Review Of Compressive Spectrum Sensing Computer Science Essay

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Spectrum is already saturated. But it has been observed by the regulatory agencies that though spectrum is statically allocated to a service, it is not always in use. Cognitive radios have the intelligence, applying which they can transmit data opportunistically through the licensed frequency band when they are not under use by the primary user and thus the efficient use of frequency band can be possible. Spectrum sensing is the technique used by cognitive radio to determine the free frequency bands. This step consists of sampling the spectrum to transmit on bands that are not being used by licensed user. Spectrum sensing with conventional sampling faces two problems as higher data sample rate than transmission rate and shortage of storage space to store huge sampled data. In reality most of the data acquired in sensing process can be discarded in the reconstruction phase without noticeable loss in recovered signal. So the main intention is to measure directly only those data which will be used at the reconstruction phase instead of acquiring all the data. Compressive sensing solves the above mentioned problems of the conventional sampling by sampling the data at sub-Nyquist rate. This paper reviews the application of Compressive Sensing for cognitive radios; particularly in the problem of spectrum sensing.

Keywords: cognitive radio, compressed sensing, spectrum sensing.


The radio frequency (RF) spectrum is a limited natural resource, which is used as the medium of communication in wireless system. The user which is licensed to a particular frequency band is known as primary user (PU) of that band and has the exclusive right to use that band. Nowadays, the increasing number of wireless users and introduction of new wireless applications have tremendously boosted the demands for the RF spectrum. But it has been surveyed and reported by different regulatory bodies that the most of the time the primary user does not use the spectrum efficiently. Considering this fact as an opportunity, cognitive radio allows secondary users (SUs) to opportunistically use the free licensed frequency band for their data transmission without interfering the activity of the authorized user [1,2]. Spectrum sensing is the technique which enables the cognitive radio to find out the free frequency bands at a particular time in a given geographical area [7]. But the spectrum sensing with conventional sampling faces problems like higher sampling rate than the transmission rate making difficult to handle the processing of data as design of high speed analog to digital converter is very much expensive. High sampling rate results in huge number of sampled data leads to the problem of shortage of storage space. Compressive sensing is the new paradigm, solves the issue of high sampling rate by sampling the data at sub-Nyquist rate and reconstructing back the original signal from the fewer sampled data set [11, 12, 13].

This paper is organized as follows. Section 2 describes a very basics overview of cognitive radio and its main tasks. Section 3 explains how important spectrum sensing is for cognitive radio. This section also emphasizes on different techniques of spectrum sensing and a comparison between them. Section 4 put a close look on how compressive sensing solves the issues raised by conventional sampling. Section 5 describes the wideband spectrum sensing for cognitive radio using compressive sensing. This section also describes the efficient reconstruction of the compressively sensed spectrum.


The term cognitive radio was first coined by Joe Mitola III in 1999. Cognitive radio (CR) is an intelligent wireless communication system that is aware of its surrounding environment, learns from the environment, can adapt to this environment and consequently can adjust its operating parameters (like transmit-power, carrier-frequency, and modulation strategy) in real time [1]. The cognitive radio is reconfigurable and built on the software-defined radio (SDR) platform. The primary objectives of the cognitive radio are to provide highly reliable communications whenever and wherever needed and to utilize the radio spectrum efficiently [1]. Awareness, intelligence, learning, adaptivity, reliability and efficiency are the key parameters which make cognitive radio as a well-organized as well as accomplished RF communication system.

The aim of the cognitive radio is to use the spectrum band efficiently. This is because now a day the spectrum is almost saturated as different users have been licensed for different frequency bands. So, spectral efficiency is playing an increasingly important role as future wireless communication systems will accommodate more and more users and high performance services. In cognitive radio technology the secondary users (SUs) can use the discovered gaps of unused licensed spectrum for their own data transmissions [1, 2]. Cognitive radios roam across borders and self-adjust to stay in compliance with local regulations. Along with the above requirement, reliable communication without affecting the activity of primary users (PUs) should be the main concern.

The three main tasks of the cognitive radio include [1, 3]:

(1) Radio-scene analysis,

(2) Channel identification, and

(3) Transmit-power control and dynamic spectrum management.

The task (1) and (2) are performed by the receiver and the task (3) is performed by the transmitter.

