Cooperative spectrum sensing and resource allocation at ICASSP 2011

After spending the weekend in Vienna, I continue today the series of posts devoted to ICASSP 2011. Here I will present some works related to cognitive radio from a couple of sessions. In the session SPCOM-L4 (Cooperative Spectrum Sensing) we could find different collaborative schemes (several of them relying in compressed sensing) for primary user monitoring/detection:

"BASIS PURSUIT FOR SPECTRUM CARTOGRAPHY"; Juan Andrés Bazerque, Gonzalo Mateos, Georgios B. Giannakis, University of Minnesota, US

This paper proposes a sparsity-aware spline-based method for field (RF power in space and frequency) estimation from a set of measurements provided by a set of sensors distributed on the region under investigation. The authors propose the adoption of an overcomplete set of basis functions, together with a sparsity-promoting regularization term, which endows the estimator with the ability to select a few of these bases that “better” explain the data. The algorithm results into a group-Lasso estimator of the spline basis expansion coefficients. Results from empirical measurements are provided.

"BEP WALLS FOR COLLABORATIVE SPECTRUM SENSING"; Sachin Chaudhari, Jarmo Lunden, Visa Koivunen, Aalto University, Finland

This works investigates the performance limitation of collaborative spectrum sensing in cognitive radios with imperfect reporting channels. The authors study the problem of hard decision based cooperative sensing, in which each secondary node sends a one-bit binary decision over a binary channel with errors and the fusion center applies a K-out-of-N fusion rule, trying to find a similar result to the SNR walls under noise uncertainty. If the bit error rate of the reporting channel is above a wall value, the authors show that constraints on the cooperative detection performance cannot be met at the fusion center irrespective of the received signal quality and sensing time. My point here is that if sensing time is allowed to grow without bounds one could also allow better error correction codes, couldn't one?

Update: Sachin Chaudhari commented that indeed their work emphasizes the need of using correction codes in the transmissions to the fusion center. Here his comment:

"Please note that the constraints on the cooperative detection performance cannot be met at the fusion center irrespective of the received signal quality 'or' the sensing time. So even for the case when the sensing time is short and the SNRs on the listening channel are very good, the performance constraints cannot be met. The whole point of the paper was to show that you may need the error correction codes while using the counting rules."

"DECENTRALIZED SUPPORT DETECTION OF MULTIPLE MEASUREMENT VECTORS WITH JOINT SPARSITY"; Qing Ling, University of Science and Technology of China, China; Zhi Tian, Michigan Technological University, US

This paper considers the problem of finding sparse solutions from multiple measurement vectors with joint sparsity. To this end the authors propose a decentralized row-based Lasso (DR-Lasso) algorithm in which a penalty term is introduced to enforce joint sparsity of the solution. In order to exchange information between neighbors the algorithm relies in a consensus based iterative procedure.

"COOPERATIVE SPECTRUM SENSING BASED ON MATRIX RANK MINIMIZATION"; Yue Wang, Beijing University of Posts and Telecommunications, China; Zhi Tian, Michigan Technological University, US; Chunyan Feng, Beijing University of Posts and Telecommunications, China

This paper develops a new cooperative spectrum sensing technique based on matrix rank minimization. A nuclear norm minimization problem is formulated to jointly identify the nonzero support of the monitored wide spectrum (featuring possibly multiple primary signals).

The session SPCOM-L3 (Resource Allocation and Game Theory) featured some works with different approaches to resource allocation and to scheduling of the transmission/sensing instants. In general they study the problem from a network level perspective, for example by assuming slotted transmissions:

"NON-CONVEX UTILITY MAXIMIZATION IN GAUSSIAN MISO BROADCAST AND INTERFERENCE CHANNELS"; Marco Rossi, New Jersey Institute of Technology, US; Antonia Maria Tulino, Bell Laboratories (Alcatel-Lucent), US; Osvaldo Simeone, Alexander M. Haimovich, New Jersey Institute of Technology, US

In this work two algorithms are proposed to sum-rate (and other utilities) maximization for multiantenna broadcast and interference channels (non-convex problem). The first finds the global optimum by performing a suitably designed branch-and-bound method (as you can imagine fairly complex). The second approach is a suboptimal iterative algorithm that converges to a stationary point fulfilling the KKT conditions, however, its final performance depends on the initial parameters and hence does not guarantee global optimality.

"STOCHASTIC ANALYSIS OF TWO-TIER NETWORKS: EFFECT OF SPECTRUM ALLOCATION"; Wang Chi Cheung, Tony Quee Seng Quek, Agency of Science, Technology And Research, Singapore; Marios Kountouris, Supélec, France

This work proposes a two-tier network modeling a macrocell/femtocells scenario. The scheme reserves a certain amount of resources for exclusive use of macrocell, a different set of resources for exclusive use of femtocells, and the remaining are left open for both tiers, hence generating cochannel interference.

"DISTRIBUTED MULTIACCESS IN HIERARCHICAL COGNITIVE RADIO NETWORKS"; Shiyao Chen, Lang Tong, Cornell University, US

This work presents a high level approach to the problem of scheduling the transmission/sensing instants among different secondary users under a global primary-user collision constraint. If secondary users are assumed to sense/transmit in a single channel each time slot the optimum policy under certain conditions is shown to be a round-robin policy in which each secondary user cycles through all the channels in the band.

Spectrum sensing: ICASSP 2011

As I promised at the end of the post about the session on compressed sensing and sparse reconstruction, here my impressions on the papers presented in my session (SPCOM-L2: Spectrum Sensing for Cognitive Radio). This year's ICASSP presentations have been recorded in video and after the talk I was asked to sign a consent form for the recorded material. Then I assume that it (when allowed by the authors) will be made publicly available in the future. Nice!

"DETECTION DIVERSITY OF MULTIANTENNA SPECTRUM SENSORS"; Gonzalo Vazquez-Vilar, Roberto Lopez-Valcarce, University of Vigo, Spain; Ashish Pandharipande, Philips Research, Netherlands

This paper applies to multiantenna spectrum sensing the concept of diversity order first proposed by Daher and Adve in the radar community. This diversity order corresponds to the slope of the average probability of detection vs. SNR curve at the point at which the average probability of detection equals 0.5, and tightly characterizes the minimum operational SNR at which a sensing scheme begins to work "well" and how fast this happens.

"THE NON-BAYESIAN RESTLESS MULTI-ARMED BANDIT: A CASE OF NEAR-LOGARITHMIC REGRET"; Wenhan Dai, Tsinghua University, China; Yi Gai, Bhaskar Krishnamachari, University of Southern California, US; Qing Zhao, University of California, US

Not so much into the topic. The idea is quite similar to the one presented by the authors last year's ICASSP: to gain knowledge of an underlying stochastic process by scheduling the sensing and transmissions. Here the abstract:

"In the classic Bayesian restless multi-armed bandit (RMAB) problem, there are N arms, with rewards on all arms evolving at each time as Markov chains with known parameters. A player seeks to activate K ≥ 1 arms at each time in order to maximize the expected total reward obtained over multiple plays. RMAB is a challenging problem that is known to be PSPACE-hard in general. We consider in this work the even harder non-Bayesian RMAB, in which the parameters of the Markov chain are assumed to be unknown a priori. We develop an original approach to this problem that is applicable when the corresponding Bayesian problem has the structure that, depending on the known parameter values, the optimal solution is one of a prescribed finite set of policies. In such settings, we propose to learn the optimal policy for the non-Bayesian RMAB by employing a suitable meta-policy which treats each policy from this finite set as an arm in a different non-Bayesian multi-armed bandit problem for which a single-arm selection policy is optimal. We demonstrate this approach by developing a novel sensing policy for opportunistic spectrum access over unknown dynamic channels. We prove that our policy achieves near-logarithmic regret (the difference in expected reward compared to a model-aware genie), which leads to the same average reward that can be achieved by the optimal policy under a known model. This is the first such result in the literature for a non-Bayesian RMAB."

