A Method to Construct Phase Spreading Sequences for CPM-CDMA Systems

C IEEJ Transactions on Electronics, Information and Systems Vol.134 No.4 pp.534 542 DOI: 10.1541/ieeeiss.134.534 CPM-CDMA a) A Method to Construct Phase Spreading Sequences for CPM-CDMA Systems Kazuyuki Morioka a), Student Member, David Asano, Non-member 2013 2 1 2013 12 17 In this paper, a construction method for phase spreading sequences which is suitable for CPM-CDMA systems is proposed. Using these sequences, the performance of asynchronous CPM-CDMA systems with traditional BPSK/OQPSK-CDMA systems and the tradeoff between spreading factor and modulation parameters are considered. Numerical results show that the optimal modulation index for CPFSK-CDMA systems is h = 0.5 and the performance is better for lower values of B b T c in GMSK-CDMA systems. Also, we found that the user capacities of MSK-CDMA systems are 2.3 times larger than that of BPSK/OQPSK-CDMA systems. (CPM) (CPFSK) (MSK) (GMSK) (CDMA) (PSS) Keywords: Continuous phase modulation, Continuous phase frequency shift keying, Minimum shift keying, Gaussian minimum shift keying, Code division multiple access, Phase spreading sequence 1. M2M (Machine to machine) IoT (Internet of things) ZigBee 1 IEEE 802.15.4 2 a) Correspondence to: Kazuyuki Morioka. E-mail: Kazuyuki. Morioka@gmail.com 380-8553 4-17-1 Department of Mathematics and System Development, The Interdisciplinary Graduate School of Science and Technology, Shinshu University 4-17-1, Wakasato, Nagano 380-8553, Japan 380-8553 4-17-1 Department of Computer Science & Engineering, Shinshu University 4-17-1, Wakasato, Nagano 380-8553, Japan OQPSK(Offset quadrature phase shift keying) OQPSK CPM(Continuous phase modulation) (1) CPM CPM CDMA(Code division multiple access) CPM-CDMA (2) (11) Garber (2) BPSK/QPSK OQPSK CDMA Lehnert (3) OQPSK MSK (Minimum shift keying) CDMA Hsu (4) MAI(Multiple access interference) CPM-CDMA Svensson (5) Lane (6) Multi-h CPM Lane CPM http://www.zigbee.org/ http://www.ieee802.org/15/pub/tg4.html c 2014 The Institute of Electrical Engineers of Japan. 534

MLSD (Maximum likelihood sequence detection) CPM CDMA CPM Hsu (7) Multi-h CPM-CDMA CPM-CDMA CPM-CDMA CPM-CDMA Yang (10) CPM-CDMA (perfect orthogonal phase spreading sequences) (10) CPM h 0.5 h (PSS:Phase spreading sequences) PSS (10) M Gold CPM h PSS CPM-CDMA CDMA CPM-CDMA Asano (11) CPM h (11) BPSK BPSK BPSK BPSK CDMA CPM-CDMA CPM-CDMA IEEE 802.15.4 OQPSK CDMA CPM-CDMA 2 CPM-CDMA 3 4 5 2. 1 CDMA 2 1 log 2 M M M 2 α (k) = {α (k) 0 0,0, α(k) 0,1,..., α(k) 0,N 1 }, + 1 α (k) = {α (k) 1 1,0, α(k) 1,1,..., α(k) 1,N 1 }, 1 k (0 k K 1) k K k i α (k),i { 1, +1} N CPM s k (t) (1) s k (t) = A cos[2π f c t + ϕ k (t, α (k) )]. (1) A f c ϕ k (t, α (k) ) k ϕ k (t, α (k) ) = 2πh α (k),i q(t it c). (2) i= T c T N = T/T c h CPM h = 2q/p (p q ) α (k),i i N 535 IEEJ Trans. EIS, Vol.134, No.4, 2014

