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This paper deals with spectrum sensing in an orthogonal frequency division multiplexing (OFDM) context, allowing an opportunistic user to detect a vacant spectrum resource in a licensed band. The proposed method is based on an iterative algorithm used for the joint estimation of noise variance and frequency selective channel. It can be seen as a second-order detector, since it is performed by means of the minimum mean square error criterion. The main advantage of the proposed algorithm is its capability to perform spectrum sensing, noise variance estimation, and channel estimation in the presence of a signal. Furthermore, the sensing duration is limited to only one OFDM symbol. We theoretically show the convergence of the algorithm, and we derive its analytical detection and false alarm probabilities. Furthermore, we show that the detector is very efficient, even for low SNR values, and is robust against a channel uncertainty.

Wireless communications are facing a constant increase of data-rate-consuming transmissions, due to the multiplications of the applications and services, while the available spectrum resource is naturally limited. Furthermore, most of the frequency bands are already allocated to specific licenses. However, some of these licensed bands are not used at their full capacity, which results in spectrum holes along the time and frequency axes [

Illustration of the principle of the spectrum sensing.

The noncooperative detection concerns a sole SU who tries to detect the presence of the PU alone. Among the wide range of methods [

In this paper, we propose to perform spectrum sensing by means of a minimum mean square error (MMSE-)based iterative algorithm developed in [

In this paper, the normal font

This paper is organized as follows: Section

We consider the problem of the detection of an OFDM pilot preamble over a Rayleigh fading channel with additive white Gaussian noise (AWGN) in a given band. After the

We now briefly recall the steps of the algorithm for the joint and iterative estimation of the channel and the noise variance as given in [

Block diagram of the iterative algorithm in the realistic scenario.

(1) At the beginning, only the LS channel estimation

(2) At the first step

(3) The noise variance is estimated by means of the MMSE criterion [

(4) For

It will be shown afterwards that the characterization of the initialization

(5) While

(6) End of the algorithm. We note

It is proved in [

Unlike the presented model, the next section investigates the behavior of the algorithm when the PU is absent, that is, under hypothesis

The signal

Let us consider that the receiver does not know if the signal is present or absent, so the same formalism as in Section

(1) From

Additionally, a stopping criterion

(2) At iteration

(3) The MMSE noise variance estimation

Indeed, it is proved in the Appendix that if the algorithm keeps on computing with

(4) Then, for

From these first four steps of the algorithm, it is now possible to prove that the algorithm converges to a nonnull solution under

The convergence of the algorithm is now going to be proved, and its limit characterized. To this end, we will first obtain a scalar expression of the sequence

Let us assume that

For a better readability, we note the following mathematical developments:

One can observe that the sequence

The sequence converges if

Since we exclude zero as a solution, the previous expressions can be simplified by

As

If we notice that when

It can be seen that by choosing a sufficiently large initialization value

Figure

Aspect of

In this section, a decision rule for the detector is proposed. To this end, whatever

The detection probability

By taking into account the previous decision rule, it is possible to extend the practical algorithm proposed in the scenario of the joint estimation of the SNR and the channel for free band detections, as it is summed up in Algorithm

Initialization:

Calculate the metric

It can be seen that the structure of Algorithm

the noise variance estimation, if

the channel and SNR estimations, if

An a priori qualitative analysis of the detector can be done. Indeed, from (

In the context of cognitive radio, the SUs have to target a given detection probability, noted

Under the hypothesis

The result in (

According to the Rayleigh distributed WSSUS channel model, whatever

The theoretical probability density function (pdf) expression of the metric under the hypothesis

The mean and the variance of this distribution are equal to

As a conclusion, the probability density functions of the metric

The detection and false alarm probabilities

By using the variable change

Since the incomplete gamma function is not directly invertible in (

The signal parameters used for the simulations are based on those of the digital radio mondiale (DRM/DRM+) standard [

Table of parameters of the channel model.

Channel model | ||||
---|---|---|---|---|

Path 1 | Path 2 | Path 3 | Path 4 | |

Delay | 0 ms | 0.7 ms | 1.5 ms | 2.2 ms |

Gain | 0.7448 | 0.5214 | 0.3724 | 0.1862 |

Figure

It can be seen that the a priori qualitative analysis is verified. Indeed, for a sufficient number of iterations (according to the value

It is shown in this section that the choice of the threshold

Detection and false alarm probabilities versus SNR, for two values

We observe that the curves of

Figure

Means of the number of iterations needed by the algorithm to stop versus SNR (in dB), for three values of threshold

Although Figures

In this part, we study the behavior of the proposed detector when a non-WSS channel is considered. To this end, we artificially correlate the different paths by inserting the gain

Detection probability versus SNR for a non-WSSUS channel.

The performance of a detector is usually evaluated by means of the receiver operating characteristic (ROC) curves, depicting the detection probability

Figure

Receiver operating characteristic (ROC) curves of the proposed method compared to the energy and MME detectors.

Proposed detector compared with the energy detector

Proposed detector compared with the MME detector

In Figure

We observe in Figure

Figure

Comparison of the receiver operating characteristic (ROC) curves obtained by simulation and in theory.

In this paper, an iterative algorithm for spectrum sensing in a cognitive radio context has been presented. Originally proposed in [

If the algorithm keeps on computing at each iteration

Perform the LMMSE channel estimation

Perform the MMSE noise variance estimation

It is assumed that

The sequence

Aspect of

It is trivial that from the expression of

The authors declare that there is no conflict of interests regarding the publication of this paper.