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1 C IEEJ Transactions on Electronics, Information and Systems Vol.134 No.8 pp DOI: /ieejeiss CPM-OFDM PAPR, a) A PAPR Reduction Method for CPM-OFDM Systems using Initial Phase Randomization Kazuyuki Morioka, a), Student Member, David Asano, Non-member In this paper, CPM-OFDM systems which use CPM (Continuous Phase Modulation) as the first modulation scheme of OFDM (Orthogonal Frequency Division Multiplexing) are considered. As is the case for conventional OFDM systems, PAPR (Peak to Average Power Ratio) reduction is the most important task in CPM-OFDM systems. PAPR reduction by varying the initial phase of each sub-carrier with a fixed offset and a random offset are proposed. In the random offset method, the initial phase of each sub-carrier is not known at the receiver side, so we propose a demodulation algorithm using the phase continuity property of CPM and MLSD (Maximum Likelihood Sequence Detection). Simulation results show that the PAPR performance is improved if we use the random offset method. Also, we found that even though the initial phase is unknown at the receiver, the proposed algorithm can demodulate CPM-OFDM symbols as well as an algorithm where the initial phase is known. (CPM), (OFDM), (PAPR) Keywords: Continuous phase modulation, Orthogonal frequency division multiplexing, Peak to average power ratio 1. (OFDM : Orthogonal frequency division multiplexing) OFDM OFDM (PSK : Phase shift keying) (QAM : Quadrature amplitude modulation) (CPM : Continuous phase modulation) (1) (2) a) Correspondence to: Kazuyuki Morioka. Kazuyuki. Morioka@gmail.com Shinshu University , Wakasato, Nagano , Japan Electronic Navigation Research Institute , Jindaiji-higashi, Chofu, Tokyo , Japan OFDM CPM (3)(14). CPM-OFDM OFDM CPM 2 1 OFDM CPM OFDM (PAPR : Peak to average power ratio) 0dB (3)(5). OFDM CPM OFDM-CPM PAPR 0dBOFDM 2 OFDM CPM (6)(14).CPM OFDM CPM-OFDM CPM c 2014 The Institute of Electrical Engineers of Japan. 1010
2 (ICI : Inter carrier interference) (9) 2 D/U (Desired to Undesired signal ratio) 4dB 10 6 SNR PSK-OFDM 3.5 db (10) CPM MSK QPSK (11) MSK QPSK CPM-OFDM CPM-OFDM OFDM PAPR CPM-OFDM PAPR CPM-OFDM Tasadduq (6) Yang (10) Weng (11) CPM-OFDM (15)(19), CPM-OFDM PAPR PSK/QAM-OFDM PAPR (22) (23) CPM-OFDM PAPR Tasadduq (20) CPM CPM-OFDM PAPR CPM CPM (20) PAPR (20) PAPR 2 CPM-OFDM 3 CPM-OFDM PAPR CPM 4 PAPR 5 2. CPM-OFDM (6). n 1 X n (t) = e jφ n(t,a), (1) Φ n (t, a) (21) Φ n (t, a) = θ n (t, a n,k ) + θ n,k + φ 0. (2) θ n (t, a n,k ) L (instant phase) θ n (t, a n,k ) = 2πh k i=k L+1 a n,i q(t it s ) (3) θ n,k k L (cumulate phase) θ n,k = [hπ k L i= a n,i ] (mod 2π), (4) φ 0 (3) q(t) q(t) = t g(τ)dτ. (5) a n,i ( 1, +1) n i h CPM L CPM L (21). g(t) L = 1 CPFSK (Continuous phase frequency shift keying) (21). 1 2LT g(t) = s, 0 t LT s (6) 0, h = 0.5 CPFSK MSK (Minimum shift keying) (21). CPM-OFDM CPM IFFT N 1 S (t) = X n (t) e j 2πnt NTs, n=0 0 t T. (7) T = NT s N T s OFDM 1 CPM-OFDM CP OFDM OFDM PAPR 1011 IEEJ Trans. EIS, Vol.134, No.8, 2014
3 n φ 0 (n) = 2π V (rand() mod V). (11) Fig. 1. Structure of CPM-OFDM transmitter. PAPR(S (t)) = max 0 t T [ S (t) 2 ]. (8) E[ S (t) 2 ] E[ S (t) 2 ] PAPR PAPR (CCDFComplementary cumulative distribution function) CCDF(z) = Pr(PAPR > z) (9) PAPR CCDF PAPR (z) 3. CPM-OFDM (6)(13) CPM-OFDM CPM 31 n φ 0 (n), n = 0,...,N 1 V 0 2π V V = 4 0,π/2,π,3π/2 n φ 0 (n) = 2π (n mod V). (10) V CPM 32 n φ 0 (n), n = 0,...,N 1 V rand() (0N 1 ) CPM MLSD (Maximum likelihood sequence detection) (25) (26). V CPM 33 CPM MLSD (25) (26). PSK/QAM-OFDM SLM (Selected mapping) PTS (Partial transmit sequence) PAPR MLSD PAPR (24). (24) CPM-OFDM [] for n = 0,...,N 1 for v = 0,...,V 1 φ 0 (n) = 2π V (v mod V) r n (t) X n (t, a,φ 0 (n)) λ a,φ0 (n) end (a,φ 0 (n)) ) end r n (t) FFT n X n (t, a,φ 0 (n)) (1) a φ 0 λ a,φ0 (n) V FPGA 2 V = IEEJ Trans. EIS, Vol.134, No.8, 2014
4 Fig. 3. CCDF of PAPR for h = Fig. 2. Structure of CPM receiver. 4. PAPR CPM h = 0.25, 0.375, 0.5, 0.625, 0.75, L = 3 OFDM N = 64 (27) PAPR 4 4 FFT 64 4 = h 0.25, 0.375, 0.5, 0.625, 0.75 PAPR PAPR CCDF V V = 1 CPM-OFDM V = 2, 4, 8 2, 4, 8 Const 31Rand (V = 1, Const) (V = 2, Const, V = 4, Const, V = 8, Const) PAPR h = 0.25 PAPR h = 0.5, 0.625, 0.75 V = 2, V = 4, V = 8 CPM Fig. 4. CCDF of PAPR for h = Fig. 5. CCDF of PAPR for h = 0.5. h = 0.25, V = 4, V = 8 V = 2 h = 0.5, 0.625, 0.75 V 2 h = 0.25, V 4 PAPR h 1013 IEEJ Trans. EIS, Vol.134, No.8, 2014
5 Fig. 6. CCDF of PAPR for h = Fig. 8. BER comparison of fixed offset method and random offset method. Fig. 7. CCDF of PAPR for h = h =0.25, 0.375, 0.5, 0.625, 0.75 AWGN 3-7 h = 0.25, V = 4 h = 0.5, 0.625, 0.75 V = 2 Const Rand 8 33MLSD V = 4 4 CPM MLSD (21). 9 h =0.25, 0.375, 0.5, 0.625, 0.75 h = 0.25, V = 4 h = 0.5, 0.625, 0.75 V = 2 AWGN Fig. 9. BER of CPM-OFDM systems in AWGN and Rayleigh fading channel. h = CPM-OFDM PAPR CPM-OFDM PAPR CPM MLSD PAPR 1014 IEEJ Trans. EIS, Vol.134, No.8, 2014
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