α (k), 1 = α(k),n 1, α(k), 2 = α(k),n 2,..., α (k), L = α(k),n L (2) q(t) q(t) = t g(τ)dτ. (3) g(t) L = 1 s k (t) CPFSK (Continuous phase frequency shift keying) (1) 1 2LT g(t) = c, 0 t LT c (4) 0,. Fig. 1. Block diagram of CPM-CDMA systems. h = 0.5 CPFSK MSK (Minimum shift keying) (1) g(t) GMSK (Gaussian MSK) (1) g(t) = 1 [ ( t Tc ) ( Q 2 t + T c )] 2πBb Q 2 2πBb 2T c ln 2 ln 2 0 B b T c 1. B b 3dB Q(t) Q(t) = t 1 exp ( τ2 ) dτ. (5) 2π 2 AWGN (Additive white Gaussian noise) K 1 r(t) = A cos[2π f c t + ϕ k (t τ k, α (k) ) + ξ k ] + n(t). k=0 (6) n(t) (AWGN) τ k [0, T] ξ k [0, 2π] 1 τ 0 ξ 0 τ k, ξ k, k = 1... K 1 1 Fig. 1 CPM-CDMA d k, k = 0... K 1 k CPM h, L, g, GMK 3dB BbTc 2 2 CPM- CDMA lt c t < (l + 1)T c (2) (1) ϕ k (t, α (k) ) = 2πh l i=l (L 1) α (k),i q(t it c) + θ l (7) θ(t, α (k) θ l = [ hπ = θ(t, α (k), l) + θ l. (8), l) = 2πh l L i= ] α (k),i l i=l (L 1) α (k),i q(t it c), (9) (mod 2π), (10) θ(t, α (k), l) l θ l (l 1) ϕ k (t, α (k) ) L (1) h = 2q/p (p q ) θ l θ l = 2π l L p q i= α (k),i (mod 2π). (11) θ l 2π/p 2π/(2π/p) = p q ( (11) q ) Fig. 2 h = 0.5, h = 0.25, h = 0.75 h = 0.5 (p = 4, q = 1) 0, π/2, π, 3π/2 4 q = 1 1 (Fig. 2 (a)) h = 0.25 (p = 8, q = 1) 0, π/4, π/2, π, 3π/4, 5π/4, 3π/2, 7π/4 8 q = 1 1 (Fig. 2 (b)) h = 0.75 (p = 8, q = 3) h = 0.25 8 q = 3 3 (Fig. 2 (c)) CPM MLSD (Maximum likelihood sequence detection) 536 IEEJ Trans. EIS, Vol.134, No.4, 2014

Table 1. 99% bandwidth of CPFSK and GMSK. CPFSK GMSK Fig. 2. Phase transitions in CPM-CDMA systems. h B 99 B b T c B 99 0.25 0.898 0.2 0.792 0.375 1.082 0.3 0.914 0.5 1.182 0.4 0.988 0.625 1.600 0.5 1.034 CPM (1) 6.5.3 (12) CPM-CDMA (1) (12) 2 3 CPM-CDMA (11) CDMA CPM CDMA % % B % B /2 S ( f )d f B /2 S ( f )d f = 100. (12) S ( f ) % B (12) (12) S ( f ) (12) CPFSK GMSK 99% ( ) Table 1 B 99 B b T c 3dB S ( f ) (13) BPSK/OQPSK-CDMA BPSK/OQPSK 99% BPSK/OQPSK 99% ( ) (14) Table 1 (14) Table 1 GMSK(BT = 0.5) 99% ((bits/s)/hz) R b /B = 0.97 GMSK R b R b = 1.0 B = R b /0.97 = 1.031 S ( f ) GMSK 99% 0.75 1.846 0.6 1.064 Table 2. 99% bandwidth of root-raised-cosine roll off filtered BPSK and OQPSK. BPSK Rb/B 99 B 99 OQPSK Rb/B 99 B 99 α = 1.0 0.610 1.639 α = 1.0 1.220 1.639 α = 0.5 0.790 1.266 α = 0.5 1.580 1.266 α = 0.0 1.010 0.990 α = 0.0 2.020 0.990 ( Table 1 B b T c = 0.5 ) (14) Table 1 BPSK/OQPSK 99% (14) Table 1 OQPSK(α = 1.0) 99% ((bits/s)/hz) R b /B = 1.220 OQPSK R b R b = 2.0 B = R b /1.220 = 1.639 1.0, 0.5, 0.0 BPSK OQPSK 99% Table 2 B 99 (14) (R b /B) OQPSK B OQPS K N OQPS K = B CPM N CPM, (13) B OQPS K N OQPS K OQPSK % B CPM N CPM CPM % (13) CPM N CPM = N OQPS K BOQPS K, (14) B CPM x x % (15) (16) α = 0.0 OQPSK N = 127 OQPS K(α) α OQPSK BPS K(α) α 537 IEEJ Trans. EIS, Vol.134, No.4, 2014

