# On the Performance Evaluation of a MIMO–WCDMA Transmission Architecture for Building Management Systems

^{*}

## Abstract

**:**

## 1. Introduction

## 2. MIMO–WCDMA Orientation

_{i}sensor nodes per floor (1 ≤ i ≤ M). It is assumed that all nodes can communicate wirelessly with the central BMS. This is a rather realistic assumption, since we consider a dynamic environment where all nodes can be placed ad hoc. In order to reduce overall transmission power, each node is equipped with M

_{t}antennas, the central BS with M

_{r}antennas, while the WCDMA physical layer protocol has been adopted for internode communications [17]. In WCDMA, which is already used by mobile terminals in 3G communications, all nodes can transmit simultaneously occupying the whole transmission bandwidth. This is achieved with the use of orthogonal spreading sequences, which multiply the information signal. These sequences have low cross correlation values, thus minimizing unwanted effects from multipath propagation. The transmitted WCDMA signal for diversity combining transmission mode (i.e., the same signal is send and received from all antennas) is given by [17]

_{n}is the power of the nth node (1 ≤ n ≤ N), c

_{n}(t) the coding sequence, and b

_{n}(t) the information signal.

_{t}antennas at the transmitter,

**w**

_{n}represents the M

_{t}× 1 transmission vector that corresponds to the complex power distribution per antenna (i.e., $\Vert {w}_{n}\Vert {}_{F}^{2}$ = 1, where ${\Vert x\Vert}_{F}$ is the Frobenius norm of vector matrix

**x**). It is assumed that b

_{n}(t) has a symbol duration equal to T, while the corresponding duration for the coding sequence is T

_{c}. The ratio T/T

_{c}is also called a spreading factor (SF). In a multipath environment, the received signal from the M

_{r}antennas of the central BS (considering uplink transmission) will be given by

**y**

_{n}(t) is the M

_{r}× 1 received signal vector matrix, L is the number of multipath components and τ

_{l}the corresponding delay of the lth multipath (1 ≤ l ≤ L). Moreover, the term TL denotes the total losses (i.e., due to pathloss, shadowing, antenna radiation patterns, etc.) from the transmitter to the receiver. Finally,

**H**

_{n,l}is the M

_{r}× M

_{t}channel matrix, and

**n**

_{n}the M

_{r}× 1 additive white Gaussian noise. In a rich scattering environment such as the inner of a building, each element of

**H**

_{n,l}is assumed to be a zero mean complex Gaussian random variable with standard deviation equal to one [18].

_{n}

_{,0}is the symbol at the current time offset, while b

_{n}

_{,−1}the corresponding symbol at the previous time offset. Moreover,

**r**

_{n,l}is the multiplying maximal ratio combining (MRC) vector matrix, given by [18,19]

_{o}is the thermal noise level. Therefore, overall signal-to-interference-plus-noise ratio (SINR) for the nth node is formulated as follows:

_{f}(n) is the floor penetration loss factor in dB, and n is the number of floors between central BS and mobile node. Considering propagation at 2 GHz, for the considered office environment, v = 3 and L

_{f}(dB) = 15 + 4 (n – 1). Hence, net pathlosses and shadowing effect are calculated as follows [20]:

_{σ}is a log-normally distributed random variable corresponding to shadowing effects.

**A**(n × n) and

**B**(n × 1) are given by

**1**(N) is an N × 1 matrix of ones.

## 3. Simulation Framework

**w**

_{n}is an M

_{t}× M

_{t}matrix. In both transmission cases,

**w**

_{n}matrices are calculated according to overall signal strength maximization. This iterative procedure is presented in Table 1 and Table 2, where tr(

**X**) is the trace of Matrix

**X**. In Table 1,

**X**(λ

_{m}(

**A**)) is the eigenvector corresponding to the maximum eigenvalue of Matrix

**A**. In Table 2,

**U**and

**V**are the left and right singular matrices after singular value decomposition (SVD) of Matrix

**A**, while

**Σ**is a diagonal matrix containing the eigenvalues of

**A**in descending order. Moreover,

**I**

_{K}is a K × K identity matrix, and diagonal matrix

**D**indicates power distribution per transmission mode (tr(

**D**) = 1). Finally, dim = min(M

_{t},M

_{r}) indicates the dimension of the MIMO orientation. Both algorithms initially assume a uniform power distribution in all antennas, and at each step the desired signal strength is calculated. This procedure comes to an end once the convergence of both algorithms (defined by parameter ε) takes place. Finally, all simulation parameters are summarized in Table 3.

