Robust Frequency-Hopping System for Channels with Interference and Frequency-Selective Fading

Robust Frequency-Hopping System for Channels with Interference and Frequency-Selective Fading Don Torrieri 1, Shi Cheng 2, and Matthew C. Valenti 2 1 US Army Research Lab 2 Lane Department of Computer Science and Electrical Engineering West Virginia University June 26, 2007 ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 1 Engine / 20

Outline 1 Why Use CPFSK for FH Systems? 2 Capacity of Noncoherent CPFSK 3 Applications 4 Conclusion ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 2 Engine / 20

Why Use CPFSK for FH Systems? Motivation A Tale of Two Philosophies B W B W Philosophy # 1 Large B. Wideband hopping channels. Better AWGN performance. Fewer hopping channels M = B/W. Worse performance with interference. Philosophy # 2 Small B. Narrowband hopping channels. Worse AWGN performance. More hopping channels M = B/W. Better performance with interference. ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 3 Engine / 20

Why Use CPFSK for FH Systems? CPFSK Modulation Modulation Choices for Frequency Hopping s d (t) = 1 Ts e j2πdt/ts, d = 0, 1,, q 1 Philosophy #1: Orthogonal FSK Suitable for noncoherent reception. Reasonable energy efficiency. Poor bandwidth efficiency because adjacent tones are 1/T s apart. Philosophy #2: Nonorthogonal CPFSK Reduce bandwidth by using modulation index h < 1. Adjacent frequency tones are h/t s apart. Continuous-phase constraint controls the spectrum. Transmitted x(t) = e jφ s d (t) where phase φ is accumulated φ = φ + 2πdh ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 4 Engine / 20

Why Use CPFSK for FH Systems? CPFSK Modulation Modulation Choices for Frequency Hopping s d (t) = 1 Ts e j2πdht/ts, d = 0, 1,, q 1 Philosophy #1: Orthogonal FSK Suitable for noncoherent reception. Reasonable energy efficiency. Poor bandwidth efficiency because adjacent tones are 1/T s apart. Philosophy #2: Nonorthogonal CPFSK Reduce bandwidth by using modulation index h < 1. Adjacent frequency tones are h/t s apart. Continuous-phase constraint controls the spectrum. Transmitted x(t) = e jφ s d (t) where phase φ is accumulated φ = φ + 2πdh ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 4 Engine / 20

Why Use CPFSK for FH Systems? Bandwidth of CPFSK CPFSK Modulation 4 3.5 q=64 3 q=32 q=16 Bandwidth B (Hz/bps) 2.5 2 1.5 q=2 q=8 q=4 1 0.5 99% Power Bandwidth 0 0 0.2 0.4 0.6 0.8 1 h (modulation index) ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 5 Engine / 20

Capacity of Noncoherent CPFSK System Model Discrete Time Model The output of q complex filers matched to the tones is: y = ae jθ E s x + n where Unlike orthogonal FSK, the x are not elementary vectors. Define K to be a correlation matrix with entry i, j k i,j = Ts 0 s i (t)s j (t)dt x is chosen from columns of K = [k 0, k 1,, k q 1 ] n is colored noise, with E(nn H ) = N 0 K. a is the fading amplitude, assumed to be constant for each hop. θ includes effects of continuous-phase constraint, fading, and oscillator frequency offset. ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 6 Engine / 20

Capacity of Noncoherent CPFSK System Model Demodulator Metric and Channel Estimation cos(2πf d t) sin(2πf d t) dt dt log I 0 ( ) The likelihood of symbol d ){0,..., q 1} is p(y x = cos(2πf k d ) q-1 t) I 0 (2 a E s N 0 y d Channel estimation a E dt s /N 0 is the channel state information (CSI). EMsin(2πf algorithm q-1 t) used to estimate the CSI for each log hop. I 0 ( ) Extrinsic information from decoder used to refine the CSI estimates. dt ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 7 Engine / 20

