Energy Detection Performance Analysis for UWB Radar Sensor Networks

Ultra-wideband (aka UWB, ultra-wide band, ultraband, etc.) is a radio technology that can be used at very low energy levels for short-range high-bandwidth communications by using a large portion of the radio spectrum. Within the past forty years, advances in analog, digital electronics, and ultra-wideband (UWB) signal theory have enabled system designers to propose some practical UWB communication systems such as in [1]. Currently, numerous companies and government agencies are investigating the potential of UWB to deliver on its promises. A wide range of UWB applications have been demonstrated [2, 3]. The application of ultra wideband (UWB) to radar systems has a long history of development [3, 4]. With the capability of excellent range resolution and penetration, UWB radar sensors attached more extensive investigation in recent years.

Today's wireless networks are regulated by a fixed spectrum assignment policy, that is, the spectrum is regulated by governmental agencies and is assigned to license holder or services on a long-term basis for larger geographical regions. In addition, according to Federal Communications Commission (FCC) [5], temporal and geographical variations in the utilization of the assigned spectrum range from 15 to 85 . UWB communications transmit in a way that doesnot interfere largely with other more traditional narrowband and continuous carrier wave uses in the same frequency band. However first studies show that the rise of noise level by a number of UWB transmitters puts a burden on existing communications services. This may be hard to bear for traditional systems designs and may affect the stability of such existing systems.

In order to ensure that UWB radar sensor networks working smoothly, one of the important requirements is to sense the spectrum holes successfully and then to mitigate the interference to the existing systems. The most efficient detection method is to detect the primary users that are receiving data within the communication range of an secondary user. In reality, however, it is difficult for a secondary user to have a direct measurement of a channel between a primary receiver and a primary transmitter. Thus, the most recent work focuses on primary transmitter detection based on local observations of secondary users. Generally, the spectrum sensing techniques can be classified into matched filter [6], energy detector, and cyclostationary feature detector [7].

When the structure of primary signal is known to secondary user, the optimal detector is a matched-filter followed by a threshold test [8]. The optimal way for any signal detection is a matched filter, since it maximizes received signal-to-noise ratio. However, implementing this type of coherent detector is difficult since a secondary user needs to have a priori knowledge of primary user signal at Physical and MAC layers, for example, modulation type and order, pulse shaping, packet format. Moreover, extra dedicated circuitry to achieve synchrony with each type of primary licenses would be needed. Therefore, there may be cases in practice where matched-filter detector is ruled out due to the lack of knowledge about primary signal's structure.

From other aspect, modulated signals are in general coupled with sine wave carriers, pulse trains, repeating spreading, hoping sequences, or cyclic prefixes that result in built-in periodicity. Even though the data is a stationary random process, these modulated signals are characterized as cyclostationary. This can be used for detection of a random signal with a particular modulation type in a background of noise and other modulated signals [9].

One common method for detection of unknown signals is energy detection, which measures the energy in the received waveform over an observation time window [10, 11]. In [12], energy detection of unknown deterministic signals is studied. Detection performance in terms of detection probability and false alarm probability is formulated. In [13, 14], multiband/wavelet approach and blind adaptive minimum output energy detection were proposed for capturing the AM-FM components of modulated signals immersed in noise and for DS/CDMA [15] over multipath fading channel separately. Performance of energy detection under channel randomness has been considered in [16, 17]. In order to improve spectrum sensing, several authors have recently proposed collaboration among secondary users [18, 19]. A group of unlicensed deices were exploited for spectrum sensing, which leads to more efficient spectrum utilization from a system-level point of view while decreasing computational complexity of detection algorithms at individual nodes.

However, energy detection has been extensively studied in the past; hidden terminal and exposed node problems are ignored through assuming that the environment is the same for transmitters and receivers. While this assumption does not always hold, especially in high-node density scenarios. In this paper, considering hidden terminal and exposed node problems, we make a theoretical analysis on the performance of energy detection in terms of detection probability. An analytical model is provided for ideal energy detection, transmitter-independent energy detection for CSMA [20]/ALOHA [21]/Schedule-based systems and transmitter/receiver-cooperated energy detection. Theoretical curves are acquired to compare the characteristics for individual energy detection methods under various situations. Moreover, the upper bound for detection probability is achieved and compared under various system traffic and sensing error. The theoretical results we acquired can supply a reference on the method selection.