Table 3. Sequence length of CPFSK and GMSK. N99 = 127 N99 = 255 N99 = 511 CPFSK GMSK CPFSK GMSK CPFSK GMSK h N 99 B b T c N 99 h N 99 B b T c N 99 h N 99 B b T c N 99 0.25 140 0.2 158 0.25 281 0.2 318 0.25 563 0.2 638 0.375 116 0.3 137 0.375 233 0.3 276 0.375 467 0.3 553 0.5 106 0.4 127 0.5 213 0.4 255 0.5 428 0.4 512 Fig. 3. Transition part of phase spreading sequences. 0.625 78 0.5 121 0.625 157 0.5 244 0.625 316 0.5 489 0.75 68 0.6 118 0.75 136 0.6 237 0.75 274 0.6 475 Table 4. Sequence length of root-raised-cosine roll off filtered BPSK and OQPSK. N99 = 127 N99 = 255 N99 = 511 BPSK OQPSK BPSK OQPSK BPSK OQPSK α N 99 α N 99 α N 99 α N 99 α N 99 α N 99 1.0 76 1.0 76 1.0 154 1.0 154 1.0 308 1.0 308 0.5 99 0.5 99 0.5 199 0.5 199 0.5 399 0.5 399 0.0 127 0.0 127 0.0 255 0.0 255 0.0 511 0.0 511 BPSK CPFS K(h) h CPFSK GMS K(B b T c ) B b T c GMSK Table 2 B99 CPFS K(0.5) 0.990, h = 0.5 B99 1.182 h = 0.5 CPM N CPFS K(0.5) = 127 0.990 = 106, (15) 1.182 CPFSK GMSK Table 3 N 99 BPSK/OQPSK Table 4 N 99 N 99 α = 0.0 OQPSK N = 127, 255, 511 3. CPM-CDMA 1 2 CPM-CDMA (PSS:Phase spreading sequences) (10). (8) h = 2q/p(p q ), PSS PSS p/4 +1 1 α 0 = {+1,..., +1, a 0, a 1,..., a N 1}, α 1 = { 1,..., 1, a 0, a 1,..., a N 1}, +1, 1 CPM h = 2q/p (p q ) N = p/4 + N Fig. 3 p/4 +1 1 +1 1 π N π PSS p/4 +π/2 π/2 CDMA M Gold +1 1 +1 N /2 1 N /2 M Gold +1 1 1 +1 1 +1 1 PSS +1 1 +1 1 1 0 0 {+1 1+1+1 1 1 + 1} h = 0.25 (p = 8, q = 1) 9 p/4 = 2 {+1 + 1} { 1 1} 6 0 {+1 1 + 1 + 1 1 1 0} 9 α 0 = {+1 + 1 + 1 1 + 1 + 1 1 1 0}, α 1 = { 1 1 + 1 1 + 1 + 1 1 1 0}, +1-1 3 h = 2p/q N PSS 538 IEEJ Trans. EIS, Vol.134, No.4, 2014

1 (M Gold ) 2 (1) N (1) 3 (2) +1-1 0 4 0 p/4 +1 1 p/4-1 PSS p/4 +1 1 +1 1 PSS +1 1 π (1) M 3 CDMA Gold (1) Gold 4 CPM-CDMA (1) Gold PSS Gold 4. CPM- CDMA AWGN PSS Gold Gold 2 M 3 PSS CDMA Gold Fig. 4 h = 0.5 Gold PSS (10) ( Orth ) (E b /N 0 ) 31 7 1 CPFSK(h = 0.5) Fig. 4 PSS 2 h = 0.5 4 16 Fig. 5 h = 0.625 Fig. 4. Comparison of PSS and gold sequences. h = 0.5. Fig. 5. Comparison of PSS and gold sequences. h = 0.625. Gold PSS (E b /N 0 ) 31 3 Fig. 5 PSS Fig. 6 CPFSK-CDMA 10 3 E b /N 0 CPM p 31 3 Fig. 6 Gold PSS 3 PSS +1 1 π α = 0.0 OQPSK 99% N 99 = 127 CPM Table 3 Table 4 N99 = 127 539 IEEJ Trans. EIS, Vol.134, No.4, 2014

Fig. 6. Comparison of PSS and gold sequences. Required E b /N 0 at BER of 10 3. Fig. 8. Performance as a function of B b T c for GMSK. Fig. 7. Performance as a function of h for CPFSK. Fig. 9. Comparison of CPFSK and GMSK. Fig. 7 E b /N 0 15dB CPFSK-CDMA h 12, 15, 18 Fig. 7 h = 0.5, MSK CPFSK h 0.6 CPFSK- CDMA 0.6 h = 0.5 4 h = 0.5 Fig. 8 E b /N 0 15dB GMSK-CDMA B b T c 12, 15, 18 Fig. 8 B b T c CPFSK GMSK Table 3 Table 4 99% N 99 = 127 Fig. 9 12 Fig. 9 h = 0.5, MSK BPSK/OQPSK-CDMA MSK-CDMA N99 = 127, 255, 511 Table 3 Table 4 18dB 10 4 AWGN BPSK/OQPSK 1.0, 0.5, 0.0 Table 5, Table 6 K MS K MSK-CDMA K BPS K BPSK-CDMA K OQPS K OQPSK-CDMA K MS K /K BPS K, K MS K /K OQPS K BPSK, OQPSK MSK Table 5 MSK-CDMA BPSK-CDMA 2.3 Table 6 MSK- CDMA OQPSK-CDMA 540 IEEJ Trans. EIS, Vol.134, No.4, 2014