Capacity of Noncoherent CPFSK System Model Demodulator Metric and Channel Estimation cos(2πf d t) sin(2πf d t) dt dt log I 0 ( ) The likelihood of symbol d ){0,..., q 1} is p(y x = cos(2πf k d ) q-1 t) I 0 (2 a E s N 0 y d Channel estimation a E dt s /N 0 is the channel state information (CSI). EMsin(2πf algorithm q-1 t) used to estimate the CSI for each log hop. I 0 ( ) Extrinsic information from decoder used to refine the CSI estimates. dt ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 7 Engine / 20

Capacity Calculation Capacity of Noncoherent CPFSK Computing Capacity Assuming equally-likely input symbols x, the capacity is the mutual information between x and y where I(x; y) = H(x) H(x y) = log q E x,y [h(x y)] h(x y) = log p(x y) x = log S p(y x ) p(y x) Monte Carlo simulation can be used to evaluate the expectation. ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 8 Engine / 20

Capacity Calculation Capacity of Noncoherent CPFSK Computing Capacity Assuming equally-likely input symbols x, the capacity is the mutual information between x and y where I(x; y) = H(x) H(x y) = log q E x,y [h(x y)] h(x y) = log p(x y) x = log S p(y x ) p(y x) Monte Carlo simulation can be used to evaluate the expectation. ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 8 Engine / 20

Capacity of Noncoherent CPFSK Computing Capacity Binary Noncoherent CPFSK Capacity in AWGN 25 1 h=1 h=0.8 dashed line 20 Mutual Information 0.8 0.6 0.4 0.6 h=0.4 Minimum Eb/No in db 15 h=0.2 10 h=0.4 0.2 h=0.2 h=0.6 h=0.8 h=1 0 10 5 0 5 10 15 20 25 Es/No in db (a) channel capacity versus E S/N 0 5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Code rate r (b) minimum E b /N 0 versus coding rate ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 9 Engine / 20

Capacity of Noncoherent CPFSK Computing Capacity Binary Noncoherent CPFSK Capacity in AWGN under Bandwidth Constraint 25 Minimum Eb/No in db 20 15 B = 1 B is normalized bandwidth in Hz/bps 10 B= 2 B= 3 B = inf. 5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 h ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 10 Engine / 20

Capacity of Noncoherent CPFSK Computing Capacity Noncoherent CPFSK Capacity in AWGN 30 B = 2 (solid lines) B = inf. (dashed) 25 q=2 Minimum Eb/No in db 20 15 10 16 8 4 32 5 64 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 h ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 11 Engine / 20

Capacity of Noncoherent CPFSK Computing Capacity Noncoherent CPFSK Capacity in Rayleigh Fading 30 B = 2 (solid lines) 25 q=2 B = 0 (dashed lines) Minimum Eb/No in db 20 15 10 4 8 16 32 5 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 h ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 12 Engine / 20

A Multi-user FH Network Applications Multiple-access Interference Interference Nodes (d<4) d=1 Transmissions Independent and asynchronous hopping. Equal transmit power. Interfering users randomly placed up to 4x away from desired transmitter. Channel Path loss coefficient of 4. Log-normal shadowing (σ = 8dB) of interfering users. Block Rayleigh fading. ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 13 Engine / 20

Applications Multiple-access Interference Waveforms for FH Network Total bandwidth W = 2000 Hz/bps. All users use the same modulation and coding UMTS turbo code 32 hops/codeword. h q Coding rate Number of channels 1 2 2048/6144 312 1 4 2048/6144 315 1 8 2048/6144 244 0.6 2 2048/3200 1000 0.46 4 2048/3456 1000 0.32 8 2048/3840 1000 Channel estimation using EM algorithm. ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 14 Engine / 20

Applications Minimum E b /N 0 for BER = 10 4 Multiple-access Interference 24 22 20 18 E b /N o in db 16 14 12 10 8 2CPFSK h = 1 4CPFSK h = 1 8CPFSK h = 1 2CPFSK h = 0.6 4CPFSK h = 0.46 8CPFSK h = 0.32 6 0 10 20 30 40 50 Users ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 15 Engine / 20

