Dynamic Spectrum Access Decisions. George F. Elmasry

Figure 3.3 4‐ary PSK and 8‐ary PSK.

Notice that using two‐dimensional signal space as in Figure 3.3 is proven to reduce computational complexity with signal encoding and decoding. Also, PSK makes the signal amplitude change due to noise or interfering signals, not affect the symbol decoding process as shown in Figure 3.4 where the decision zones are depicted with dashed lines. Figure 3.5 shows the probability distribution function (PDF) contours of one of the signal symbols, S₁, in relation to the decision line (perpendicular bisector) between S₁ and S₀. Notice in Figures 3.4 and 3.5 how the received signal vector, v, minor phase shifting will not cause a probability of a symbol error and how amplitude increase or decrease will never affect symbol errors. With this signal type, symbol error occurs only with considerable phase shifting. This modulation technique is widely used with military communications signals and can be useful in adding same‐channel in‐band sensing to the existing communications signal.

Figure 3.4 Decisions zones for 8‐ary PSK.

Figure 3.5 PDF contour of a PSK signal and perpendicular bisector between two symbols in signal space.

Same‐channel in‐band sensing of n‐ary PSK signals leverages the signal characteristics where the hypotheses in Equations (3.15)–(3.18) can be simplified. The left‐hand side of Figure 3.6 shows how the inner grey circle can define a noise floor (similar to a decision zone for the presence of only noise) and how a measured signal power outside of the outer circle can define an interfering signal that drastically affected the signal amplitude. The right‐hand side of Figure 3.6 shows how these circles can be projected into decision lines (thresholds) in terms of the energy detection. Keep in mind that a major difference between symbol decoding and energy detection is that energy detection projects the signal vector into a one‐dimensional positive axis shown as the signal energy axis on the right of Figure 3.6, while symbol decoding deals with the signal based on it SiS dimensions and characteristics.

Figure 3.6 Hypothesizing the presence of noise and interfering signal with PSK signals.

The approach illustrated in Figure 3.6 allows for the estimation of noise floor when the preamble is not acquired and the energy level is low. Noise floor estimation can be a moving average such that the inner dashed line on the left of Figure 3.6, which maps to λ₁ for the noise energy threshold, is an adaptable threshold. Similarly, the λ₂ threshold defines the separation between a signal and noise versus a signal plus noise plus an interfering signal. λ₂ can be adapted as the noise floor estimation changes and as the estimated received signal power is changed.¹⁵ Notice that if the communications waveform has an adaptable power control feature, knowledge of the signal transmission power, the distance between the transmitter and the sensor, and the terrain type can help decide where λ₂ changes adaptively.

      Equations (3.15)–(3.18) and Figure 3.6 explain an overlay concept of the noise, in‐band signal, and interfering signal. If the noise floor estimation is accurate, the sensor can subtract w(n) from Equations (3.11)–(3.14). If the sensor has information regarding the transmission power of the in‐band signal, the distance to the emitter and terrain information, then s(n) can be estimated, allowing the sensor to hypothesize the presence of an interfering signal in a close to optimal way.¹⁶

      It is critical to understand the importance of collecting large samples by the spectrum sensor to make the ROC model viable in implementation. More importantly, noise and the interfering signal are manifested not by a simple increase in energy detection level, but by an increase in the variance of the collected samples. Relying on a small sample can lead to suboptimal results as the set of small samples can be misleading. Estimating the deviation in the energy samples is what accurately reflects the impact of noise and interfering signals and what should be used for dynamically adapting the thresholds.

3.3 Decision Fusion

      The ROC model implementation at the sensing node could be the first step towards making spectrum sensing decisions. The next step is referred to as decision fusion (DF), which uses the ROC model hypotheses outcome to make more comprehensive spectrum sensing decisions. This section presents local, distributed, and centralized decision fusion approaches to help the reader decide the most suitable place to make a DSA decision in a hybrid DSA system.

      3.3.1 Local Decision Fusion

With a spectrum sensor performing a simple energy detection decision, this may be the end of the decision‐making process that can be made locally. The local decision fusion process would rely on the local hypotheses that differentiate if the frequency band being sensed is occupied or not. If a hypothesis is persistent for the presence or absence of a signal, the decision fusion will turn the hypotheses into a decision. However, if an augmented sensor is able to utilize a multisector antenna or antenna arrays, there could be further fusion steps before making a decision. An example of a further fusion step is to identify the direction of the interfering signal when the local process hypothesizes the presence of interference relying on the difference in the energy received per sector. This case is covered in Section 3.3.1.2 The more common case to perform further local decision fusion is for the same‐channel in‐band sensing in a MANET where the reception of the sensed communications signal can be mapped to an RF neighbor. This can make the spectrum sensor in the MANET node able to create a more detailed spectrum map (i.e., identify interference directionality) without using sectored antennas,¹⁷ as explained in Section 3.3.1.1

      Notice that if the local fusion process stops without further fusion of spectrum sensing information, the higher