"ON AUTOCORRELATION-BASED MULTIANTENNA SPECTRUM SENSING FOR COGNITIVE RADIOS IN UNKNOWN NOISE"; Jitendra Tugnait, Auburn University, US

This work presents a spectrum sensing scheme for spatially rank-1 primary signals in spatially uncorrelated noise with unequal noise variances across antennas. Unlike in the paper we presented at CIP'10 the method is not based on the GLRT. The proposed method uses the properties of the autocorrelation function of the received signal. Additionally, an asymptotic analysis of the statistic distribution under both hypothesis is provided. At the end of the talk J. Tugnait presented an sketch of the extension of the algorithm to consider spatial correlation between the noise process observed at each of the antennas, similarly to the work by Stoica and Cedervall in ”Detection tests for array processing in unknown correlated noise fields,” 1997, IEEE Trans. Signal Process.


"MULTIANTENNA DETECTION UNDER NOISE UNCERTAINTY AND PRIMARY USER'S SPATIAL STRUCTURE"; David Ramirez, University of Cantabria, Spain; Gonzalo Vazquez-Vilar, Roberto Lopez-Valcarce, University of Vigo, Spain; Javier Vía, Ignacio Santamaría, University of Cantabria, Spain

The model considered in this work is the same as the one of the previous paper except for the fact that now primary user's signal may present a spatial rank larger than 1 and which is assumed known at the receiver. Hence, assuming a generic diagonal noise covariance matrix, the authors propose a GLRT based detection scheme. Although asymptotic in the low SNR regime, the proposed detector offers good performance even for moderate SNR values. This work is part of a journal paper accepted for publication in IEEE Trans. Signal Process.

"TONE DETECTION OF NON-UNIFORMLY UNDERSAMPLED SIGNALS WITH FREQUENCY EXCISION"; André Bourdoux, Sofie Pollin, Antoine Dejonghe, Liesbet Van der Perre, IMEC, Belgium

In this work the authors perform narrowband signal detection from a set of compressed measurements using a modified basis pursuit algorithm. At first I couldn't get the point of this algorithm. However now I think I understand it: the basis pursuit is applied in the spectral domain so that there exists an important leakeage of the signal power that increases the noise floor. Once the largest frequency component is identified, the modied algorithm estimates its corresponding phase before subtracting it in the original domain. Hence in the next iteration the noise floor has been reduced noticeably. A pity I haven't though about the "small detail" of the phases last year.

"A UNIFIED FRAMEWORK FOR GLRT-BASED SPECTRUM SENSING OF SIGNALS WITH COVARIANCE MATRICES WITH KNOWN EIGENVALUE MULTIPLICITIES"; Erik Axell, Erik G. Larsson, Linköping University, Sweden

The last paper of the session also focuses on multiantenna spectrum sensing. The authors compute the GLRT for a general model that comprises several practical scenarios as a special case, namely spectrum sensing of signals which have covariance matrices with known eigenvalue multiplicities (all other parameters are assumed unknown and need to be estimated). Nice presentation.

Recent papers on wideband spectrum sensing for cognitive radio sytems

In this post I include a list of papers recently published on the topic of wideband detection in cognitive radio. This post complements and updates the survey I did some time ago on wideband spectrum sensing.

A Class of Spectrum-Sensing Schemes for Cognitive Radio Under Impulsive Noise Circumstances: Structure and Performance in Nonfading and Fading Environments, by HG Kang, I Song, S Yoon, YH Kim. This paper exploits a nonlinear diversity-combining strategy together with the generalized likelihood ratio test detectors on each of the antenna branches.

A Parallel Cooperative Spectrum Sensing in Cognitive Radio Networks. In this work S. Xie, Y. Liu, Y. Zhang and R. Yu propose a sensing scheme in which several secondary users are selected to perform sensing in different channels. They present an analytical model to investigate the tradeoff between the transmitted data and the sensing overhead, which results into a throughput maximization problem.

Multiantenna spectrum sensing: The case of wideband rank-one primary signals. In this work D Ramırez, J Via and I Santamaria derive multiantenna detector based on the asymptotic likelihood under the asumptions of a wideband rank-one signal under spatially uncorrelated noise with equal or different power spectral densities.

Distributed Compressive Spectrum Sensing in Cooperative Multihop Cognitive Networks. In this paper F Zeng, C Li, Z Tian present a cooperative approach to wideband spectrum sensing. Their scheme utilizes a compressive sampling mechanism which exploits the signal sparsity induced by network spectrum under-utilization by enforcing consensus among local spectral estimates.

A Wideband Spectrum Sensing Method for Cognitive Radio using Sub-Nyquist Sampling. In this preprint M Rashidi, K Haghighi, A Owrang and M Viberg present a wideband spectrum sensing scheme that utilizes a sub-Nyquist sampling in order to reconstruct the correlation matrix. This method does not require the knowledge of signal properties mitigating the uncertainty problem. Also by Moslem Rashidi is this long preprint (maybe a book chapter?): Non-uniform sampling and reconstruction of multi-band signals and its application in wideband spectrum sensing of cognitive radio. It may be an useful introduction to the topic.


On the use of Compressive Sampling for Wide-band Spectrum Sensing by D. Sundman, S. Chatterjee and M. Skoglund. For wideband signals sampling at the Nyquist rate is a major challenge. In this work they propose a wideband detection scheme of multiple simultaneous signals using sub-Nyquist sampling rates. This work is extended to incorporate memory from previous slots in slow varying scenarios.


Evidence Theory Based Cooperative Spectrum Sensing with Efficient Quantization Method in Cognitive Radio. In this work N. Nguyen-Thanh and I. Koo study an enhanced scheme for cooperative spectrum sensing based on efficient quantization and the Dempster-Shafer Theory of Evidence. They propose an effective quantizer for the sensing data which takes advantage of special properties of the statistic distribution for different signal-to-noise ratios of the primary signal, hence reducing the required bandwidth for the reporting channel occupancy.

Adaptive Spectrum Sensing and learning in Cognitive Radio Networks by A. Taherpour, S. Gazor and A. Taherpour. This paper proposes an iterative primary user activity detection algorithm for a wideband frequency range using a Markov Model (MM) with two states to model the activity of the primary users.

If you know any additional paper related to wideband sensing which has been recently published you can leave a comment with the link.

Spectral Sensing at CIP 2010

The International Workshop in Cognitive Information Processing (CIP) is a small conference focused on Cognitive Radio. This year's conference was on Elba Island, Italy. While it took place a while ago (in June) I did not have the opportunity to write over it yet.

Surveys and comparisons of spectrum sensing strategies

The works included in this review will present a slightly different classification to the previous ones (ICASSP, ICC). I will start discussing four works that either survey or compare different spectrum sensing techniques:

In "Overview of Spectrum Sensing for Cognitive Radio", Erik Axell, Geert Leus and Erik G. Larsson present a survey of state-of-the-art algorithms for spectrum sensing. The algorithms discussed range from energy detection to feature detectors exploiting some known structure of the transmitted signal (cyclostationarity properties, known eigenvalue structure of the signal's covariance...), including cooperative detection schemes.