Fig. 1. Basic cognitive cycle. [1]

Fig. 1. shows a basic cognitive cycle model which mainly focuses on the three fundamental cognitive tasks. The radio-scene analysis estimates the interference temperature of the radio environment and detects the spectrum holes as well. Channel identification estimates the channel-state information (CSI) and predicts the channel capacity to realize whether the transmitter will be able to transmit data or not. The transmit-power control and dynamic spectrum management collects the feedback information from radio-scene analysis and channel-state analysis and based on the collected data it selects the transmission power levels and frequency holes for transmission.



Spectrum sensing is the technique used by cognitive radio to sense the presence of any primary user in the environment and hence find the unused frequency bands for the secondary user's communication process. In other words cognitive radios keep on monitor to detect the spectrum holes. A spectrum hole is a band of frequencies assigned to a primary user, but, at a particular time and specific geographic location, the band is not being utilized by that user [4].

Importance of Spectrum Sensing

The demand for RF spectrum is increasing day by day as the consumers of wireless products are growing. Quick introduction of new wireless devices as well as applications like "broadband wireless access" are accelerating the rate of demand of radio spectrum.

For so many years government has granted certain licensed frequency bands to each of different operators. As a result most of the useful radio spectrum has already been allocated. So the assignment of vacant bands to either new services or for enhancement of existing ones are getting difficult. To resolve this issue, for the last decade, agencies like FCC (Federal Communications Commission) in USA and other similar agencies in different countries have been studying and analyzing the statistical data for the usage of spectrum band over a certain time period and geographical location. This study has shown that licensed spectrum is rarely utilized continuously by the authorized user across time and space [5]. A statistical measurement for spectrum usage in the frequency bands between 30 MHz and 3 GHz, averaged over six locations; data collected from NSF Spectrum Occupancy Measurements Project Summary [6] has shown that at a particular time the maximum spectrum usage has gone up to 25% or even lower and many licensed frequency bands are not occupied by the primary user at a certain time. At frequencies above 3GHz the actual utilization is even dramatically lower. So, it can be concluded that the inefficient fixed frequency allocation is the main reason for spectrum scarcity. This observation has prompted the regulatory bodies to investigate a different access paradigm where secondary (unlicensed) systems are allowed to opportunistically utilize the unused primary (licensed) bands, commonly referred to as spectrum holes. But in this process care should be taken not to disturb the activities of the primary user. In order to protect the primary systems from the interferences created by the secondary users, spectrum holes across frequency, time and space should be reliably identified. There are different approaches available for identifying unused spectrum bands; like Database registry, Beacon signals and spectrum sensing. Among all these candidates, spectrum sensing is more popular because of its relatively low infrastructure cost and its compatibility with the legacy primary systems [7].

Different Spectrum Sensing Techniques

In this section, some of the most common spectrum sensing techniques in the cognitive radio literature are explained [8].

Energy Detector Based Sensing

Energy detector based sensing is the most common way of spectrum sensing because of its simplicity in implementation and the short sensing time [7, 9]. In this sensing method receivers do not need any knowledge on the primary users' signal. The detection of the free band is accomplished by simply measuring the energy level received on a primary band during an observation interval and then comparing it with a properly set threshold. If it is found that the measured energy is less than the threshold, then the corresponding primary band is considered as the spectrum hole. Challenges associated with this sensing method are selection of the threshold, inability to discriminate between sources of received energy whether from the primary signal or from the noise, detection of spread spectrum signal etc.

Waveform Based Sensing

Waveform based sensing is the method where already known patterns are utilized for the sensing purpose. Sensing can be performed by correlating the received signal with a known copy of itself. This method is also known as coherent sensing and is only applicable to the systems where signal patterns are known.

Cyclostationarity-Based Sensing

In cyclostationary based sensing, cyclic correlation function is used for detecting signals present in a given spectrum instead of power spectral density (PSD) [8, 10]. This method exploits the cyclostationarity features of the received signals. The periodicity in the signal or in its statistics like mean and autocorrelation are the cause behind the cyclostationary features of the signal. This sensing method can differentiate between the noise and the primary signal as the noise is wide sense stationary with no correlation while modulated signals are cyclostationary with spectral correlation.

