The Capacity of Noncoherent Continuous-Phase Frequency Shift Keying

Transcription

1 The Capacity of Noncoherent Continuous-Phase Frequency Shift Keying Shi Cheng 1 Rohit Iyer Seshadri 1 Matthew C. Valenti 1 Don Torrieri 2 1 Lane Department of Computer Science and Electrical Engineering West Virginia University 2 US Army Research Lab March 14, 2007 Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, West 2007Virginia 1 / Unive 20

2 Outline 1 Motivation 2 Noncoherent CPFSK 3 Capacity Analysis under Bandwidth Constraint 4 Application 5 Conclusion Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, West 2007Virginia 2 / Unive 20

3 Bandwidth Efficiency Motivation x i (t) = 1 TS e j π(2k (M 1))t T S, k = 0, 1,, M 1 Orthogonal FSK Known to achieve Gaussian capacity when the number of tones M goes to infinity Adjacent frequency tones are at least 1/T S apart. Nonorthogonal FSK Nonorthogonal FSK saves the bandwidth by using modulation index h < 1. Adjacent frequency tones are h/t S apart. Full response CPM with rectangular pulse shape, also called CPFSK Partial response CPM has more compact bandwidth, but leads to complex signal processing Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, West 2007Virginia 3 / Unive 20

4 Bandwidth Efficiency Motivation x i (t) = 1 e j hπ(2k (M 1))t +φ T S, k = 0, 1,, M 1 TS Orthogonal FSK Known to achieve Gaussian capacity when the number of tones M goes to infinity Adjacent frequency tones are at least 1/T S apart. Nonorthogonal FSK Nonorthogonal FSK saves the bandwidth by using modulation index h < 1. Adjacent frequency tones are h/t S apart. Full response CPM with rectangular pulse shape, also called CPFSK Partial response CPM has more compact bandwidth, but leads to complex signal processing Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, West 2007Virginia 3 / Unive 20

5 Bandwidth of CPFSK Motivation M=64 3 M=32 M=16 Bandwidth (Hz/bps) M=2 M=8 M= % Power Bandwidth h Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, West 2007Virginia 4 / Unive 20

6 CPFSK Detection Motivation Coherent Detection Decoding through trellis h needs to be rational Phase synchronization Noncoherent Detection Symbol by symbol noncoherent detection Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, West 2007Virginia 5 / Unive 20

7 CPFSK Detection Motivation Coherent Detection Decoding through trellis h needs to be rational Phase synchronization Noncoherent Detection Symbol by symbol noncoherent detection Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, West 2007Virginia 5 / Unive 20

8 CPFSK Detection Motivation Coherent Detection Decoding through trellis h needs to be rational Phase synchronization Noncoherent Detection Symbol by symbol noncoherent detection Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, West 2007Virginia 5 / Unive 20

9 Noncoherent CPFSK Noncoherent CPFSK Discrete Time Model y = ae jθ E s x + n n is colored noise, with E(nn H ) = N 0 K x is chosen from columns of K = [k 0, k 1,, k M 1 ] ) p(y x = k ν ) I 0 (2 a E s N 0 y ν Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, West 2007Virginia 6 / Unive 20

10 Noncoherent CPFSK A Binary Example: Minimum Shift Keying (MSK) MSK: M = 2, h = 1/2 The normalized correlation matrix for n is [ j K = j 1 ] The modulator selects the columns of K, depending on the M-ary input d. [ x = d = 0 d = j ] [ j x = 1 ] Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, West 2007Virginia 7 / Unive 20

11 Noncoherent CPFSK Noncoherent CPFSK Detector Diagram cos(2πf 0 t) sin(2πf 0 t) dt dt log I 0 ( ) cos(2πf M-1 t) sin(2πf M-1 t) dt dt log I 0 ( ) Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, West 2007Virginia 8 / Unive 20

12 Capacity Analysis under Bandwidth Constraint Capacity Calculation Instantaneous capacity i(x; y) = x log M log S p(y x ). p(y x) Capacity I (x; y) = log M E x [log x S p(y x ) p(y x) ]. Monte Carlo simulation Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, West 2007Virginia 9 / Unive 20