A more involved review on cooperative detection schemes is presented by Luca Bixio, Marina Ottonello, Mirco Raffetto, Carlo S Regazzoni and Claudio Armani in the paper "A Comparison among Cooperative Spectrum Sensing Approaches for Cognitive Radios". This paper compares the three main fusion rules in cooperative spectrum sensing, i.e. OR, AND and optimal, in terms of required processing capabilities at the fusion center and at the secondary terminals, and required control channel capacity.

In "Multiantenna spectrum sensing for Cognitive Radio: overcoming noise uncertainty" Roberto López Valcarce, Gonzalo Vazquez-Vilar and Josep Sala propose a novel multiantenna spectrum sensing paradigm for detection of rank-1 primary signals with uncalibrated multiantenna detectors. However this paper also includes in the discussion most of the previously proposed multiantenna detectors derived under several assumptions for both calibrated and uncalibrated receivers.

In "Performance Comparison for Low Complexity Blind Sensing Techniques in Cognitive Radio Systems" Bassem Zayen, Wael Guibène and Aawatif Hayar classify and compare different low complexity sensing strategies. Specifically, two blind sensing algorithms: the distribution analysis detector and the algebraic detector, which are compared with the energy detector as reference algorithm.

Mixing topics

Estimating the rank of the covariance matrix of a given random process is a recurrent topic in the literature. However it received limited attention in the context of Cognitive Radio systems. In "Estimating the Number of Signals Observed by Multiple Sensors" Marco Chiani and Moe Win show how the exact (non asymptotic) distribution of the eigenvalues of the empirical covariance matrix can be used to find the ML estimate of the actual eigenvalues. However, since this procedure presents a high complexity, they finally propose a rank estimator based on the usual eigenvalue estimate.

Erik Axell and Erik G. Larsson (authors of the overview previously commented) also present "Optimal and Near-Optimal Spectrum Sensing of OFDM Signals in AWGN Channels". In this work they derive the OFDM signal GLR detector for unknown noise and signal powers, which exploits the non-stationary correlation structure of the OFDM signal. Additionally they discuss the optimality of Energy Detection when the noise level is known.

In every conference focused on Cognitive Radio there are some papers on Compressed sensing. In "Compressive sampling based MVDR spectrum sensing" Ying Wang, Ashish Pandharipande and Geert Leus use the minimum variance distortionless response (MVDR) estimator to perform detection from a set of compressed measurements. As opposed to other works they derive the probability distribution of the CS MVDR spectrum estimate, which can be used to determine the detection thresholds.

Finally, Miguel López-Benítez and Ferran Casadevall explore in "On the Spectrum Occupancy Perception of Cognitive Radio Terminals in Realistic Scenarios" the perceived spectrum occupancy in different practical scenarios via empirical measurements. Nice to see that things work in practice.

Cooperative Spectrum Sensing

To finish with, just a list of the works presented in the session on cooperative spectrum sensing for cognitive radio networks:

• Sensor Fusion by Two-Layer Conflict Solving. Volker Lohweg, Uwe Mönks. Approach to data fusion which provides a stable conflict scenario handling, extendable to fuzzy classification.
• On Multi-Step Sensor Scheduling via Convex Optimization. Marco Huber. Two efficient multi-step sensor scheduling approaches are proposed in this paper for optimization over long time horizons.
• Bayesian Joint Recovery of Correlated Signals in Distributed Compressed Sensing. Pablo Viñuelas-Peris and Antonio Artés-Rodríguez. Distributed Compressed Sensing (DCS) of sparsely correlated signals.
• A Robust Approach for Optimization of The Measurement Matrix in Compressed Sensing Vahid Abolghasemi, Delaram Jarchi and Saeid Sanei. Optimized matrices can improve the quality of reconstruction and satisfy the conditions for efficient sampling.
• A novel adaptive algorithm for diffusion networks using projections onto hyperslabs. Symeon Chouvardas, Konstantinos Slavakis and Sergios Theodoridis. A new diffusion based algorithm to implement cooperation among neighboring nodes and the corresponding analysis.
• Node Localization and Tracking Using Distance and Acceleration Measurements. Benjamin R. Hamilton, Xiaoli Ma, Robert John Baxley and Brett Walkenhorst. Algorithm to combine acceleration measurements with RSS readings to achieve accurate localization of a distributed sensor network.

While the CIP is just a small workshop compared to the main conferences on signal processing, we have seen that the CIP 2010 proceedings include very trendy papers.

Cognitive Radio in arXiv.org

Sometimes I wonder how research could be done before the Internet era. I can imagine how long it would take to get something published: after finished, the article had to be submitted by post to the associated editor, then to the reviewers, comments and responses back and forth, back and forth and so on. When the article is finally accepted it would take a couple of months before the research community had access to the printed journal.

While the publishing time got drastically reduced with the invention of the email and electronic documents, it can still be considered slow compared to the current pace of the research. Since this may hinder the interaction between different groups working in the same topic, some researchers choose to submit an early (non peer-reviewed) electronic version of their work to e-print repositories, such as arXiv.org.

In this repository there exists no section dedicated exclusively to signal processing articles. Nevertheless, many of them are archived under the Information Theory (cs.IT) tag. If we search arXiv.org for "cognitive radio" we can find some related papers.

Presented at CrownCom'10 last June, the paper "Binary is Good: A Binary Inference Framework for Primary User Separation in Cognitive Radio Networks" by Huy Nguyen, Rong Zheng and Zhu Han poses the problem of distinguishing and characterizing primary users when we have a large number of collaborating secondary users. The observations by secondary users are modeled as boolean OR mixtures of underlying binary vectors. I had not seen before this approach, kind of "binary processing".

In the paper "Spectrum Sensing in Cooperative Cognitive Radio Networks with Partial CSI" Chong Han, Ido Nevat, and Jinhong Yuan develop an algorithm for cooperative spectrum sensing in a relay based cognitive radio network. To this end they use a bayesian expectation maximisation to approximate the solution of the non-convex problem resulting from a simplification of the likelihood. Beats the energy detector. From almost the same authors is the paper "Blind Spectrum Sensing in Cognitive Radio over Fading Channels and Frequency Offsets", which studies the effect of frequency offsets due to oscillator mismatch and Doppler effect. A novel approach to approximate the Likelihood Ratio Test (LRT) using a single point estimate using a low complexity Adaptive Notch Filter (ANF).

Other papers present the key word compressive in their title, such as "Compressive Wideband Spectrum Sensing for Fixed Frequency Spectrum Allocation" and "Robust Compressive Wideband Spectrum Sensing with Sampling Distortion" by Yipeng Liu and Qun Wan. These papers attempt to use compressive sensing techniques to wideband spectrum reconstruction.

However, I want to finish this post with two of Yonina Eldar's papers about the modulated converter entitled "Xampling", which made me discover arXiv.

P.S. Congratulations Spain!

2010 Qualcomm Cognitive Radio Competition

A group of students of the ECE Illinois won the 2010 Qualcomm Cognitive Radio Contest. While the 3rd Smart Radio Challenge consisted in developing an integral framework for detection and tracking of different radios on an emergency scenario, the 2010 Qualcomm Cognitive Radio Competition required students to develop and implement algorithms that detect wireless microphone signals within a spectrum band.

While detecting digital television signals using the ATSC (American standard for digital television broadcasting) is not a big deal (given their embedded pilot tones), detecting 200 KHz wide wireless microphone signals with the detection performance required by the FCC proposal becomes a challenge. Qualcomm provided the different teams with training data, consisting on both signal sets with a wideband of 6 MHz and information on the frequencies where microphone signals were located. Contestants had to use this data to find a fitting model for the microphone signals and develop algorithms to detect them. The algorithm was judged based on its performance, novelty and implementation complexity.