Matched-Filtering Based Sensing

Matched filtering followed by a threshold test is the optimum method for detection of primary users when the transmitted signal is known [7, 8]. Short sensing time is the main advantage of matched filtering. The must needed demodulation of received signal in this sensing technology requires knowledge regarding the features of primary signal like bandwidth, operating frequency, modulation type etc. As receivers for all signal types are required, the implementation complexity of sensing unit is impractically large. Large power consumption is another concern for matched filtering sensing methodology.

Comparison among various Sensing Techniques

Though several other sensing methods are also available the above mentioned methods are frequently adopted. Selection of a particular sensing method depends on different parameters like complexity of the system, accuracy of the detection needed, cost involved etc. A comparison between the different spectrum sensing techniques has been explained in the following content of this section.

Matched filtering and waveform based sensing are the two techniques which are very accurate in detecting the spectrum holes. Match filtering takes very less sensing time to sense the spectrum. The problem associated with the waveform based sensing is the requirement of the priori information about the primary user's characteristics and the primary users should transmit known patterns. Large power consumption and implementation complexity are two major drawbacks of matched filtering. The implementation complexity level of energy detector is very low. But it takes more sensing time than the matched filtering. The performance of energy detector based sensing is limited as it faces challenges in selecting the threshold level. In the situations like variable noise of unknown variance, this detector is unable to discriminate between sources of received energy whether from the primary signal or from the noise. The cyclostationary based methods perform worse than energy detector based sensing methods when the noise is stationary. However, in the presence of co-channel or adjacent channel interferers, noise becomes non-stationary. Hence, energy detector based schemes fail while cyclostationarity based algorithms are not affected. Based on the facts that energy detector based sensing is very simple to implement, computationally efficient in stationary noise environment and requires no prior information about the signals, it is still most commonly used in spectrum sensing for cognitive radios.


Data acquisition and sampling for transmission and reconstruction of data after reception are important factors in communication systems. According to Shannon's theorem for the exact recovery of a signal from its samples needs the sampling process to be at least two times faster than the signal bandwidth (Nyquist rate). As in most of the applications the Nyquist rate is very high so that huge amount of sampled data generated creates problems like shortage of data storage space. Design of high speed analog to digital converter needed for the processing of high rate sampled data is very expensive [11]. This leads to the need of compression of sampled data.

Fig. 2. Traditional sampling and data reconstruction

Fig. 3. Compressive sampling

Most of the data acquired can be thrown away with almost no perceptual loss in signal reconstruction. The questions arise here are why to waste so much effort in acquiring all the data while most of them are going to be thrown away and can't the data which will be required in reconstruction process be measured directly? The solution is the compressive sampling, popularly known as compressed sensing or CS which goes against the traditional approach of data acquisition. According to CS theory certain signals can be recovered from far fewer samples than traditional methods use [11, 12, 13]. This leads to the fact that CS samples the signal at some sub-Nyquist rate and then at the receiver end the original signal can be reconstructed from these sampled data. Fig. 2. and Fig. 3. are representing the block diagrams of "traditional sampling and data reconstruction" and "compressive sampling" respectively.


The spectrum band is utilized inefficiently by the primary user, so the RF spectrum can be considered as sparse. This section explains the whole procedure of wideband spectrum sampling at sub-Nyquist rate and the reconstruction of spectrum from the sampled data. First the analog spectrum is multiplied by a bank of periodic waveforms. The product is then lowpass filtered and sampled uniformly at a low rate, in the order smaller than Nyquist rate [15]. The problem of recovering the original signal from the low rate samples can be studied within the framework of compressive sampling. Perfect recovery from the proposed samples is achieved under certain necessary and sufficient conditions.

Detection of Spectrum Holes

The main objective of the spectrum sensing is to detect the unused frequency bands or in other words to locate the spectrum holes.

Fig. 4. N frequency bands with piecewise smooth PSD [14]

In Fig. 4. a wideband signal x(t) has been represented that occupies N consecutive spectrum bands, with their frequency boundaries located at f0 < f1 < ... fN. Depending on whether the PSD level is high, medium or low, each frequency segment can be categorized into black, gray or white spectrum spaces respectively [1, 14]. White holes, and sometimes gray spaces, can be considered as spectrum holes and picked by the CR for opportunistic transmission, while the black holes are to be avoided for interference control.