## 4. Results and Discussion

_{n}is the set of transmit antennas for the nth node,

**H**

_{n}

_{,j,l}is the equivalent channel matrix considering transmission from the antennas in the subset j, and the set TR includes all possible combinations of transmit antennas. For example, considering a use case scenario with two selected transmit antennas, TR = {(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)}.

_{t}× L independent signals. Hence, diversity combining is the most appropriate solution for this type of communication, especially if we are interested in low-rate communications.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

**Α**,x} indicates the x

^{th}line of Matrix

**Α**. Moreover,

_{n,d}is the transmission power per active user and mode, subject to

_{e}is the error probability, ${p}_{{\mathsf{\gamma}}_{n,d}}\left({\mathsf{\gamma}}_{n,d}\right)$ is the probability density function (pdf) of the desired user signal of Equation (A5), and the Gaussian function is given by

^{7}different channel realizations, where γ

_{n}

_{,d}is calculated for each transmission mode. For a 4 × 2 MIMO network with six multipath components, the pdf functions of the two transmission modes follow the Gamma distribution [24]:

_{t}, M

_{r}) Kbps to 1200 × min(M

_{t}, M

_{r}) Kbps, i.e., from 60 to 2400 Kbps. Note that the basic transmission rate of 30 Kbps corresponds to a PG equal to 128. As can be observed in Figure A2, Figure A3 and Figure A4, the Gaussian approximation for the error probability and consequently the mean BER can be quite accurate for the performance evaluation of a MIMO–WCDMA system operating in spatial multiplexing mode. Moreover, the selection of all multipath components (i.e., 6) leads to an improved BER compared to the case of two multipath components. As expected, this gain reduces for high values of overall throughput, since for an increased number of active users, MAI can be significantly increased.