Table 5. Table 6. Capacity comparison of MSK and BPSK. BPSK K MS K K BPS K K MS K /K BPS K α = 1.0 16 7 2.3 N Base = 127 α = 0.5 16 8 2.0 α = 0.0 16 10 1.6 α = 1.0 23 13 1.8 N Base = 255 α = 0.5 23 14 1.6 α = 0.0 23 15 1.5 α = 1.0 53 27 2.0 N Base = 511 α = 0.5 53 29 1.8 α = 0.0 53 33 1.6 Capacity comparison of MSK and OQPSK. OQPSK K MS K K OQPS K K MS K /K OQPS K α = 1.0 16 7 2.3 N Base = 127 α = 0.5 16 8 2.0 α = 0.0 16 8 2.0 α = 1.0 23 13 1.8 N Base = 255 α = 0.5 23 14 1.6 α = 0.0 23 15 1.5 α = 1.0 53 29 1.8 N Base = 511 α = 0.5 53 29 1.8 α = 0.0 53 34 1.6 2.3 Table 3, Tble 4 N Base = 255 127 511 CPFS K(0.5) N 99 N99 MSK MSK MLSD MSK-CDMA OQPSK- CDMA MSK-CDMA MSK- CDMA PAN(Personal aerea network) 5. CPM-CDMA CDMA Gold CPM-CDMA CPFSK-CDMA h = 0.5 MSK GMSK-CDMA B b T c BPSK/OQPSK-CDMA MSK-CDMA BPSK-CDMA OQPSK-CDMA 2.3 CPM-CDMA CPM-CDMA IEEE 802.15.4 CDMA CPM-CDMA 1 F. iong, F. iong, and F. iong: Digital modulation techniques, Artech House Norwood, MA, USA (2000) 2 F. Garber and M. Pursley: Performance of offset quadriphase spreadspectrum multiple-access communications, IEEE Trans. Communications, Vol.29, No.3, pp.305 314 (1981) 3 J.S. Lehnert: Serial MSK spread-spectrum multiple-access communications, IEEE Trans. Communications, Vol.40, No.6, pp.1119 1127 (1992) 4 F. Hsu and J.S. Lehnert: A characterization of multiple-access interference in generalized quadriphase spread-spectrum communications, IEEE Trans. on Communications, Vol.42, No.234, pp.2001 2010 (1994) 5 A. Svensson, C. Sundberg, and G. Lindell: On direct sequence spread spectrum systems with continuous phase modulation, Proc. Annual Conference on Information Sciences and Systems, Baltimore, Maryland, pp.526 531 (1985) 6 W.D. Lane and A.M. Bush: Spread-spectrum multi-h modulation, IEEE Journal on Selected Areas in Communications, Vol.8, No.5, pp.728 742 (1990) 7 R. Hsu and J.S. Lehnert: The performance of continuous-phase-coded DS/SSMA communications, IEEE Trans. on Communications, Vol.46, No.4, pp.533 543 (1998) 8 T.M. Lok and J.S. Lehnert: DS/SSMA communication system with trellis coding and CPM, IEEE Journal on Selected Areas in Communications, Vol.12, No.4, pp.716 722 (1994) 9 L.H.J. Lampe, R. Tzschoppe, J.B. Huber, and R. Schober: Noncoherent continuous-phase modulation for DS-CDMA, Communications, 2003. ICC 03. IEEE International Conference on, Vol.5, pp.3282 3286 (2003) 10 F. Yang, S. Leung, C. Ngan, and G. Bi: The performance and design criterion of phase spreading sequences for DS/SSMA communications with full response CPM over Rayleigh fading channels, Global Telecommunications Conference, 1999. GLOBECOM 99, Vol.1, pp.914 918 (1999) 11 D.K. Asano, T. Hayashi, and R. Kohno: Modulation and processing gain 541 IEEJ Trans. EIS, Vol.134, No.4, 2014

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