*4.3.2 PD*<sup>0</sup> v/s *N*

1.'Th' case with Rayleigh distributed fading vectors (*ηP*, *μP*, *σ<sup>P</sup>* = 1, 0 dB,

*Comparative ROC for the second group of fusion rules for different measured large scale parameters (varying ηP, μ<sup>P</sup> and σP) with S* ¼ 8*, N* ¼ 8 *and Rayleigh distributed fading vector. Results for no shadowing condition,*

2.SC scenario with Rician distributed fading vectors (*ηP*, *μP*, *σ<sup>P</sup>* = 2.72,

*Comparative ROC for all fusion rules for the* SC *environment with S* ¼ 8*, N* ¼ 8 *in Rician fading condition.*

*Results for Rayleigh fading-only condition ('Th') are plotted for comparison.*

*<sup>s</sup>* with ½*Ks*, min ,*Ks*, max � ¼ ½ � 0*:*5, 4 ),

0 dB; **h***<sup>n</sup>*,*<sup>s</sup>* � N ð Þ 0, 1 ),

*Wireless Sensor Networks - Design, Deployment and Applications*

*denoted by 'Th' are also plotted for comparison.*

**Figure 11.**

**Figure 12.**

**204**

1.22 dB, 2.4 dB; **h**Rice

In **Figures 15** and **16**, we show system probabilities of detection, *PD*<sup>0</sup> with two groups of fusion rules as an interpolated function of the number of receive antennas *N* under *PF*<sup>0</sup> ≤0*:*01.

• *Impact of measurement environment*: If both large and small scale channel parameters are varied, the probability of detection *PD*<sup>0</sup> with MRC and CV-MMSE rules saturates with the increase in *N* over the SC scenario, but increases

#### **Figure 13.**

*Comparative ROC for all fusion rules for the* DC *environment with S* ¼ 8*, N* ¼ 8 *in TWDP fading condition. Results for Rayleigh fading-only condition ('Th') are plotted for comparison.*

**Figure 14.**

*Comparative ROC for all fusion rules for the* SI *environment with S* ¼ 8*, N* ¼ 8 *in double-Rayleigh (DR) fading condition. Results for Rayleigh fading-only condition ('Th') are plotted for comparison.*

**5. Conclusions**

**Figure 16.**

50% cases.

**207**

specific rule and channel SNR.

dynamic (people moving around) environments.

*impact of both large scale and small scale channel parameters.*

*Cross-Layer Inference in WSN: From Methods to Experimental Validation*

*DOI: http://dx.doi.org/10.5772/intechopen.93848*

This chapter summarizes design of sub-optimal fusion rules propounded for decision fusion at a DFC equipped with multiple antennas. Such rues are more efficient than exact LLR based optimal fusion rule for practical implementation. The sub-optimal fusion rules offer a plethora of choices for fusing sensor decisions at the DFC energy efficiently with lower requirement of system knowledge and computational complexity, thereby eliminating all problems with fixed point implementation. All these rules still significantly benefit from the addition of multiple antennas at the DFC, with a saturation on performance depending on the

*PD*<sup>0</sup> *v/s N for the second group of fusion rules with S* ¼ 8 *for different measurement environments reflecting the*

We also investigate and study the practical implications of employing distributed MIMO based WSN, especially in the light of the recently proposed decision fusion algorithms for DFC equipped with multiple integrated antennas. A detailed measurement campaign is conducted for an indoor-to-outdoor distributed MIMO scenario with transmit antennas, representing sensors, deployed in a wide variety of indoor environments and receive antennas mounted on top of an outdoor tower, thereby replicating a DFC. Measurements are accumulated both in static and

For each measurement scenario, large and small scale statistics are derived from the accumulated data, and average values of pathloss and shadowing variations are

calculated. Fading distributions derived from the recorded channel impulse responses (CIRs) are found to closely match the double Rayleigh distribution in 21.4% cases, the TWDP distribution in 28.6% cases and the Ricean distribution in

