3 Introduction OFDM Signal: Frequency domain {X}  IFFT  time domain {x}

4 Introduction In OFDM systems, peak-to-average power ratio (PAPR) reduction is a very important issue in order to improve the efficiency of the transmitter power amplifier. Numerous techniques have been proposed to reduce the PAPR of OFDM signals in the time-domain. Partial transmit sequence (PTS) is believed to be one of the promising methods for PAPR reduction.

5 PAPR Definition Definition of PAPR: High PAPR=16Low PAPR=2.25 Ex:

6 PAPR Reduction Techniques Two categories: 1. Signal distortion ex: Clipping 2. Symbol scrambling ex: Coding (Golay complementary codes), Partial Transmit Sequence (PTS) Selected Mapping (SLM) Dummy Sequence Insertion (DSI)

7 PTS Algorithm S/P And Partition IFFT Phase factor Optimization +

8 Partition Methods Three partition methods: (a) Adjacent (b) Interleaved (c) Random (a) (b) (c)

9 Notations N: number of sub-carriers M: number of disjoint sub-blocks for k = 0, 1, …, N-1: the frequency-domain data sequence for n = 0, 1, …, N-1: the time- domain data sequence : the corresponding time-domain signal of sub-block i after N-point IDFT W: number of available phase factors

10 OFDM Signal Without applying PTS, the overall output signal can be represented as Let The PAPR is defined as

11 Relative Phases The sample with the peak power, i.e. the k- th sample, can be re-written as : the phase of sub-block i in the k-th sample Taking the phase,, as a reference, we define

12 The pdf of relative phases N = 128 M = 4

13 Observations For a high power peak (such as the 1-st peak), the corresponding phases of different sub-blocks are more concentrated to compose a large amplitude. Hence, the distribution of is more concentrated for the samples with higher power.

14 Example Assume M=4 k

15 Phase Adjustments To reduce the amplitude of a high power sample, one straightforward means is To adjust the phases of some chosen sub-blocks to the reverse of the reference phase To keep the phases of the other sub-blocks unchanged Thus the amplitude of the composed signal vector in this sample can be substantially reduced.

16 The pdf of the phase adjustments (minimize the 1-st peak) N = 128 M = 4 Gaussian-like

17 Observations It is found that the phase adjustments of these M sub-blocks are not in uniform distribution. The distribution contains a delta function at zero, corresponding to the probability of maintaining the original phase in a sub- block, and a Gaussian-like distribution with the mean .

18 Example M=4, l=1, consider k

19 PTS with Non-uniform Phase Set For M = 2, which leads to two rotational phase factors 1 and -1 being the same as that applied in the conventional PTS However, for M > 2 we need to figure out the optimal set of phase factors in the minimum mean square error (MMSE) sense

20 PTS with Non-uniform Phase Set The distribution of the phase adjustments can be approximated as where  is the probability of maintaining the original phase and  is the standard deviation that fit in with the Gaussian-like distribution

21 PTS with Non-uniform Phase Set Assume that the set of chosen phase factors is for i = 0, 1, …, W-1 Due to the delta function, is chosen as a phase factor The other W-1 factors are chosen to fit in with the Gaussian-like distribution

22 PTS with Non-uniform Phase Set Based on the MMSE sense, we define the error function as

23 PTS with Non-uniform Phase Set The phase factors that minimize J are By iterative calculations, we can figure out the optimal set of phase factors that minimizes J

24 PTS with Non-uniform Phase Set Apply  = and  = 0.92 The non-uniform phase factor sets for W = 4 and 8 are For conventional PTS

25 Performance (Interleaved Partition)

26 Performance (Adjacent Partition)

27 Conclusion In this work, we have proposed a modified PTS scheme by applying pre- determined non-uniform phase sets for PAPR reduction in OFDM systems. It is found that an improvement of 0.8 – 0.25 dB in PAPR reduction for different scenarios can be obtained when compared with the conventional PTS scheme with uniform phase sets.

28 Conclusion Equivalently, the outage probability can be improved by a factor of 10 for a specific PAPR threshold. It must be noted that the optimal set of phase factors can be determined in advance based on system parameters The required side information is the same as the conventional PTS scheme with uniform phase factors.

29 References [1] R. van Nee and R. Prasad, OFDM for Wireless Multimedia Communication. Boston, MA: Artech House, [2] T. A. Wilkinson and A. E. Jones, “Minimization of the peak-to-mean envelope power ratio of multicarrier transmission schemes by block coding,” in Proc. IEEE 45th Vehicular Technology Conf., Chicago, IL, pp. 825–829, [3] J. A. Davis and J. Jedwab, “Peak-to-mean power control in OFDM, golay complementary sequences, and Reed–Muller codes,” IEEE Trans. Inf. Theory, Vol. 45, no. 7, pp. 2397–2417, [4] J. A. Davis and J. Jedwab, "Peak-to-mean Power control and error correction for OFDM transmission using Golay sequences and Reed-Muller codes"' Electronic, Letters, Vol. 300, No. 4, pp , [5] S. H. Muller, J.B. Huber, "OFDM with reduced peak-to-average power ratio by optimum combination of partial transmit sequences", Electron. Letters, Vol.33, pp , 27, [6] R. W. Bauml, R. F. H. Fischer, and J. B. Huber, “Reducing the peak-to-average power ratio of multicarrier modulation by selected mapping,” Electron. Letters, Vol. 32, no. 22, pp. 2056– 1257, [7] H. G. Ryu, J. E. Lee, and J. S. Park, "Dummy sequence insertion (DSI) for PAPR reduction in the OFDM communication system," IEEE Trans. Consum. Electron., Vol.50, pp.89–94, 2004.

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32 Thank You~