Distributed Statistical Inference using Type Based Random Access - PowerPoint PPT Presentation

Type Based Random Access Performance Metric Optimal TBRA Conclusion Distributed Statistical Inference using Type Based Random Access over Multi-access Fading Channels Animashree Anandkumar and Lang Tong Adaptive Communication and Signal Processing Group School of Electrical and Computer Engineering Cornell University, Ithaca, NY 14853. Supported by the MURI under Office of Naval Research and Army Research Laboratory CTA 03/22/2006. Anima Kumar at CISS ’06 1 / 27

Type Based Random Access Performance Metric Optimal TBRA Conclusion Classical Distributed Inference Node n Node 2 Node 1 • Sensors : Sense physical phenomenon and transmit their local decisions. � � � � � � � � � � � � � � � � • Fusion Center: Make inference on the �� phenomenon. �� C n C 1 C 2 �� • Sensor-Fusion Center Communication �� Perfect (Error - free) with rate constraints. �� • Typically in Radar communication. Fusion Center Key Issues • Quantization @ sensors. • Inference @ fusion center. Anima Kumar at CISS ’06 2 / 27

Type Based Random Access Performance Metric Optimal TBRA Conclusion Inference in Large Wireless Sensor Networks Characteristics • Low Power and Low Rate Transmissions. • Bandwidth Allocation. Mobile Access • Multiaccess Channel with Fading. • Energy Efficiency to prolong network life-time. • Faulty, sleeping or poorly placed sensors. • Deterministic scheduling (TDMA) may Cluster head not be appropriate. Medium Access Design is a key component. Anima Kumar at CISS ’06 3 / 27

Type Based Random Access Performance Metric Optimal TBRA Conclusion Random Access • Model : Random Number of Sensors in a data collection. • Probabilistic Wake-up : Transmit based on a coin-flip. • Transmit only Significant Data. • Fusion center is a Mobile Access Point : collects data from different geographic regions. Anima Kumar at CISS ’06 4 / 27

Type Based Random Access Performance Metric Optimal TBRA Conclusion Distributed Inference over Multi-Access Channels Detection ( Binary Hypothesis) and Estimation. Physical Phenomenon Random number of sensors per collection θ ∈ Θ N i are IID with mean λ . Sensor Quantization: X i,j quantized to M levels Sensor Sensor Sensor and Conditionally IID given θ 1 2 n X ij ∼ p θ = ( p θ (1) , · · · , p θ ( M )) Multi-access model • Flat IID fading: H i,j • AWGN W ( t ) with PSD = σ 2 . Inference at Fusion Center • Neyman Pearson or Bayesian Detection. • Maximum Likelihood Estimation. Multiple collections: i –time index, j –sensor index. Anima Kumar at CISS ’06 5 / 27

Type Based Random Access Performance Metric Optimal TBRA Conclusion Distributed Inference over Multi-Access Channels Detection ( Binary Hypothesis) and Estimation. Physical Phenomenon Random number of sensors per collection θ ∈ Θ N i are IID with mean λ . Sensor Quantization: X i,j quantized to M levels Sensor Sensor Sensor and Conditionally IID given θ 1 2 n X i, 2 X i, 1 X i,n i X ij ∼ p θ = ( p θ (1) , · · · , p θ ( M )) Multi-access model • Flat IID fading: H i,j • AWGN W ( t ) with PSD = σ 2 . Inference at Fusion Center • Neyman Pearson or Bayesian Detection. • Maximum Likelihood Estimation. Multiple collections: i –time index, j –sensor index. Anima Kumar at CISS ’06 5 / 27

Type Based Random Access Performance Metric Optimal TBRA Conclusion Distributed Inference over Multi-Access Channels Detection ( Binary Hypothesis) and Estimation. Physical Phenomenon Random number of sensors per collection θ ∈ Θ N i are IID with mean λ . Sensor Quantization: X i,j quantized to M levels Sensor Sensor Sensor and Conditionally IID given θ 1 2 n X i, 2 X i, 1 X i,n i X ij ∼ p θ = ( p θ (1) , · · · , p θ ( M )) Multi-access model Multiaccess Channel Noise W • Flat IID fading: H i,j • AWGN W ( t ) with PSD = σ 2 . Y i Inference at Fusion Center • Neyman Pearson or Bayesian Detection. • Maximum Likelihood Estimation. Multiple collections: i –time index, j –sensor index. Anima Kumar at CISS ’06 5 / 27

Type Based Random Access Performance Metric Optimal TBRA Conclusion Distributed Inference over Multi-Access Channels Detection ( Binary Hypothesis) and Estimation. Physical Phenomenon Random number of sensors per collection θ ∈ Θ N i are IID with mean λ . Sensor Quantization: X i,j quantized to M levels Sensor Sensor Sensor and Conditionally IID given θ 1 2 n X i, 2 X i, 1 X i,n i X ij ∼ p θ = ( p θ (1) , · · · , p θ ( M )) Multi-access model Multiaccess Channel Noise W • Flat IID fading: H i,j • AWGN W ( t ) with PSD = σ 2 . Y i Detector / Estimator Inference at Fusion Center ˆ θ Fusion Center • Neyman Pearson or Bayesian Detection. • Maximum Likelihood Estimation. Multiple collections: i –time index, j –sensor index. Anima Kumar at CISS ’06 5 / 27

Type Based Random Access Performance Metric Optimal TBRA Conclusion Spatio-Temporal Tradeoff • Mean Transmitting Rate λ and Number of Data Collections l . • Suppose we fix mean number of transmissions is ρ ∆ = λl , (proportional to energy budget). Number of collections l • Should energy be allocated to simultaneous transmissions : large λ ? • Or should we collect more data : large l ? ρ = λl • Small λ : not enough sensors transmit , cannot counter noise. • But, large λ : Less Observations as l is small. Transmission Rate λ • Role of multi access channel : Coherence or Cancelation ? Anima Kumar at CISS ’06 6 / 27

Distributed Statistical Inference using Type Based Random Access - PowerPoint PPT Presentation

Type Based Random Access Performance Metric Optimal TBRA Conclusion Distributed Statistical Inference using Type Based Random Access over Multi-access Fading Channels Animashree Anandkumar and Lang Tong Adaptive Communication and Signal

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