Large and small scale channel parameters calculated from the accumulated measurements are used to model the MAC scenario over which performance of the formulated fusion rules is analyzed for virtual MIMO-based WSN. All the suboptimal fusion rules, on an average, exploit diversity offered by multiple antennas

**Figure 15.**

*PD*<sup>0</sup> *v/s N for the first group of fusion rules with S* ¼ 8 *for different measurement environments reflecting the impact of both large scale and small scale channel parameters.*

with *N* for the DC and SI scenarios at a rate slower with higher *N*, as is evident in **Figures 15** and **16**. *PD*<sup>0</sup> with CV-ML and Max-Log rules increases proportionately with *N* for all scenarios. It is worth-mentioning that this set of performances is limited to the chosen channel of 20 dB, and cannot be generalize to any value of channel SNR.

*Cross-Layer Inference in WSN: From Methods to Experimental Validation DOI: http://dx.doi.org/10.5772/intechopen.93848*

**Figure 16.**

*PD*<sup>0</sup> *v/s N for the second group of fusion rules with S* ¼ 8 *for different measurement environments reflecting the impact of both large scale and small scale channel parameters.*

## **5. Conclusions**

This chapter summarizes design of sub-optimal fusion rules propounded for decision fusion at a DFC equipped with multiple antennas. Such rues are more efficient than exact LLR based optimal fusion rule for practical implementation. The sub-optimal fusion rules offer a plethora of choices for fusing sensor decisions at the DFC energy efficiently with lower requirement of system knowledge and computational complexity, thereby eliminating all problems with fixed point implementation. All these rules still significantly benefit from the addition of multiple antennas at the DFC, with a saturation on performance depending on the specific rule and channel SNR.

We also investigate and study the practical implications of employing distributed MIMO based WSN, especially in the light of the recently proposed decision fusion algorithms for DFC equipped with multiple integrated antennas. A detailed measurement campaign is conducted for an indoor-to-outdoor distributed MIMO scenario with transmit antennas, representing sensors, deployed in a wide variety of indoor environments and receive antennas mounted on top of an outdoor tower, thereby replicating a DFC. Measurements are accumulated both in static and dynamic (people moving around) environments.

For each measurement scenario, large and small scale statistics are derived from the accumulated data, and average values of pathloss and shadowing variations are calculated. Fading distributions derived from the recorded channel impulse responses (CIRs) are found to closely match the double Rayleigh distribution in 21.4% cases, the TWDP distribution in 28.6% cases and the Ricean distribution in 50% cases.

Large and small scale channel parameters calculated from the accumulated measurements are used to model the MAC scenario over which performance of the formulated fusion rules is analyzed for virtual MIMO-based WSN. All the suboptimal fusion rules, on an average, exploit diversity offered by multiple antennas

with *N* for the DC and SI scenarios at a rate slower with higher *N*, as is evident

proportionately with *N* for all scenarios. It is worth-mentioning that this set of

in **Figures 15** and **16**. *PD*<sup>0</sup> with CV-ML and Max-Log rules increases

generalize to any value of channel SNR.

*impact of both large scale and small scale channel parameters.*

**Figure 14.**

**Figure 15.**

**206**

performances is limited to the chosen channel of 20 dB, and cannot be

*PD*<sup>0</sup> *v/s N for the first group of fusion rules with S* ¼ 8 *for different measurement environments reflecting the*

*Comparative ROC for all fusion rules for the* SI *environment with S* ¼ 8*, N* ¼ 8 *in double-Rayleigh (DR)*

*fading condition. Results for Rayleigh fading-only condition ('Th') are plotted for comparison.*

*Wireless Sensor Networks - Design, Deployment and Applications*

at the DFC to achieve considerable gain in performance. Among all the rules, CV-ML performs worst and CV-MMSE performs best in all scenarios. MRC, EGC and Max-Log perform in between the two extremes of CV-ML and CV-MMSE. In this case, EGC performs better than MRC and MRC performs better than Max-Log.

