an instant detection of energy within the length of the frame and N in Equation (3.2) can be selected for the number of samples (instants) collected during the frame time. N should be large enough to smooth the effect of noise spikes. This sampling can occur when the preamble is acquired and when the preamble is not acquired separately.
The goal of same‐channel in‐band sensing has two folds. The first is to hypothesize for the presence of an interfering signal plus noise or hypothesize the presence of only noise when the communications signal is known to be absent. The second is when the communications signal is known to be present, the ROC model would then hypothesize if the interfering signal and noise power are too high to warrant a change of the operating frequency. The ROC model explained in the previous section has to be adapted to consider two different thresholds instead of one threshold. With same‐channel in‐band sensing, Equation (3.1) becomes:
3.14
where r(n) is the interfering signal.
When the same‐channel in‐band demodulation finds a preamble and it is demodulating and decoding an over‐the‐air frame, the same‐channel in‐band energy detection process is faced with the following two hypotheses:
3.15
3.16
When the same‐channel in‐band demodulation does not find a preamble and it is not demodulating and decoding an over‐the‐air frame, the same‐channel in‐band energy detection process is faced with the following two hypotheses:
3.17
3.18
Same‐channel in‐band sensing and the presence of the communications signal's marks such as preambles should lead the ROC model to minimizing PF, with very low probability that the receiver falsely decides that the preamble exist when it does not exist.12 With same‐channel in‐band detection, PF is the probability of deciding an interfering signal r exists when it does not exist. The key here is to have a good estimation of the noise floor energy and a good estimation of the communication signal energy in order to effectively hypothesize the presence or the absence of an interfering signal.
Let us consider one of the most suitable signal types for same‐channel in‐band sensing with minimal computational power requirements. This is the n‐ary phase shift keying (PSK) signal type13. This signal can be used with OFDM as 4‐ary PSK when noise level is high to increase range and reduce data rate, or it can be used as 8‐ary PSK when noise level is low and the signal needs to achieve a higher transmission rate.14 This signal is depicted in Figure 3.3 with the 4‐ary case encoding two bits per symbol and the 8‐ary case encoding three bits per symbol.
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
