Dynamic Spectrum Access Decisions. George F. Elmasry

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 S_i(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 S_i(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, , is simply the received signal energy. While the communications receiver takes further steps to decode the projected signal based on the squared intra‐signal distances, an outcome of the communications signal receiver,, is energy detection that can be utilized for same‐channel in‐band sensing. Calculating is the common process between signal decoding and signal energy detection. As will become clear in Chapter 3, the purpose of same‐channel in‐band sensing is to decide if the communications signal utilized frequency band suffers from an interference level that requires using a different frequency band or if the interference level is tolerable.

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 a center frequency f₀ and a bandwidth W to define the frequency range to sense. The sensor uses a bandpass filter, as with time domain energy detection, followed by an analog‐to‐digital convertor (ADC) to digitize the signal and FFT to convert the signal to the frequency domain (Figure 2.6). The squaring device calculates the energy per each frequency coefficient and the mean value stage is used to calculate the average energy over the observed frequency band.

Figure 2.6 Frequency domain energy detection.

      As with time domain energy detection, frequency domain energy detection has to consider the presence of noise. The method used to estimate the noise power spectral density can rely on discrete Fourier transformation (DFT) where the digitized data is divided into segments and a sliding window is used to estimate the average noise spectral density. One reason to choose frequency domain energy detection over time domain energy detection in augmented sensors is the higher