**References**

[1] R. Jiang, S. Misra, B. Chen, and A. Swami. Robust suboptimal decision fusion in wireless sensor networks. Proceedings in IEEE Military Communications Conference, 2005. MILCOM 2005. Oct. 2005, pp. 2107–2113.

*DOI: http://dx.doi.org/10.5772/intechopen.93848*

*Cross-Layer Inference in WSN: From Methods to Experimental Validation*

[8] F. Li, J. S. Evans, and S. Dey. Decision fusion over non-coherent fading multi-access channels. IEEE Transactions on Signal Processing. 59 (9), pp. 4367–4380, Sep. 2011.

[9] E. Nurellari, D. McLernon, M. Ghogho, and S. Aldalahmeh. Distributed Binary Event Detection Under Data-Falsification and Energy-Bandwidth Limitation. IEEE Systems Journal. 16 (16), pp. 6298–6309, Aug. 2016.

[10] Y. Zhang, J. Ye, G. Pan and M.-S. Alouini. Secrecy Outage Analysis for Satellite-Terrestrial Downlink Transmissions. IEEE Wireless Communication Letters. May. 2020, DOI: 10.1109/LWC.2020.2999555.

[11] N. B. Rached, A. Kammoun, M.-S. Alouini, and R. Tempone. Accurate Outage Probability Evaluation of Equal Gain Combining Receivers. 2018 IEEE Global Communications Conference (GLOBECOM). Dec. 2018, Abu Dhabi,

[12] M. Ivanov, C. Häger, F. Brännström, A. Amat, A. Alvarado and E. Agrell. On the Information Loss of the Max-Log Approximation in BICM Systems. IEEE Transactions on Information Theory. 62

(6), pp. 3011–3025, Jun. 2016.

[13] E. Yoon. Maximum Likelihood Detection with a Closed-Form Solution for the Square QAM Constellation. IEEE

Communications Letters. 21(4),

IEEE Transactions on vehicular Technology. 66(7), pp. 6586–6590,

and F. Adachi. Statistical CSI

[14] M. L. Ammari and P. Fortier. Low Complexity ZF and MMSE Detectors for the Uplink MU-MIMO Systems with a Time-Varying Number of Active Users.

[15] G. Wang, W. Peng , D. Li, T. Jiang,

pp. 829–832, Apr. 2017.

Jul. 2017.

UAE, DOI: 10.1109/ GLOCOM.2018.8647776.

[2] J. O. Berger, J. M. Bernardo, and D. Sun. Reference priors for discrete parameter space. Technical Report. h ttp://www.uv.es/bernardo/publications.

[3] M. K. Banavar, A. D. Smith, C. Tepedelenlioglu, and A. Spanias.

Distributed detection over fading MACs with multiple antennas at the fusion center. Proceedings in 2010 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP).

[4] H. Saghlatoon, R. Mirzavand and P. Mousavi. Fixed-Frequency Low-Loss Dielectric Material Sensing Transmitter.

[5] G. D. Durgin, T. S. Rappaport, and D. A. de Wolf. New analytical models and probability density functions for fading in wireless communications. IEEE Trans. Commun. 50(6), pp. 1005–1015,

[6] E. Chatziantoniou, B. Allen, V. Velisavljevic, P. Karadimas and J. Coon. Energy Detection Based Spectrum Sensing Over Two-Wave With Diffuse

Power Fading Channels. IEEE

66(1), pp. 868–874, Jan. 2017.

Transactions on Vehicular Technology.

[7] Y. Alghorani, A. S. Chekkouri, D. A. Chekired, and S. Pierre. Improved S-AF and S-DF Relaying Schemes Using Machine Learning Based Power Allocation Over Cascaded Rayleigh Fading Channels. IEEE Transactions on Intelligent Transportation System. Jun. 2020, DOI: 10.1109/TITS.2020.3003820.

IEEE Transactions on Industrial Electronics. Mar. 2020, DOI: 10.1109/

TIE.2020.2977550.

Jun. 2002.

**209**

html, Tech. Rep. 2010.

Mar. 2010, pp. 2894–2897.