13 Capacity Analysis under Bandwidth Constraint Capacity Calculation Instantaneous capacity i(x; y) = x log M log S p(y x ). p(y x) Capacity I (x; y) = log M E x [log x S p(y x ) p(y x) ]. Monte Carlo simulation Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, West 2007Virginia 9 / Unive 20

14 Capacity Analysis under Bandwidth Constraint Capacity Calculation Instantaneous capacity i(x; y) = x log M log S p(y x ). p(y x) Capacity I (x; y) = log M E x [log x S p(y x ) p(y x) ]. Monte Carlo simulation Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, West 2007Virginia 9 / Unive 20

15 Capacity Analysis under Bandwidth Constraint Binary Noncoherent CPFSK Capacities in AWGN 25 1 h=1 h=0.8 dashed line 20 Mutual Information h=0.4 Minimum Eb/No in db 15 h= h= h=0.2 h=0.6 h=0.8 h= Es/No in db (a) channel capacity versus E S /N Code rate r (b) minimum E b /N 0 versus coding rate Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, 2007 West Virginia 10 / Unive 20

16 Capacity Analysis under Bandwidth Constraint Binary Noncoherent CPFSK Capacities in AWGN under Bandwidth Constraint 25 Minimum Eb/No in db η = 1 η (bits/s/hz) is the Bandwdith Efficiency 10 η = 1/2 η=1/3 η = h Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, 2007 West Virginia 11 / Unive 20

17 Capacity Analysis under Bandwidth Constraint Noncoherent CPFSK Capacities in AWGN Channel 30 η = 1/2 (solid lines) η = 0 (dashed lines) 25 M=2 Minimum Eb/No in db h Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, 2007 West Virginia 12 / Unive 20

18 Capacity Analysis under Bandwidth Constraint Noncoherent CPFSK Capacities in AWGN Channel Minimum Eb/No in db M=2 M=4 4 M=8 M=16 2 M=32 M= η in bps/hz Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, 2007 West Virginia 13 / Unive 20

19 Capacity Analysis under Bandwidth Constraint Noncoherent CPFSK Capacities in Rayleigh Channel 30 η = 1/2 (solid lines) 25 M=2 η = 0 (dashed lines) Minimum Eb/No in db h Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, 2007 West Virginia 14 / Unive 20

20 Capacity Analysis under Bandwidth Constraint Noncoherent CPFSK Capacities in Rayleigh Channel Minimum Eb/No in db M=2 6 M=4 4 M=8 M=16 2 M=64 M= η in bps/hz Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, 2007 West Virginia 15 / Unive 20

21 Application Coded Noncoherent CPFSK in Frequency Hopping Networks FH Network Scenario Interference Nodes (d<4) d=1 Multiple access interference Tradeoff on the bandwidth of each sub-channel and the possibility of interference Equal received average SNR, Rayleigh fading, Interference nodes subject to log normal shadowing σ = 8dB Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, 2007 West Virginia 16 / Unive 20

22 FH Network Scenario Application Coded Noncoherent CPFSK in Frequency Hopping Networks Total bandwidth W = 2000/T u h M Coding rate Number of channels / / / / All users use the same modulation and coding strategy Channel estimator using EM algorithm, the same as the one of orthogonal FSK Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, 2007 West Virginia 17 / Unive 20

23 Application Coded Noncoherent CPFSK in Frequency Hopping Networks Noncoherent CPFSK FH Network against MAI Eb/No (db) CPFSK h = 1 4CPFSK h = 1 8CPFSK h = CPFSK h = 0.46 SNR collected at BER = 10 4 UMTS turbo code 32 hops Users Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, 2007 West Virginia 18 / Unive 20

24 Conclusion Conclusion This paper outlines a methodology for finding the coded modulation (CM) capacity of CPFSK with noncoherent detection. For a specific number of tones M and spectral efficiency η, the minimum required E b /N 0 can be optimized over the modulation index h and coding rate r. For a fixed spectral efficiency, it is better to use a higher order M and smaller h. However, when the spectral efficiency is sufficiently high, the benefit is small by using M > 8. Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, 2007 West Virginia 19 / Unive 20

25 Conclusion Thank you Shi Cheng et al. ( The LaneCapacity Department of Noncoherent of Computer CPFSK Science and Electrical Engineering March 14, 2007 West Virginia 20 / Unive 20