The approaches followed by the 14 participating teams were fairly different. For example, the ECE Virginia Tech team:

"The students developed a fairly robust solution. They determined a baseline noise correlation matrix from a data set with no wireless microphone signals. To see if a signal is present in a new environment, they compare the new correlation matrix with the baseline matrix using singular value decomposition. If their algorithm determines there is a signal, it calculates the center frequency from the measured auto correlation of the signal."

The winning team (ECE Illinois), advised by V. V. Veeravalli, commented that the key problem was learning to distinguish wireless microphone signals from narrowband interference caused by other electrical devices. They addressed this problem by characterizing the unique features of this narrowband interference.

Congratulations to the winners!

Edit: In the CRT blog appears a link (that I missed) to a presentation by Stephen J. Shellhammer about this contest. Since it includes some technical details I decided to include it here.

New sensing schemes (ICC 2010)

Yesterday Spain could not have started worse the World Cup Soccer championship in South Africa. At least I had a chance to look at the ICC proceedings (from South Africa too), with better results. In a previous post I had made a list of the papers related to spectral sensing. I will leave out for now the papers related to cooperative sensing and comment only on the non-cooperative sensing schemes:

The paper Wavelet-Thresholded Multitaper Spectrum Sensing for Cognitive Radios in Unknown Noise by Jitendra Tugnait deals with spectrum sensing techniques belonging to the class of wavelet-thresholded multitaper spectrum estimators using sine tapers and relates it to the classical Welch windowed spectral estimator. The resulting detector does not need knowledge of the background noise level.

In Spectrum Sensing of OFDM Waveforms Using Embedded Pilot Subcarriers, Arash Zahedi-Ghasabeh et al. propose a new detection method for OFDM signals exploiting the available embedded pilot tones that translates into spectral correlation between the frequencies associated to the different pilots. Just looking at the signal model I realized that a certain synchronization is assumed at the cognitive receiver.

I could not find in the proceedings the papers related to "Stochastic Resonance" based spectrum sensing I had seen in the ICC program. Where did they go?

The paper Spectrum Sensing based on the Detection of Fourth-Order Cyclic Features by Julien Renard et al. proposes a fourth-order detector that performs similarly to the more complex second order detectors at SNR around 0 dB. The proposed detector is derived using the theory of higher-order cyclostationarity (HOCS). The performance is shown in the simulations section by means of a 4-QAM signal.

In Trace Based Semi-blind and Blind Spectrum Sensing Schemes for Cognitive Radio by Xi Yang et al. propose an ad-hoc detector based on the fact that the statistical covariance matrices of received signal samples and noise samples are different with high probability. The resulting detector is something like the trace of the prewhitened empirical covariance matrix.

The abstract of Cognitive Radio Wideband Spectrum Sensing Using Multitap Windowing and Power Detection with Threshold Adaptation Tsung-Han Yu et al. reads:

A common technique for cognitive radio wideband spectrum sensing is energy/power detection of primary users (PU) in frequency domain. Specifically, power spectrum estimation methods are combined with power detection statistics to test the PU presence. However, when detecting in a particular band of interest these techniques suffer from energy leakage and adjacent channel interference. In this paper, we derive a common matrix framework for the analytical performance of power detectors when FFT, windowed FFT, or multitap windowed FFT are used. Our matrix model is verified by simulations of modulated PU signals. We further propose a low-complexity compensation method to adapt the thresholds in the presence of large power difference between channels. By using both the multitap windowing and the constant false-alarm-rate method in the presence of strong signals, we demonstrate a 2-times increase in the detection rate performance as compared to existing methods. The proposed algorithm achieves similar P_FA and P_D as FFT at lower sample complexity, leading to reduced sensing times.

The paper Cyclostationarity Approach for the Recognition of Cyclically Prefixed Single Carrier Signals in Cognitive Radio by Qiyun Zhang et al. does not address the detection of primary users, but the recognition of which modulation they are employed. To this end it uses a cyclostationarity approach that does not require the recovery of carrier, waveform, and symbol timing information.

In Spectrum Sensing for DTMB System Based on PN Cross-Correlation Aolin Xu et al. disscuss spectrum sensing methods based on PN cross-correlation (PNCC) are proposed for the digital terrestrial television broadcasting standard in China (DTMB). This standard features a PN sequence both as guard interval between data blocks which gives cyclic property to DTMB signals.

Finally, the abstract of Spectrum Sensing Technique for Cognitive Radio Systems with Selection Diversity by Chang Kyung Sung et al. reads:

In this paper, we consider complementary sensing nodes to increase the spectrum sensing efficiency of cognitive radio (CR) systems. As the CR system has no prior knowledge about the operation of the licensed network, it is difficult to employ efficient diversity techniques such as the selection diversity. In this paper, by jointly designed with a medium access layer protocol, we propose a sensor node selection technique on the channel where the primary user is active. Collaborated with the mode of operation defined for CR nodes, the proposed scheme selects the dedicated sensing node for the channel with the best sensing performance. Numerical results show that the performance of the proposed scheme is almost the same as the cooperative spectrum sensing while our proposed scheme requires only one sensing node for the spectrum sensing.

Spectrum Sensing at the ICC 2010

The International Communications Conference (ICC) was recently hold in Cape Town, South Africa... just before the World Cup Soccer championship kicks off. In the ICC's final program we can find quite a lot of papers related to spectrum sensing. While I do not have access to the proceedings of the conference yet I wrote down a list of the spectrum sensing related papers organized in the sections sensing schemes, coopearitve spectrum sensing, sensing policy, and other papers related to spectrum sensing. Let's go.

Edit: I had access to a copy of the proceedings and I revised some of these papers. If you are interested take a look at the posts related to the ICC 2010. Proceedings available online: IEEE Xplore.

Spectrum sensing schemes

Wavelet-Thresholded Multitaper Spectrum Sensing for Cognitive Radios in Unknown Noise
Jitendra Tugnait (Auburn University, USA)

Spectrum Sensing of OFDM Waveforms Using Embedded Pilot Subcarriers
Arash Zahedi-Ghasabeh (University of California, Los Angeles, USA), Alireza Tarighat (Wilinx Corp., USA) and Babak Daneshrad (University of California, Los Angeles, USA)

A Cyclostationary-Based Spectrum Sensing Method Using Stochastic Resonance in Cognitive Radio
Yingpei Lin, Chen He, Lingge Jiang, Di He (Shanghai Jiao Tong University, China)
Spectrum Sensing Approach Based on Optimal Stochastic Resonance Technique under Color Noise Background in Cognitive Radio Networks
Di He, Chen He, Lingge Jiang, Yingpei Lin (Shanghai Jiao Tong University, China)
This was the first time I see the term Stochastic Resonance. Googling it I found that Stochastic Resonance refers to a peak that appears in the power spectrum of a dynamical system subject to both periodic forcing and random perturbation. This peak dissapears when either the forcing or the perturbation is absent.

Spectrum Sensing based on the Detection of Fourth-Order Cyclic Features
Julien Renard, Jonathan Verlant-Chenet, Jean-Michel Dricot, Philipe De Doncker and François Horlin (Université Libre de Bruxelles, Belgium)

Trace Based Semi-blind and Blind Spectrum Sensing Schemes for Cognitive Radio
Xi Yang (Southeast University, China), Kejun Lei (Jishou University, China) and Shengliang Peng, Xiuying Cao (Southeast University, China)

Cognitive Radio Wideband Spectrum Sensing Using Multitap Windowing and Power Detection with Threshold Adaptation
Tsung-Han Yu (University of California, Los Angeles, USA), Santiago Rodriguez-Parera (University of California, Los Angeles, Belgium) and Dejan Markovic, Danijela Cabric (University of California, Los Angeles, USA)
This paper is related to the one I cited in the last post.
A Low-Complexity Wideband Spectrum-Sensing Processor with Adaptive Detection Threshold and Sensing Time by Tsung-Han Yu, Oussama Sekkat, Santiago Rodriguez-Parera, Dejan Marković, and Danijela Čabrić.

