signal space constellation for this case from s0 to sM − 1 symmetrically around the zero‐power point.Calculate the ideal signal energy for the inner six transmitted symbols in terms of a.Is simple energy detection ideal for this type of signal? Why?4 Consider the 32‐QAM constellation case shown below. QAM signals are commonly used with microwave links. This is a two‐dimensional signal in space. In QAM, inner constellation points have four nearest neighbors, the edge points have three nearest neighbors, and the corner points have two nearest neighbors.Assuming signal spacing is d = 2a in each dimension, what are the various energies for the different points of the constellation?How many instantiations are there for each energy level?Is this type of signal a better candidate for energy detection than the one‐dimensional case in Problem 3? Why?What would you consider as another important metric in addition to energy detection when detecting microwave signals?
5 Comparing to AM and QAM, what do you think of the suitability of 4‐ary PSK and 8‐ary PSK signals for energy detection?
Appendix 2A: The Difference Between Signal Power and Signal Energy
There is a significant difference between energy and power when analyzing a signal. A signal can be categorized in different ways, as shown in Table 2A.1, including an energy/power signal category. Notice that in Table 2A.1 the signal can be either category A or category B.
Table 2A.1 Different categories of signals
| Signal category | Category A | Category B |
| 1 | Continuous time | Discrete time |
| 2 | Deterministic | Random |
| 3 | Periodic | Aperiodic |
| 4 | Even | Odd19 |
| 5 | Energy | Power |
A signal is time varying and can convey information or not convey information. Noise is a type of signal that does not convey information. Some jammers can also be a type of signal that does not convey information. A signal can be a function of time and a function of other independent variables.
A signal is categorized as an energy signal if it has finite energy, that is, 0 < E < ∞. When the signal is analyzed over a given time duration and the signal energy can be measured, it is an energy signal. An example of that signal is a pulse signal where the pulse is either positive or negative. A decaying pulse signal is also an energy signal because its energy can be measured over a given time duration. On the other hand, a sinusoidal signal energy cannot be measured in time domain, and hence it cannot be categorized19 as an energy signal. The sinusoidal signal is a power signal. Moving from time domain to frequency domain, the sinusoidal signal power spectral density can be measured. The sinusoidal signal is a power signal over infinite time. A signal can be categorized as a power signal when it has finite power without time limitation.
Notice that with spectrum sensing, we may sense a modulated signal over a sinusoidal wave (carrier). We look at frequency bands of carrier frequencies and hence we measure the signal power. The term “energy detection” is used loosely with spectrum sensing and it means integrating the measured signal power over a limited time period (time of sensing or dwell time). With spectrum sensing, the correct term for energy detection should be power integration over a finite time. The term “energy detection” is widely used because spectrum sensors integrate the sensed power spectral density over the sensing time period and the process of integration over time leads to using the term energy detection. In spectrum sensing references, spectrum sensing is a multidimensional process that considers time, frequency, and power. Power here can be power spectral density measured over limited time. The simplest way of spectrum sensing is known as energy detection, which integrates the power spectral density measured by the spectrum sensor, in frequency domain, over a given sensing period.
Bibliography
1 Abdulstar, M. and Hussein, Z., Energy detection techniques for spectrum sensing in cognitive radio: A survey. International Journal of Compute Networks and Communications, vol. 4, no. 5, September 2012.
2 Cabric, D.B., Cognitive radios: System design perspective. University of California, Berkeley, UMI Microform 3306077.
3 Cabric, D., Tkachenko, A., and Brodersen, R., Spectrum sensing measurements of pilot, energy, and collaborative detection. In Proceedings of the IEEE Military Communications Conference, Washington, D.C., USA, October 2006.
4 Cordeiro, C., Challapali, K., and Birru, D., IEEE 802.22: An introduction to the first wireless standard based on cognitive radios. Journal of Communications, vol. 1, no. 1, April 2006.
5 Digham, F., Alouini, M., and Simon, M., On the energy detection of unknown signals over fading channels. In Proceedings of the IEEE International Conference on Communication, vol. 5, Seattle, Washington, USA, May 2003, pp. 3575–3579.
6 Elmasry, G.F., Tactical Wireless Communications and Networks, Design Concepts and Challenges. Wiley, 2012. ISBN: 978‐1‐1199‐5176‐6.
7 Federal Communications Commission, Notice of proposed rulemaking and order: Facilitating opportunities for flexible, efficient, and reliable spectrum use employing cognitive radio technologies. ET Docket No. 03‐108, February 2005.
8 Gandetto, M. and Regazzoni, C., Spectrum sensing: A distributed approach for cognitive terminals. IEEE Journal on Selected Areas of Communications, vol. 25, no. 3, pp. 546–557, April 2007.
9 Geirhofer, S., Tong, L., and Sadler, B., A measurement‐based model for dynamic spectrum access in WLAN channels. In Proceedings of the IEEE Military Communications Conference, Washington, D.C., USA, October 2006.
10 Geirhofer, S., Tong, L., and Sadler, B., Dynamic spectrum access in the time domain: Modeling and exploiting white space. IEEE Communications Magazine, vol. 45, no. 5, pp. 66–72, May 2007.
11 Ghasemi, A. and Sousa, E.S., Asymptotic performance of collaborative spectrum sensing under correlated log‐normal shadowing. IEEE Communications Letters, vol. 11, no. 1, pp. 34–36, January 2007.
12 Guzelgoz, S., Celebi, H., and Arslan, H., Statistical characterization of the paths in multipath PLC channels. Proceedings of the IEEE Transactions on Power Delivery, vol. 26, no. 1, pp. 181–187, January 2011.
13 Haykins, S, Cognitive radio: brain empowered wireless communications. IEEE Journal on Selected Areas in Communications, pp. 201–220, February 2005.
14 Hu, W., Willkomm, D., Abusubaih, M., et al., Dynamic frequency hopping communities for efficient IEEE 802.22 operation. IEEE Communications Magazine, vol. 45, no. 5, pp. 80–87, May 2007.
15 Lehtomäki, J., Vartiainen, J., Juntti, M., and Saarnisaari, H., Spectrum sensing with forward methods. In Proceedings of the IEEE Military Communications Conference, Washington, D.C., USA, October 2006.
16 Leu, A., McHenry, M., and Mark,
