Dynamic Spectrum Access Decisions. George F. Elmasry

for an explanation of the use of the term “energy detection” in spectrum sensing.

      2 2 Notice that dB is a logarithmic scale that is used to describe the ratio of signal to noise.

      3 3 WiFi is a trademarked phrase that means IEEE 802.11.

      4 4 Opportunistic use of a spectrum by a secondary user is one example of opportunistic spectrum use. The more common opportunistic spectrum use is with unlicensed frequency bands where any user looks for spectrum holes to transmit on.

      5 5 This one unit of energy can be dependent on the sensing time period.

      6 6 The reader can refer to digital communications specialized references on how a signal is constructed in multidimensional SiS.

      7 7 With same‐channel in‐band sensing, T is well correlated to the dwell time, as explained in Chapter 3.

      8 8 M is typically a power of 2. With a binary antipodal signal, M = 2. With a 4‐ary phase shift keying signal, M = 4. With 8‐ary phase shift keying, M = 8. QAM signals can be 16, 32, 64, etc. Except for the binary antipodal signal, which has one direction, all of these examples have a two‐dimensional signal (i.e., N = 2). Orthogonal signals can have higher dimensions.

      9 9 Statistical decisions in symbol detection also have a probability of false alarm and a probability of misdetection. However, both probabilities result in detecting the wrong symbol and hence most signal detection techniques are interested in the probability of symbol error without the distinction between the probability of false alarm and the probability of misdetection.

      10 10 The differences between S(t) and S*(t) are two‐fold. The first difference is the added noise in S*(t). The second difference, which can have a larger impact, is the time lag between the samples of S*(t) and S(t). If the time lag is zero, S*(t) is aligned to S(t) and this process becomes a convolution process.

      11 11 Signal detection using autocorrelation can also happen in frequency domain where noise covariance can be better estimated.

      12 12 OFDM is used in both commercial and defense signals. Commercial signals include WiMAX, LTE 5 MHz, LTE 20 MHz, and 5G. Defense signals include the wideband networking waveform (WNW) and the soldier radio waveform (SRW).

      13 13 This opportunistic use can be by another commercial signal or a military signal.

      14 14 All the jammer needs to do is to jam enough frequency slots to cause error patterns that make the military signal error correction coding fail to correct the error patterns. This type of spectrum sensing is a cat and mouse game. The defense signal platform spectrum sensing can monitor if the jammer succeeds in overcoming the defense signal before switching the signal to a different mode or using another signal type.

      15 15 Spread spectrum based sensing was covered earlier in this chapter.

      16 16 The preambles mentioned here are different from the time domain preamble, which is a sequence of symbols in the transmitted frame. The preambles here are frequency domain preambles.

      17 17 In defense applications, this area of operation is referred to as the theater of operation.

      18 18 Wavelet transform is widely used in digital image processing. With spectrum sensing, it can be used with sensing signals that use a wideband.

      19 19 An even signal is symmetric around the vertical axes. An odd signal is symmetric about the origin.

Chapter 3 Receiver Operating Characteristics and Decision Fusion

Receiver operating characteristic (ROC) is not a unique methodology to DSA decision making. It is widely used in many areas where statistical decisions are adaptively made based on myriad metrics. ROC is a generic approach developed for low computational and implementation complexities. This chapter covers different DSA scenarios that rely on using ROC models. A ROC model can be used when probing a frequency band to discover if it is occupied or not at a certain geographical location (e.g., a secondary user is sensing if a primary user is using this frequency band or not). Another scenario that uses a different ROC model is the case of same‐channel in‐band sensing where the ROC model can hypothesize the presence or absence of an interfering signal. The detected energy of the sensed frequency band is compared to an adaptive threshold to hypothesize the presence of the interfering signal. This threshold adaptation is highly dependent on noise estimation and is decided based on tradeoffs driven by the design needs. Estimating ROC models' thresholds can be challenging when noise variance increases and when signal power is too low.¹ The spectrum sensor can be looking into interference from other signals overlaid with the noise without being able to distinguish between the interfering signal power and the noise power. In other cases, the spectrum sensor can be looking at an overlay of different signals occupying the same frequency band. This can mislead the decision‐making process and result in increasing the probability of false alarm and of misdetection.²

      With DSA, the ROC methodology can be implemented in different approaches depending on the sensing metrics and where the decision is made. This chapter will start with the generic aspects of the ROC hypothesizing process in DSA applications and present simple ROC‐based decision fusion cases while gradually moving to the harder cases. Statistical decision models in modulation and coding are well studied and well presented in textbooks. This chapter covers decision models for spectrum sensing pointing to the similarities and difference with modulation and coding models. While a demodulator may use fixed thresholds and rely on well‐known statistical models such as AWGN and the communication signal known power spectral density characteristics to decode a symbol, spectrum sensing models use adaptive thresholds and machine learning techniques to account for the many factors that can compound the spectrum sensing hypotheses. If the reader is not familiar with the ROC models, the reader is encouraged to refer to Appendix A of this chapter to get some basic understanding of the ROC methodology.

3.1 Basic ROC Model Adaptation for DSA

This ROC model is the most basic model where a sensor is probing a frequency band to check for the presence or absence of a communications signal. This basic model relies on energy detection and can assume that the noise is AWGN such that the signal received by the sensor can be expressed as follows:

3.1

      In Equation (3.1), s(n) is the sensed signal, w(n) is the AWGN, and n is the sampling index. If the sensed frequency band has no signal occupying it, then s(n) = 0 and the sensing process will detect the energy level of the AWGN.

      The sensed signal energy can be expressed as a vector of multiple sampling points as follows:

3.2

      where N is the size of the observation vector.

      The value of N and the definition of sampling points can differ from one sensor to another and any pre‐knowledge of the sensed signal waveform characteristics can guide the sensor into creating more optimal sampling points.

      The energy detection process can compare the decision metric M from Equation (3.2) against a fixed threshold λ_E. This processes needs to distinguish between two hypotheses, one hypothesis is for the presence of only noise and the other hypothesis is for the presence of signal and noise. These two hypotheses are:

      3.3

      3.4