Cyclostationarity Approach for the Recognition of Cyclically Prefixed Single Carrier Signals in Cognitive Radio
Qiyun Zhang, Octavia A. Dobre (Memorial University of Newfoundland, Canada), Sreeraman Rajan, Robert J. Inkol (DRDC-Ottawa, Canada), Erchin Serpedin (Texas A&M University, USA)

Spectrum Sensing for DTMB System Based on PN Cross-Correlation
Aolin Xu, Qicun Shi, Zhixing Yang Kewu Peng (Tsinghua University, China), Jian Song (Research Institute of Information Technology, China)

Spectrum Sensing Technique for Cognitive Radio Systems with Selection Diversity
Chang Kyung Sung, Iain B. Collings (CSIRO, Australia)

Cooperative spectrum sensing

Cyclic Prefix Based Cooperative Sequential Spectrum Sensing Algorithms for OFDM
Arunkumar Jayaprakasam, Vinod Sharma, Chandra R. Murthy and Prashant Narayanan (Indian Institute of Science, India)

Cooperative Spectrum Sensing for Multiband under Noise Uncertainty in Cognitive Radio Networks
Zhaoxia Song, Xuan Sun, Zhichao Qin, Zheng Zhou (Beijing University of Posts and Telecommunications, China)

A Robust and Efficient Cooperative Spectrum Sensing Scheme in Cognitive Radio Networks
Feng Gao, Wei Yuan, Wei Liu, Wenqing Cheng, Shu Wang (Huazhong University of Science and Technology, China)

Doubly Sequential Energy Detection for Distributed Dynamic Spectrum Access
Nikhil Kundargi, Ahmed Tewfik (University of Minnesota, USA)

We study the distributed sequential energy detection problem in the context of spectrum sensing for cognitive radio networks. We formulate a novel Doubly Sequential Energy Detector (DSED) and provide a comprehensive study of its performance. Specifically, we present the first method that sequentially combines the decisions of the Cognitive Radio nodes wherein each node is running an independent Sequential Energy Detector (SED). Through extensive simulations it is demonstrated that (i) our novel sequential version of the energy detector delivers a significant throughput improvement of 2 to 6 times over the fixed sample size test while maintaining equivalent operating characteristics as measured by the Probabilities of Detection (P_D) and False Alarm (P_FA), and (ii) the Doubly Sequential Procedure at the Base Station further boosts the SED performance while improving the robustness for shadowed Cognitive Radio nodes. For example, for a P_D > 0.95, our simulations demonstrate that the DSED has a P_FA < 0.20 while utilizing upto 8 times fewer samples than the equivalent energy detector upto a Signal to Noise Ratio of -10 dB, below which its performance gracefully degrades.

Cooperative Spectrum Sensing with Multi-channel Coordination in Cognitive Radio Networks
Chengqi Song, Qian Zhang (Hong Kong University of Science and Technology, Hong Kong)

Cooperative Cyclostationary Spectrum Sensing in Cognitive Radios at Low SNR Regimes
Mahsa Derakhshani (McGill University, Canada), Masoumeh Nasiri-Kenari (Sharif University of Technology, Iran) and Tho Le-Ngoc (McGill University, Canada)

Distributed Compressive Spectrum Sensing in Cooperative Multi-hop Cognitive Networks
Zeng Fanzi (School of Computer and Communication Hunan University, China) and Zhi Tian, Chen Li (Michigan Technological University, USA)

Centralized Cooperative Spectrum Sensing for Ad-hoc Disaster Relief Network Clusters
Nuno Pratas (Center for TeleInFrastructure / Aalborg University, Denmark), Nicola Marchetti (Aalborg University, Denmark), Neeli Rashmi Prasad (Center for TeleInFrastructure, Denmark), António J. Rodrigues (IT / Instituto Superior Técnico, Portugal) and Ramjee Prasad (Center for TeleInFrastruktur / Aalborg University, Denmark)

Time-Divisional Cooperative Periodic Spectrum Sensing for Cognitive Radio Networks
Sithamparanathan Kandeepan (Create-Net International Research Centre, Italy) and Andrea Giorgetti, Marco Chiani (University of Bologna, Italy)

No-Regret Learning in Collaborative Spectrum Sensing with Malicious Nodes
Quanyan Zhu (University of Illinois, Urbana-Champaign, USA), Zhu Han (University of Houston, USA) and Tamer Basar (University of Illinois, Urbana-Champaign, USA)

Spectrum Sensing policy

An Optimal Algorithm for Wideband Spectrum Sensing in Cognitive Radio Systems.
Pedram Paysarvi Hoseini, Norman C. Beaulieu (University of Alberta, Canada)

An optimal wideband spectrum sensing algorithm which jointly detects the primary activities over multiple narrowband channels is presented. The algorithm enhances the overall secondary user performance while protecting the primary network at a desired level. The problem is formulated as an optimization problem to maximize the available secondary throughput capacity given a bound on the imposed aggregate interference. It is demonstrated that the problem can be solved as a convex optimization if certain practical constraints are applied. Simulation results attest that the proposed algorithm achieves a superior performance compared to contemporary algorithms.

Opportunistic Wideband Spectrum Sensing for Cognitive Radios with Genetic Optimization.
Michele Sanna, Maurizio Murroni (University of Cagliari, Italy)

Energy-Efficient Spectrum Sensing for Cognitive Radio Networks
Hang Su, Xi Zhang (Texas A&M University, USA)

This paper focuses on the spectrum sensing issues in the unslotted cognitive radio networks with wireless fading channels. To overcome the energy-inefficiency problem of the existing continuous/fixed-schedule spectrum sensing schemes in the cognitive radio networks, we propose an efficient spectrum sensing scheme for secondary users (SUs). The design goal of our proposed scheme is to save the sensing energy consumption while guaranteeing the priority of the primary users (PUs) and the spectrum opportunity for SUs in terms of available spectrum usage time. In particular, our proposed energy-efficient spectrum sensing scheme adaptively adjusts the spectrum sensing periods and determines between the presence and vacancy of the PU by taking advantage of PU’s activity patterns. We also develop a novel two-threshold based sequential sensing policy to reduce the false alarm probability while limiting the missed detection probability. We conduct simulations to validate and evaluate our proposed scheme.