## References

- Al-Daraiseh, A.; Shah, N.; El-Qawasmeh, E. An intelligent energy management system for educational buildings. Int. J. Distrib. Sens. Netw.
**2013**. [Google Scholar] [CrossRef] - Bolchini, C.; Geronazzo, A.; Quintarelli, E. Smart buildings: A monitoring and data analysis methodological framework. Build. Environ.
**2017**, 121, 93–105. [Google Scholar] [CrossRef] - Skouby, K.E.; Lynggaard, P. Smart home and smart city solutions enabled by 5G, IoT, AAI and CoT services. In Proceedings of the International Conference on Contemporary Computing and Informatics (IC3I), Mysore, India, 27–29 November 2014. [Google Scholar]
- Gungor, V.C.; Sahin, D.; Kocak, T.; Ergüt, S.; Buccella, C.; Cecati, C.; Hancke, G.P. Smart Grid technologies: Communication technologies and standards. IEEE Trans. Ind. Inform.
**2011**, 7, 529–539. [Google Scholar] [CrossRef] - Mahmood, A.; Javaid, N.; Razzaq, S. A review of wireless communications for smart grid. Renew. Sustain. Energy Rev.
**2015**, 4, 248–260. [Google Scholar] [CrossRef] - Clark, G.; Mehta, P. Artificial intelligence and networking in integrated building management systems. Autom. Constr.
**1997**, 6, 481–498. [Google Scholar] [CrossRef] - Shang, W.; Ding, Q.; Marianantoni, A.; Burke, J.; Zhang, L. Securing building management systems using named data networking. IEEE Netw.
**2014**, 28, 50–56. [Google Scholar] - Kheirabadi, F.; Talebiyan, S.R. Proper communicative protocols in building management system. J. Electr. Electron. Eng.
**2015**. [Google Scholar] [CrossRef] - Bharadwaj, C.V.; Velammal, M.; Raju, M. A BMS Client and gateway using BACnet protocol. In Advances in Computing and Information Technology, Communications in Computer and Information Science; Wyld, D.C., Wozniak, M., Chaki, N., Meghanathan, N., Nagamalai, D., Eds.; Springer: Berlin/Heidelberg, Germany, 2011; Volume 198. [Google Scholar]
- Bovet, G.; Hennebert, J. Offering Web-of-Things connectivity to building networks. In Proceedings of the 2013 ACM Conference on Pervasive and Ubiquitous Computing, Zurich, Switzerland, 8–12 September 2013. [Google Scholar]
- Khajenasiria, I.; Estebsarib, A.; Verhelsta, M.; Gielena, G. A review on Internet of Things solutions for intelligent energy control in buildings for smart city applications. In Proceedings of the 8th International Conference on Sustainability in Energy and Buildings, Turin, Italy, 11–13 September 2016. [Google Scholar]
- Hayduk, G.; Kwasnowski, P.; Mikoś, Z. Building management system architecture for large building automation systems. In Proceedings of the IEEE 17th International Carpathian Control Conference (ICCC), Tatranska Lomnica, Slovakia, 29 May–1 June 2016. [Google Scholar]
- Jang, I.; Pyeon, D.; Kim, S.; Yoon, H. A survey on communication protocols for wireless sensor networks. J. Comput. Sci. Eng.
**2013**, 7, 231–241. [Google Scholar] [CrossRef] - Holland, M.; Wang, T.; Tavli, B.; Seyedi, A.; Heinzelman, W. Optimizing physical layer parameters for wireless sensor networks. ACM Trans. Sens. Netw.
**2011**, 7. [Google Scholar] [CrossRef] - Wong, K.D. Physical layer considerations for wireless sensor networks. In Proceedings of the IEEE International Conference on Networking, Sensing and Control, Taipei, Taiwan, 21–23 March 2004. [Google Scholar]
- Fadel, E.; Gungor, V.C.; Nassef, L.; Akkari, N.; Malik, M.G.A.; Almasri, S.; Akyildiz, I.F. A survey on wireless sensor networks for smart grid. Comput. Commun.
**2015**, 71, 22–33. [Google Scholar] [CrossRef] - Holma, H.; Toskala, A. (Eds.) WCDMA for UMTS: HSPA Evolution and LTE, 5th ed.; Wiley: New York, NY, USA, 2010. [Google Scholar]
- Goldsmith, A. Wireless Communications; Cambridge University Press: Cambridge, UK, 2005. [Google Scholar]
- Dong, X.; Beaulieu, N.C. Optimal maximal ratio combining with correlated diversity branches. IEEE Commun. Lett.
**2002**, 6, 22–24. [Google Scholar] [CrossRef] - Propagation Data and Prediction Models for the Planning of Indoor Radiocommunication Systems and Radio Local Area Networks in the Frequency Range 900 MHz to 100 GHz. Available online: https://www.itu.int/rec/R-REC-P.1238/en (accessed on 8 January 2018).
- Paulraj, A.; Gore, D.; Nabar, R.; Bolcskei, H. An overview of MIMO communications—A key to gigabit wireless. Proc. IEEE
**2004**, 92, 198–218. [Google Scholar] [CrossRef] - Choi, W.; Andrews, J.G. Spatial multiplexing in cellular MIMO—CDMA systems with linear receivers: Outage probability and capacity. IEEE Trans. Wirel. Commun.
**2007**, 6, 2612–2621. [Google Scholar] [CrossRef] - Efthymoglou, G.P.; Piboongungon, T.; Aalo, V.A. Performance of DS-CDMA receivers with MRC in nakagami-m Fading channels with arbitrary fading parameters. IEEE Trans. Veh. Technol.
**2006**, 55, 104–114. [Google Scholar] [CrossRef] - Papoulis, A. Probabilities, Random Variables and Stochastic Processes, 3rd ed.; McGraw Hill: New York, NY, USA, 1991. [Google Scholar]

**Figure 6.**Mean power of nodes for various MIMO orientations with antenna selection—diversity combining transmission mode.