The remainder of this paper is organized as follows. In Section 2, we summarize motivations for our work. We summary all definitions used through this paper in Section 3. Sections 4 and 5 describe our theoretical analysis on different energy detection methods. Theoretical results are given in Section 6. Section 7 concludes this paper.

Two nodes are said to be hidden from one another (out of signal range) when both attempt to send information to the same receiving node, resulting in a collision of data at the receiver node. On the other hand, overhearing a data transmission from neighboring nodes can inhibit one node from transmitting to other noes. Those are very well-known hidden terminal problem and exposed node problem for contention-based MAC protocols [22]. The hidden terminal problem causes failure communication with collision, while exposed node problem decreases frequency utilization due to unnecessarily blocking of some communications. RTS-CTS method is one of the most popular solutions to the hidden terminal problem, such as in IEEE80.2.11 [23]. In existing systems, hidden terminal problem and exposed node problem also should be considered for energy detection, since the strength of received signal is various at transmitter side and receiver side. To the best of our knowledge, it is the first paper to study the influence of hidden and exposed problems on energy detection capability.

We classify the frequency band/channel state into three categories.

Generally, network topology, traffic type, and communication capability of primary user system determine channel state. In this paper, we exploit , , and to express the chance of channel state might be at certain point of time. They always satisfy . The definitions are

(i) is the probability of a channel being Idle;

(ii) is the probability of a channel being Busy;

(iii) is the probability of a channel being Fake Busy.

During energy detection, the sensed signal can come from primary transmitters and, for some cases, from primary receivers, which are not determined. We use and to stand the probability that the sensed signal coming from primary transmitters and from primary receivers.

The sensing probabilities are defined as:

Studies in [12, 16, 17] showed that the detection probability and false alarm probability were the functions of signal-to-noise ratio . Hence we note those sensing probabilities as , , and .

The probability of correct decision ( ) is the probability that a SU makes a correct decision on utilizing or not utilizing a particular frequency band when sensing a particular frequency band is Idle/Fake Busy or Busy, defined as:

While energy detection has been extensively studied in the past, hidden terminal and exposed node problems are ignored through assuming that the environment is often same for transmitters and receivers. However, this assumption cannot always hold in the real world. In this section, we use the generic model, in which the signal sensed by secondary transmitters (STs) might not be identical for secondary receivers (SRs). Moreover, in real world, there is always error for signal sensing, that is, , , , . In this case, for real system design, we evaluate the performance in terms of detection probability for ideal energy detection method, transmitter-independent energy detection method, and transmitter/receiver-cooperated energy detection method.

When the environments for secondary transmitters and receivers are same. In this case, all possible values for are shown in Table 4. We will obtain for various energy detection methods separately.

While energy detection has been extensively studied in the past, hidden terminal and exposed node problems are ignored through assuming that the environment is the same for transmitters and receivers. In this paper, considering hidden terminal and exposed node problems, we make a theoretical analysis on the performance of commonly used energy detection methods, such as ideal method, transmitter-independent method and transmitter/receiver-cooperated method, in terms of detection probability. Corresponding analytical models are provided. Performance theoretical curves are acquired to compare the characteristics for individual energy detection methods under various scenarios. Moreover the upper bound for detection probability is achieved and is compared under various system traffic intensity and sensing capability. From the theoretical results, we found that it is easy to correctly detection the channel status when primary systems are heavily occupied for ideal energy detection method and tansmitter/receiver-cooperated energy detection method. Otherwise, transmitter-independent method is a better scheme to monitor the primary systems. Commonly, increasing the sensitivity of secondary users can upgrade the detection performance. However, in our analysis, it is not true for transmitter-independent method and transmitter/receiver-cooperated method under certain situations. We have concluded those special cases in this paper. Therefore, the theoretical results can supply a reference on the choosing of energy detection method according to system scenario, such as traffic load, sensing capability, and so forth.