Queue-Aware Spectrum Sensing for Interference-Constrained Transmissions in Cognitive Radio Networks
Qinghe Du, Xi Zhang (Texas A&M University, USA)

On Spectrum Probing in Cognitive Radio Networks: Does Randomization Matter?
Chao Chen, Zesheng Chen, Todor Cooklev (Indiana University / Purdue University, Fort Wayne, USA) and Carlos A. Pomalaza-Ráez (University of Oulu, Finland)

Overcoming the Sensing-Throughput Tradeoff in Cognitive Radio Networks
Stergios Stotas, Nallanathan Arumugam (King's College London, UK)

Agile Spectrum Evacuation in Cognitive Radio Networks
Mohammad Iqbal Bin Shahid, Joarder Kamruzzaman (Monash University, Australia)

Related to spectrum sensing

Interference-Aware Power Allocation in Cognitive Radio Networks with Imperfect Spectrum Sensing
Sami M. Almalfouh, Gordon Stuber (Georgia Institute of Technology, USA)

Fair and Efficient Channel Allocation and Spectrum Sensing for Cognitive OFDMA Networks
Chunhua Sun (Hong Kong University of Science and Technology, China),Wei Chen (Tsinghua University, China) and Khaled Ben Letaief (Hong Kong University of Science & Technology, Hong Kong)

Sampling Clock Frequency Offset Compensation for Feature Detection in Spectrum Sensing
Arash Zahedi-Ghasabeh (University of California, Los Angeles, USA), Alireza Tarighat (Wilinx Corp., USA) and Babak Daneshrad (University of California, Los Angeles, USA)

About wideband sensing hardware and the winners of the 3rd Smart Radio Challenge

Pretty busy these days: just a couple of hints. Related to the last post about wideband spectrum sensing I found the following paper that presents a wideband spectrum-sensing processor with reduced complexity achieved by taking advantage of the multitap windowing: A Low-Complexity Wideband Spectrum-Sensing Processor with Adaptive Detection Threshold and Sensing Time by Tsung-Han Yu, Oussama Sekkat, Santiago Rodriguez-Parera, Dejan Marković, and Danijela Čabrić. The interesting part is that they have built a prototype of the system and thus multiple practical issues are presented and studied in this paper.

I also would like to comment on the cognitive radio architecture winner of the Smart Radio Challenge. From the press release:

The system consists of portable base stations – each slightly larger than a laptop computer – and mobile communication units. A central command station is able to monitor the positions of all the rescuers in real time – including indoor locations where GPS signals don’t work – and issue instructions for their proper coordination in the rescue operation, even if there’s no existing mobile phone service."

The winner team, iRADIO team from the University of Calgary, consisted of 5 graduate students:

• K Rawat, Team Leader,
• R. Darraji,
• F. Esparza (visiting student from University of Navarra, Spain),
• M. Rawat, and
• A S. Bassam

Top picture: Astrocytes in culture. Blue color from from the astrocytes DNA and red color from the body. Credit: The Beautiful Mind, a spectacular online photo exhibition featuring images of the brain taken by neuroscientists.

Quick survey on wideband spectrum sensing for CR

As I commented in the post about recent surveys on spectrum sensing I miss a review of the different approaches to multichannel spectrum sensing for cognitive radio. The problem is that when the whole bandwidth to monitor is large, sequential individual sensing of many primary channels may not be feasible due to speed constraints. It is here where wideband spectrum sensing comes into play: the bandwidth of interest can be downconverted, digitized and processed directly by the spectral monitor. I will try here to sumarize some recent publications on this topic.

Wideband spectrum sensing can be described as a complex topic not only because of its technical difficulty but also due to the large number of problems that appear at each of the steps of the detection/estimation procedure. In fact research efforts in multichannel monitoring range from the low level physical sensing to higher level resource allocation problems. That is the reason I prefer to classify the works in this area in terms of the level of the problem they address instead of using the classical division on energy, cyclostationarity or matched filter detection.

Network level: cooperation among nodes.

In "Distributed Spectrum Sensing for Cognitive Radio Networks by Exploiting Sparsity" J.A. Bazerque and G.B. Giannakis propose an architecture in which the estimation algorithm, based on the sparsity of the primary signals in both fequency and space, is distributed among the nodes and converges to the spectrum reconstruction given by a centralized compressive sampling implementation.

Similarly A. Taherpour, S. Gazor, and M. Nasiri-Kenari propose in "Wideband spectrum sensing in unknown white Gaussian noise” a distributed network of secondary users that collaborate in order to detect multiple primary users under the assumption that the level of each frequency–domain subband is provided by a filterbank and the noise level is unknown to the monitor.

Node level: sensing resources scheduling.

Some of the works presented this year at the ICASSP fit under the topic of sensing resources scheduling, such as "Two-stage Spectrum Sensing for Cognitive Radios", "Two-stage Spectrum Detection in Cognitive Radio Networks" of "Adaptive Spectrum Sensing for agile Cognitive Radios" already commented in the post about the sensing session at the ICASSP.

Also in this direction is the paper "Sequential and Cooperative Sensing for Multichannel Cognitive Radios" by S.J. Kim, and G.B. Giannakis, that formulates the problem of finding the policy that chooses the best time to stop taking measurements and the best set of channels to access for data transmission.

Node level: sensing algorithms.

More in the algoritmic direction Z. Quan, S. Cui, A.H. Sayed, and H.V. Poor propose in "Optimal Multiband Joint Detection for Spectrum Sensing in Cognitive Radio Networks" a multiband joint detector formulated as a class of convex optimization problem that maximize the aggregated opportunistic throughput.

C.-H. Hwang, G.-L. Lai, and S.-C. Chen propose in “Spectrum sensing in wideband OFDM cognitive radios” an OFDM based wideband detector using the idea that a primary user channel appears at a segment of continuous subcarriers. Then in a first step, the maximum likelihood (ML) estimates of the frequency bands are calculated; while in a second step, detection is performed at each suspected band.

In "Invariant wideband spectrum sensing under unknown variances” A. Taherpour, M. Nasiri-Kenari and S. Gazor propose a white space detector based on the Generalized Likelihood Ratio Test given that a minimum number of subbands is vacant. In their model the level of each frequency subband is provided by the output of a filterbank.

Physical node level: sensing paradigms.

In wideband spectral sensing the large bandwidth involved makes Nyquist-rate monitoring impractical, due to power consumption and analog implementation complexity constraints. Different sensing paradigms try to deal with this problem:

For example in "A Wavelet Approach to Wideband Spectrum Sensing for Cognitive Radios" Z. Tian and G.B. Giannakis propose a wavelet approach in which the signal spectrum over a wide frequency band is decomposed into elementary building blocks of subbands that carry the relevant information on the frequency locations and power spectral densities of the subbands. Wavelet transform allows to monitorize simultaneously all the possible bandwidths for each of the channels present in the band.

Y. L. Polo, Y. Wang, A. Pandharipande and G. Leus propose in "Compressive wide-band spectrum sensing" a spectrum reconstruction process based on the autocorrelation of a compressed version of the received signal (however it is not clear to me how a non-stationary compressed signal can have an autocorrelation) and assuming sparsity in the spectral edges domain. They use then the reconstructed spectrum for detecting signal occupancy. A distributed version of this approach is presented in "Distributed Compressive Wide-Band Spectrum Sensing" by Y. Wang, A. Pandharipande, Y. L. Polo and G. Leusy.

The work presented in "Compressive Detection for Wide-band Spectrum Sensing" by V. Havary-Nassab, S. Hassan and S. Valaee proposes a wideband detector based on a set of random overlapping filters: the energies at the filter outputs are used as compressed measurements to reconstruct the signal energy in each channel.

From arXiv we have "Compressive Wideband Spectrum Sensing for Fixed Frequency Spectrum Allocation" and "Robust Compressive Wideband Spectrum Sensing with Sampling Distortion" by Y. Liu and Q. Wan, where the authors propose an ad-hoc compressed sampling architecture based on the a priori knowledge of the frequency spectrum allocation of primary radios. The second paper is about the various non-ideal physical effects that in practice appear in the Analog to Information Converter, modeled here as a bounded additive noise.

I will finish with this post with some shameless self-promotion commenting two of my conference publications related to wideband spectrum sensing: "Wideband Spectrum Sensing in Cognitive Radio: Joint Estimation of Noise Variance and Multiple Signal Levels" and "Wideband Spectral Estimation from Compressed Measurements Exploiting Spectral a priori Information in Cognitive Radio Systems" that can be found in the publications section of my homepage. While the first proposes a ML reconstruction of the spectrum when the spectral shape of the primary transmission is assumed known a priori, the second studies a similar setup when only a compressed version of the input signal is available to the spectrum monitor (and only a subset of the channels are occupied).

