style="font-size:15px;"> 2 The time T = Tf − Tg is a critical factor in detecting the signal energy.7 If the signal is too weak, the integration of the square value of the signal voltage may need a long period of time to yield reliable energy detection.
The receiver of a communications signal detects a multicoefficient signal in N‐dimensional SiS and attempts to match the received signal with one of M signals.8 The energy detector cares only for the signal energy not the signal decoding.
The signal's ith dimension projected on the kth base can be expressed as follows:
(2.1)
where Φk(t) is the signal basis per coefficient.
Notice that both the signal receiver and the spectrum sensor performing energy detection need to carry similar steps to calculate the received signal energy. Chapter 3 covers how to use same‐channel in‐band sensing to hypothesize the presence of an interfering signal. This section is intended to show how to piggyback on the communications receiver's energy calculation to create same‐channel in‐band energy sensing.
Figure 2.4 shows how a communications receiver recovers a signal Si(t) based on knowing its base per each dimension. The projection of the signal per each dimension is expressed in Equation (2.1). The baseband signal Si(t) is then mapped to a point in the N‐dimensional SiS. The square distance from the origin to the projected point from Figure 2.4,
Figure 2.4 Leveraging signal receiver reconstruction of the received signal for same‐channel in‐band spectrum sensing.
A communication receiver also calculates SNIR. The SNIR calculation is based on the energy detection of the signal and the energy detection of the noise (known as the noise floor). Signal energy detection and noise floor energy detection are metrics that can be leveraged for same‐channel in‐band spectrum sensing because they are common between signal decoding and same‐channel in‐band sensing. The value of using SNIR in same‐channel in‐band sensing will become clear in Chapter 3.
While energy detection is a natural outcome of signal decoding, building specialized hardware for spectrum sensing can perform energy detection in different ways. This specialized hardware, which is sometimes referred to as an augmented sensor, may or may not have prior knowledge of the signal bases. The following subsections show different methods that can be utilized by the augmented sensors to perform energy detection.
2.3.2 Time Domain Energy Detection
With this technique, the spectrum sensor has to rely on using bandpass filters. The spectrum sensor is given a center frequency f0 and a bandwidth W to define the frequency range to sense. The spectrum sensor inputs the signal s(t) through the bandpass filter followed by a squaring device and an integrator, as shown in Figure 2.5. The details of how to build such a sensor are beyond the scope of this book. However, these sensors have the ability to define bandpass filters for any given center frequency f0and any given bandwidth W in the broad‐spectrum range they are designed for. These sensors also have the ability to perform energy detection on a wide band of frequency divided into smaller sub‐bands in parallel.
Figure 2.5 Time domain energy detection.
Notice the importance of T in the integrator in Figure 2.5. A signal with weak power spectral density such as a spread spectrum signal would needs a longer time period T. With augmented sensors, the bandpass filter has a critical transfer function that can be expressed as follows:
(2.2)
The reason for emphasizing Equation (2.2) is that the augmented sensor needs to estimate the noise one‐sided power spectral density N0, which is a challenge when the augmented spectrum sensor may have no prior knowledge of the signal it is sensing and hence has no means to directly estimate the noise floor, as in the case of same‐channel in‐band sensing. Instead, the augmented sensor relies on normalizing for the noise power and uses this normalization to compute the probability of a false alarm and the probability of detection as detailed in Chapter 3. If we conceptualize how the sensor creates an energy detection sample every T seconds, then in a large number of samples we have a high probability that the signal being sensed was not transmitted during the entire time period T. Thus, the noise floor becomes the energy sample collected with the minimum energy detection. The importance of Equation (2.2) is that it expresses the noise one‐sided power spectral density that correlates to the noise floor.
In time domain spectrum sensing, the time duration that the sensed signal remaining in a particular state can affect the outcome of the spectrum sensor. This time duration is referred to as the dwell time. The spectrum sensor observation time length should correlate to dwell time. Chapter 3 shows that one advantage of same‐channel in‐band sensing is that the in‐band signal is sensed during a known state and the sensing technique does not observe the signal during multiple states within a single sensing window. That is, the sensing technique can have knowledge of whether the transmitted signal is present or not during the entire sensing window. On the other hand, augmented sensors using time domain energy detection, where the sensed signal may change state during the observation time, can lend a higher probability of false alarm.
2.3.3 Frequency Domain Energy Detection
With this energy detection technique, the sensor also has to be configured for