**Figure 7.**Mean bit error rate (BER) for various MIMO orientations—diversity combining and spatial multiplexing.

Step 1: Set i ←1, ${w}_{n,i}\leftarrow \left(1/\sqrt{{M}_{t}}\right),{P}_{i}\leftarrow {w}_{n,i}^{\mathrm{H}}{w}_{n,i}$ , ε = 10^{−3} |

Step 2: ${r}_{n,l,i}={\left({H}_{n,l}{w}_{n,i}\right)}^{\mathrm{H}},1\le l\le L\mathrm{and}A\leftarrow {\displaystyle \sum _{l=1}^{L}{\displaystyle \sum _{l\prime =1}^{L}{\left({r}_{n,l,i}{H}_{n,l}\right)}^{\mathrm{H}}}}{r}_{n,l\prime ,i}{H}_{n,l\prime}$ |

Step 3: ${w}_{n,i+1}\leftarrow X\left({\lambda}_{m}\left(A\right)\right)$ and ${P}_{i+1}\leftarrow {w}_{n,i+1}^{\mathrm{H}}A{w}_{n,i+1}$ |

Step 4: If $\frac{\left|\mathrm{tr}\left({P}_{i+1}\right)-\mathrm{tr}\left({P}_{i}\right)\right|}{\mathrm{tr}\left({P}_{i}\right)}\ge \epsilon $ go to Step 2 |

Step 1: Set i ←1, ${w}_{n,i}\leftarrow \frac{1}{\sqrt{{M}_{t}}}{I}_{dim}$, ${P}_{i}\leftarrow {w}_{n,i}^{\mathrm{H}}{w}_{n,i}$, ε = 10^{−3} |

Step 2: ${r}_{n,l,i}={\left({H}_{n,l}{w}_{n,i}\right)}^{\mathrm{H}},1\le l\le L$ and$A\leftarrow {\displaystyle \sum _{l=1}^{L}{\displaystyle \sum _{l\prime =1}^{L}{\left({r}_{n,l,i}{H}_{n,l}\right)}^{\mathrm{H}}}}{r}_{n,l\prime ,i}{H}_{n,l\prime},A\leftarrow U\Sigma {V}^{\mathrm{H}}$ |

Step 3: ${w}_{n,i+1}\leftarrow V{D}^{1/2}$ and ${P}_{i+1}\leftarrow {w}_{n,i+1}^{\mathrm{H}}A{w}_{n,i+1}$ |

Step 4: If $\frac{\left|\mathrm{tr}\left({P}_{i+1}\right)-\mathrm{tr}\left({P}_{i}\right)\right|}{\mathrm{tr}\left({P}_{i}\right)}\ge \epsilon $ go to Step 2 |

Parameter | Units | Value/Assumption |
---|---|---|

Frequency | MHz | 2000 |

Total bandwidth | MHz | 3.84 |

Number of floors | 3 | |

Standard deviation of shadow fading | dB | 10 |

MC snapshots per simulation | 10^{6} | |

Multipath components (L) | 6 | |

Processing gain (PG) | 32, 64, 128 | |

Antenna radiation pattern per antenna | Omnidirectional | |

Number of antennas at the transmitter (M_{t}) | 2,3,4 | |

Number of antennas at the receiver (M_{r}) | 2,3,4 | |

Number of nodes per floor | 1–21 | |

SINR_{th} | dB | 3/5/7/10 |

Floor height (F_{h}) | m | 3 |

Transmission mode | Diversity combining/spatial multiplexing |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Tsampasis, E.; Gkonis, P.K.; Trakadas, P.; Zahariadis, T.
On the Performance Evaluation of a MIMO–WCDMA Transmission Architecture for Building Management Systems. *Sensors* **2018**, *18*, 155.
https://doi.org/10.3390/s18010155

**AMA Style**

Tsampasis E, Gkonis PK, Trakadas P, Zahariadis T.
On the Performance Evaluation of a MIMO–WCDMA Transmission Architecture for Building Management Systems. *Sensors*. 2018; 18(1):155.
https://doi.org/10.3390/s18010155

**Chicago/Turabian Style**

Tsampasis, Eleftherios, Panagiotis K. Gkonis, Panagiotis Trakadas, and Theodοre Zahariadis.
2018. "On the Performance Evaluation of a MIMO–WCDMA Transmission Architecture for Building Management Systems" *Sensors* 18, no. 1: 155.
https://doi.org/10.3390/s18010155