Here I did not try to be exhaustive in the enumeration of all the existing publications on wideband spectrum sensing. Instead I gave a general view of some of the research directions within this topic. If you find any missing paper or topic it would be nice to let me know with a comment on this post or an email.

Survey of surveys on spectrum sensing for Cognitive Radio

Several reviews on spectrum sensing techniques for cognitive radio have been published. In this post I comment three recent surveys that focus on different aspects of the problem of primary user detection in cognitive radio environments, finding that some important (at least to me) questions are surprisingly left out.

[Y09] offers a high level overview of spectrum sensing for cognitive radio describing the main challenges (such as the hidden node problem, detection of spread spectrum users...) and classifying the different sensing methods as shown in the following figure:


We can see that while they maintain the classical division into Energy detection, Cyclostationarity detection and Matched filter detectors; they also introduce the concepts of Waveform-based sensing and Radio identification.

Waveform-based sensing refers to the detection of known transmitted patterns such as pilots or preambles, and of course increases the accuracy of the detector with a relatively low complexity. On the other hand radio identification refers to using the available a priori knowledge about the transmitter technology we are interested in (such as transmission range, frequency hops, spectral shape...).

The topics covered in [Y09] also include cooperative detection and how to use historic data, such as temporally correlated traffic, to improve detection performance. Additionally this survey includes an interesting part dedicated to how Spectrum Sensing is performed in current wireless standards, including IEEE 802.11k, Bluetooth or IEEE 802.22.


[A09] is a short review focusing on spectral estimation. Different approaches to power spectral density (psd) reconstruction are discussed, including pilot detection, multi taper spectrum estimation or filter banks. Once the psd has been estimated it can be used to detect primary users in cognitive radio systems.


Finally, [Z10] focuses on technical aspects of detection theory applied to cognitive radio environments. This includes using space and time correlation, cyclostationarity detection or cooperative sensing. Other more involved topics are threshold derivation, noise power uncertainty, or what they call robust spectrum sensing. Robust spectrum sensing theory is useful when the a priori knowledge of the noise or signal distribution is limited or imprecise.

The section Future Developments in [Z10] poses some problems related to primary user detection that did not get so much attention from the research community. Here is briefly presented one of the points I missed in all these reviews, namely wideband spectral sensing. Most of the articles cited in these reviews focus on the problem of detecting a single primary user present in the band of interest, however, in general it can be expected that the spectral monitor simultaneously processes multiple channels, and thus more sophisticated detection techniques have to be used (such as, e.g. compressive sensing).


Remember that another way to keep track of the most recent research on spectrum sensing is to take a look to key conferences on cognitive radio, such as the marathonian spectrum sensing sessions at the ICASSP 2010.

[Y09]	T. Yucek and H. Arslan A survey of spectrum sensing algorithms for cognitive radio applications. IEEE Communications Surveys & Tutorials, Volume: 11 Issue:1. First Quarter 2009.
[A09]	D.D. Ariananda, M.K. Lakshmanan and H. Nikoo A survey on spectrum sensing techniques for Cognitive Radio. Second International Workshop on Cognitive Radio and Advanced Spectrum Management, May 2009. CogART 2009.
[Z10]	Y. Zeng, Y. Liang, A. T. Hoang, and R. Zhang A Review on Spectrum Sensing for Cognitive Radio: Challenges and Solutions. EURASIP Journal on Advances in Signal Processing Volume 2010.

Signal processing with compressed measurements

This post is about two papers related to signal processing in the compressed domain. In the special issue on Compressive Sensing in the Journal of Selected topics in Signal Processing we can find an article with title "Signal Processing With Compressive Measurements" [D10]. The abstract reads:

The recently introduced theory of compressive sensing enables the recovery of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be much smaller than the number of Nyquist-rate samples. Interestingly, it has been shown that random projections are a near-optimal measurement scheme. This has inspired the design of hardware systems that directly implement random measurement protocols. However, despite the intense focus of the community on signal recovery, many (if not most) signal processing problems do not require full signal recovery. In this paper, we take some first steps in the direction of solving inference problems-such as detection, classification, or estimation-and filtering problems using only compressive measurements and without ever reconstructing the signals involved. We provide theoretical bounds along with experimental results."

A general framework for signal processing of compressed measurements without reconstructing the original signal would be of major importance. However I find that the paper fails to address a key point of the problem: sparsity. If sparsity is ignored the compressed (in the usual setting) measurements reduce to a linearly transformed version of the original signal, what fits into the classical signal processing framework (since the compression matrix is assumed known). [D10] analyzes the performance of different signal processing algorithms (detection, estimation and filtering) from compressed meassurements when the compression matrices are chosen randomly fulfilling a modified RIP property. Since the only reference to the sparsity of the original signal is then through the RIP of the compression matrices higher processing performance may be achieved by reconstructing the signal (remember that RIP is a sufficient but not necessary condition for reconstruction).

A much more involved analysis for the estimation setting was presented in the compressed sensing's day at the ICASSP. In "On unbiased estimation of sparse vectors corrupted by Gaussian noise" [J10] Alexander Jung theoretically analyzes the behavior of the achievable estimation performance in the sparse setting, as opposed to [D10] that only analyzes a quite simple estimation problem from a set of compressed measurements.

[J10] studies the problem of estimating a sparse vector of parameters with unknown support. The interesting result appears when the cardinality of this support is assumed known. In this setting the Cramer Rao Lower Bound (CRB) of the estimate coincides with the minimum square error obtained by an estimator that has a priori knowledge about the positions of the non-zero entries (support) of the vector to estimate [B09]. It is easy to see that this bound is not achievable if this support cannot be determined from the measurements, e.g. in the low SNR regime. The Barankin Bound (BB) is also a lower bound on the unbiased estimation performance and in general it is tighter than the CRB. The interesting part is that it shows a behaviour similar to the Maximum Likelihood (ML) estimate of the parameter vector.


In the Fig. 1 it is shown the behaviour of the different bounds for a given problem instance. We can see that while the CRB is constant even for low SNR values, in this regime the BB rises due to the impossibility of completely determinig the support. We can also see that the ML estimator presents a similar behaviour, with the only difference of the higher SNR threshold where its MSE drops to the CRB.

[D10]	M.A. Davenport, P.T. Boufounos, M.B. Wakin and R.G. Baraniuk Signal Processing With Compressive Measurements. Selected IEEE Journal of Topics in Signal Processing, April 2010.
[J10]	A. Jung, Z. Ben-Haim, F. Hlawatsch, and Y. C. Eldar On unbiased estimation of sparse vectors corrupted by Gaussian noise  in Proc. 2010 IEEE International Conference on Audio, Speech and Signal Processing (ICASSP 2010), Dallas, TX, March 2010.
[B09]	Z. Ben-Haim and Y. C. Eldar The Cramer–Rao bound for sparse estimation   IEEE Trans. Signal Processing, May 2009, submitted.

Patent: Signal Detection in Cognitive Radio Systems

After writing the post about the companies with most patents on cognitive radio I wondered how innovative these patents could be. To check it I present here one of the lastest patents filed by Motorola related to spectral sensing: US20100081387: Signal detection in cognitive radio systems.