Signal Model

Occupancy of frequency bands by primary users consist of small number of narrowband transmissions spread across a wide territory of spectrum. These signals can be described as the multiband model. The transmissions occur over several continuous small frequency ranges in a wide spectrum but vanishes elsewhere. The multiband signal model and the sampling as well as the reconstruction model have been collected from the research work of Moshe Mishali, Yonina C. Eldar and Joel A. Tropp for the paper "Efficient Sampling of Sparse Wideband Analog Signals" [15]. Fig. 5. Shows the signal model of the multiband signal x(t). Let the Fourier transform of x(t) is . Let considering a multiband signal model M where band of a signal x(t) is limited to F =[−fNYQ/2 , fNYQ/2] and the support of X(f) consists of at most 2N frequency interval, i.e., maximum N number of transmission with maximum bandwidth as B of each transmission. The objective is; the sample rate of the signal should be as low as possible. As the system has no prior knowledge of band locations, so the reconstruction of signal will be a blind detection.

Fig. 5. Three RF transmissions with different carriers fi. A multiband signal as the bottom drawing will be seen by the receiver [15].

For a perfect blind reconstruction the lowest average sampling rate required is 4NB samples/sec [16]. This rate is proportional to the effective bandwidth of x(t) and far less than the Nyquist rate as fNYQ depends only on the maximum frequency in x(t).

The blind detection of spectrum holes comprises of two steps.

Sampling and



Fig. 6. is showing the sampling stage of the multiband signal x(t). The signal x(t) is fed to m sampling channels simultaneously.

The first stage in the sampling chain is a mixer. In this stage the signal will be multiplied by a mixing function pi(t) with period Tp which is a piecewise constant function that alternates between the levels ±1 for each of M equal time intervals. The mixing function pi(t) can be represented as follows:

, (1)

Where αik ∈ {+1,−1}, and pi(t+nTp) = pi(t) for every n∈Z.

After mixing, the signal in each channel is truncated by a low pass filter with cutoff 1/(2Ts) and the filtered signal is sampled at rate 1/Ts. The mixing function aliases the spectrum as shown in Fig. 7. so that a portion of each band appears in base band. Though each sampling channel operates independently, the cutoff and the sampling rate of each channel match.




Fig. 6. (a) Sampling stage for multiband signals

(b) The mixing function pi(t)

(c) Frequency response of h(t) [15]

Fig. 7. Single Sampling chain with the aliased signal

As each sampling chain implements a different mixing function, we will find different aliasing effect at the end of each chain. So a sufficiently large number of mixtures generating different aliased signals will allow to recover a relatively sparse signal, i.e. the original analog multiband spectrum.


This is the second stage of the compressive sensing process. From the sampling stage with m channels we have system of equations with m equations as follows:

y(f) = (SF) (DX(f)), f ∈ F0 (2)

where F0 = [−1/(2T) , 1/(2T)] , T = Tp = Ts ,

y(f) expresses the samples collected from the sampling phase with samples represented by yi(f) , 1 ≤ i ≤ m. S is an mÃ-M matrix whose ikth entry Sik = αik. The MÃ-M matrix F is a certain cyclic columns shift of the discrete Fourier transform matrix of order M. Since D has non-zero diagonal entries, it can be absorbed into X(f) while keeping supp (X(F0)) = supp (DX(F0)).  The support of a function supp (x) is the set of points where the function x is not zero-valued, and the closure of that set. Recovery of the joint support S can be obtained by applying Continuous to finite (CTF) block method [15, 16].

We can replace SF as a sensing matrix A. Once the support 'S' recovery of supp (DX(F0)) will be acquired, then the equation (2) can be reduced to:

y(f) = (AS) (DX(f))S, f ∈ F0 (3)

where the support S = supp (DX(F0)), and the sub matrix AS consists of the columns of A indicated by S.

Now equation (3) can be rewritten as

(DX(f))S = (AS) † y(f) (4)

Where (AS) † =

The original spectrum recovery is a trivial solution of equation (4).


This paper has highlighted the importance of cognitive radio which facilitates the secondary users to opportunistically use the licensed frequency band when the same is not occupied by the primary user. This solves the problem of spectrum scarcity and improves the efficiency of RF spectrum use. This paper also emphasized the need of spectrum sensing technique which enables the secondary users to locate the spectrum holes. Different spectrum sensing techniques have been discussed and the comparison among them has been represented. Spectrum sensing of a wideband analog signal through sampling and the reconstruction of the same has been accomplished using compressive sensing method.