Partial-band Jamming Applications Partial-band Jamming Waveforms Three systems: q h info bits code bits code rate 2 0.6 2048 3200 0.64 4 0.46 2048 3456 0.59 8 0.32 2048 3840 0.53 All three have BW efficiency η = 0.5 bps/hz. Turbo code from UMTS standard used. 16, 32, or 64 hops per codeword. Interference Interference covers fraction µ of the band. I 0 is interference spectral density when µ = 1. Additional noise power of I 0 /µ if hop has interference. E b /I 0 = 13 db. ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 16 Engine / 20

Partial-band Jamming Applications Partial-band Jamming Waveforms Three systems: q h info bits code bits code rate 2 0.6 2048 3200 0.64 4 0.46 2048 3456 0.59 8 0.32 2048 3840 0.53 All three have BW efficiency η = 0.5 bps/hz. Turbo code from UMTS standard used. 16, 32, or 64 hops per codeword. Interference Interference covers fraction µ of the band. I 0 is interference spectral density when µ = 1. Additional noise power of I 0 /µ if hop has interference. E b /I 0 = 13 db. ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 16 Engine / 20

Applications Influence of Alphabet Size Partial-band Jamming 24 22 20 q=2 Perfect CSI EM estimator E b /N o in db 18 16 14 12 10 8 Rayleigh AWGN q=4 q=8 q=2 q=4 Minimum E b /N 0 for BER = 10 3. 32 hops/codeword. 6 q=8 4 0 0.2 0.4 0.6 0.8 1 μ ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 17 Engine / 20

Applications Influence of the Number of Hops Partial-band Jamming E b /N o in db 26 24 22 20 18 16 14 12 10 4-ary CPFSK, 16 hops 4-ary CPFSK, 32 hops 4-ary CPFSK, 64 hops 8-ary CPFSK, 16 hops 8-ary CPFSK, 32 hops 8-ary CPFSK, 64 hops Minimum E b /N 0 for BER = 10 3. Block Rayleigh fading. 8 0 0.2 0.4 0.6 0.8 1 μ ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 18 Engine / 20

Conclusion Conclusion In FH systems, the bandwidth B per hopping channel must be carefully chosen. Large B gives better performance in interference-free environment. Small B is beneficial in presence of interference. Capacity analysis can be used to determine best h and r for a particular bandwidth constraint. Channel estimation can be performed using EM algorithm. Nonbinary signaling (q > 2) with small h can provide additional gains. ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 19 Engine / 20

Conclusion Conclusion In FH systems, the bandwidth B per hopping channel must be carefully chosen. Large B gives better performance in interference-free environment. Small B is beneficial in presence of interference. Capacity analysis can be used to determine best h and r for a particular bandwidth constraint. Channel estimation can be performed using EM algorithm. Nonbinary signaling (q > 2) with small h can provide additional gains. ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 19 Engine / 20

Conclusion Conclusion In FH systems, the bandwidth B per hopping channel must be carefully chosen. Large B gives better performance in interference-free environment. Small B is beneficial in presence of interference. Capacity analysis can be used to determine best h and r for a particular bandwidth constraint. Channel estimation can be performed using EM algorithm. Nonbinary signaling (q > 2) with small h can provide additional gains. ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 19 Engine / 20

Conclusion Conclusion In FH systems, the bandwidth B per hopping channel must be carefully chosen. Large B gives better performance in interference-free environment. Small B is beneficial in presence of interference. Capacity analysis can be used to determine best h and r for a particular bandwidth constraint. Channel estimation can be performed using EM algorithm. Nonbinary signaling (q > 2) with small h can provide additional gains. ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 19 Engine / 20

Conclusion Questions ( US Army Robust Research Frequency-Hopping Lab, Lane Department of Computer Science June 26, and 2007 Electrical 20 Engine / 20