The first claim, the soul of the patent, reads like that:

A method, with a cognitive radio wireless device, for dynamically managing signal detection in a cognitive radio system, the method comprising:

• performing spectrum sensing for a first sensing frame on at least one communication channel;
• receiving, in response to performing spectrum sensing, at least one observed signal on the at least one communication channel;
• and performing a detection decision to determine if the observed signal is one of noise and an active signal associated with an active user, wherein performing the detection decision comprises:
  1. determining an energy estimation .epsilon. associated with the at least one observed signal;
  2. comparing the energy estimation .epsilon. with a current detection threshold, wherein the current detection threshold is one of an arbitrarily defined threshold and a detection threshold based on a previous detection decision for a sensing frame immediately prior to the first sensing frame;
  3. setting, in response to the energy estimation being above the current detection threshold, a first new detection threshold equal to the current detection threshold;
  4. and setting, in response to the energy estimation .epsilon. being below the current detection threshold, a second new detection threshold as a function of the current detection threshold and the energy estimation .epsilon.;
  wherein one of the first and second new detection threshold is used for at least one subsequent detection decision for at least a second sensing frame."

That is, they use energy detection in a given channel by comparing the meassured energy with a threshold that is updated in the case that the channel is decided as vacant.

A patent by definition

must be innovative to the point that it wouldn't be obvious to others."

Then my question is if updating the threshold after non-detection of a primary user is innovative enough in order to justify a patent, or most of these patents are just for the future work of their lawyer's offices.

Sensing, sensing and more sensing at ICASSP

After enjoying a conference reception colored by an unconveniently loud experimental jazz group, the actual ICASSP begins. Here I will give my impressions on some of the papers cited in the previous post. Two of today's sessions were about Spectrum Sensing for Cognitive Radio, and the works presented covered all the current trends.

Sensing paradigms

The paper SEMI-BLIND LOCALLY OPTIMUM DETECTION FOR SPECTRUM SENSING IN COGNITIVE RADIO by Marco Cardenas-Juarez et al. assumes the secondary node slot-synchronized (strong assumption) to a primary system transmitting a training sequence. Then this work proposes a detector based on a mixed matched filter/energy detection strategy.

On A PERFORMANCE STUDY OF NOVEL SEQUENTIAL ENERGY DETECTION METHODS FOR SPECTRUM SENSING by Nikhil Kundargi et al. an adaptive energy detector is proposed. While the classical energy detector compares the energy received during a given time with a threshold, the proposed sequential energy detection compares the likelihood ratio of the signal up to a time instant with two thresholds, deciding hypothesis H0, H1 or, if the likelihood falls between the two threshold values undecided. In this case the operation is repeated with a longer sample of the signal.

Related to cyclostationarity is the work in AM-SIGNAL DETECTION IN COGNITIVE RADIOS USING FIRST-ORDER CYCLOSTATIONARITY by Yi Zhou et al. As the title describes they propose a cyclostationarity based detector for AM signals, what is an interesting theoretical exercise but it is in my opinion not very practical. They assume only rough information on the signal bandwidth and carrier frequency, but this implies that a search of the right cyclic frequency has to be performed.
Similarly, SPECTRAL COVARIANCE FOR SPECTRUM SENSING, WITH APPLICATION TO IEEE 802.22 by Jaeweon Kim et al. uses existing spectral correlation to propose a detector robust to noise uncertainty. However, like other cyclostationarity based approaches offers poor performance in OFDM signal detection.

An interesting idea is presented in SPECTRUM SENSING OF ORTHOGONAL SPACE-TIME BLOCK CODED SIGNALS WITH MULTIPLE RECEIVE ANTENNAS by Erik Axell et al. In this paper the authors use the aditional structure of space-time coded signals to increase detection performace. In fact I had tried this idea recetly with Alamouti coded signals observing no detection gain... my naive result is confirmed by this work since when noise power is known OSTBC based detection offers no gains with respect to energy detection. However for unknown noise level (here was the key point I had missed) there exists a significant gain.

MULTIANTENNA SPECTRUM SENSING: DETECTION OF SPATIAL CORRELATION AMONG TIME-SERIES WITH UNKNOWN SPECTRA by David Ramirez et al. asumes a multiantenna cognitive node. Then it uses the spatial uncorreldaness of the noise process to derive a detector robust to noise level (and temporal correlation) uncertainty.

Multichannel spectrum sensing

In TWO-STAGE SPECTRUM SENSING FOR COGNITIVE RADIOS Sina Maleki et al. propose the use of a two level detector with a first (energy based) coarse detection phase followed by a (cyclostationarity based) fine detection stage. The most interesting part is that when the two stages thresholds are optimized the global detector takes the advantages of the two detection schemes. Unfortunately to optimize the detection thresholds working SNR must be known.

With the almost equal title TWO-STAGE SPECTRUM DETECTION IN COGNITIVE RADIO NETWORKS Siavash Fazeli-Dehkordy et al. present a different idea. The authors propose to use energy detection in both detection stages in order to reduce the average empty channel search time. The first stage is short and defides if a channel is candidate for a (longer) second test.

Similarly, ADAPTIVE SPECTRUM SENSING FOR AGILE COGNITIVE RADIOS by Ali Tajer et al. proposes an adaptive sensing scheme for the band of interest based on discarding first the clearly ocuppied channels in order to concentrate sensing resources in the remaining doubtful channels. As oposed to the previous paper, it estimates the set of empty channels and not only one empty channel.

Seung-Jun Kim et al. pose the problem of determining the best sensing strategy for a band with multiple channels, taking into account that when sensing is performed not useful transmission is performed by the secondary system. This paper entitled SEQUENTIAL COOPERATIVE SENSING FOR MULTI-CHANNEL COGNITIVE RADIOS was presented by G. Giannakis in a heavy lecture.

The paper WIDEBAND SPECTRAL ESTIMATION FROM COMPRESSED MEASUREMENTS EXPLOITING SPECTRAL A PRIORI INFORMATION IN COGNITIVE RADIO SYSTEMS by G Vazquez-Vilar (that's me) et al. poses the estimation (and as a byproduct detection) of multiple primary signals from compressed meassurements. As opposed to other compressed sampling (CS) reconstruction schemes the paper starts with the MAP estimator derivation and incidentally produces a formulation similar to other CS methods. A (quite trivial) greedy approach is used to deal with the norm 0 term.

The work presented in COMPRESSIVE DETECTION FOR WIDE-BAND SPECTRUM SENSING by Veria Havary-Nassab et al. proposes a wideband detector of spectral holes. To this end wideband signal is fed into a set of random overlapping filters, then the energies of the filter outputs are used as compressed measurements to reconstruct the signal energy in each channel. The white spaces are then detected by comparing the energy vector with a given threshold.

Collaborative spectrum sensing

The paper COLLABORATIVE SPECTRUM SENSING FROM SPARSE OBSERVATIONS USING MATRIX COMPLETION FOR COGNITIVE RADIO NETWORKS by Jia (Jasmine) Meng et al. assumes multiple nodes taking a linear combination of the sparse signals to estimate. To guarantee the sparsity of the solution the estimation is performed based on a nuclear norm minimization algorithm robust to transmission loss of measurements matrix entries.

To finish with this long post a comment on two last papers. While BANDWIDTH EFFICIENT COMBINATION FOR COOPERATIVE SPECTRUM SENSING IN COGNITIVE RADIO NETWORKS by Xiangwei Zhou et al. studies the possibility of combining likelihoods on the air to increase the bandwidth efficiency of the transmission of sensing data obtained by multiple cognitive nodes; the work in DIVERSITY-BASED SPECTRUM SENSING POLICY FOR DETECTING PRIMARY SIGNALS OVER MULTIPLE FREQUENCY BANDS by Jan Oksanen et al. proposes a cooperative spectrum sensing scheme that facilitates mitigating the effects of shadowing and fading through spatial diversity.