ADAPTIVE TECHNIQUES FOR CYCLOSTATIONARY SPECTRUM SENSING IN COGNITIVE RADIOS

Abstract

Cognitive or environment aware radio has emerged as one of the major technologies to improve the utilization of the limited communication spectrum. The cognition cycle proposed in the literature for an environment aware radio entails the tasks of spectrum sensing, spectrum allocation and reliable transmission. Out of these, spectrum sensing has emerged as an active area of research during the past decade. This involves the detection of primary user or licensed user signals in order to determine the availability of a spectrum band for transmission. Two major challenges faced by spectrum sensing algorithms are very low SNRs of the order of −22 dB; and a limited knowledge about the signal to be sensed. It is known that the energy detector is the optimal detector for random signals. However, this is known to fail under low SNRs when the noise power is not known correctly. Therefore, it becomes important to look for alternative approaches for spectrum sensing. Several spectrum sensing algorithms based on the cyclostationarity or spectral coherence of the primary user signal have been proposed during the past years. It has been established that cyclostationarity of a signal may be used to detect as well to as enhance it. Optimal filters to enhance cyclostationary signals have also been derived. These filters are observed to exhibit a FRESH (FREquency SHift) structure. Cyclostationarity has also been employed for the purpose of antenna array beam-forming. In the past, both FRESH filtering as well as cyclostationary beam-forming have been used to enhance cyclostationary signals prior to detection. The first problem that we consider in this thesis is a combination of these two approaches. We propose a Space-Time FRESH filtering structure to enhance the primary user signal by exploiting its spatial, temporal and spectral coherence. The proposed structure is made adaptive to adjust its weights as per the primary signal of interest. The Adaptive Cross SCORE (ACS) algorithm put forward in literature is modified to adapt the proposed structure, and a spectrum sensing algorithm is subsequently developed. However, the resulting algorithm has a complexity of the order of O((KLM)2) for K antennas, M frequency shift branches per antenna, and L temporal taps per branch. This is observed to act as a bottleneck in the spectrum sensing procedure. Therefore, we formulate the correlation maximization problem of the ACS algorithm as a constrained MMSE problem to develop a constrained doubly adaptive LMS (C2-LMS) algorithm. It is then shown, using simulation techniques, that the proposed structure, adapted using the proposed algorithm, may result in gains of as much as 10 dB xiii Abstract over conventional Energy and Cyclostationarity detectors. Following this, we study the performance enhancement achieved in conventional spectrum sensing systems by FRESH filtering the signal prior to the detection stage. A quasianalytical theory of spectrum sensing based on FRESH filtering is developed. A quasianalytical approach is required because the variance of the test statistics is found to have an intractable form and should, therefore, be determined empirically. Bounds on this variance have however been derived. It is shown that significant performance gains are achievable in both energy detection and cyclostationarity detection via FRESH filtering of the received signal prior to the detection step. It is observed that FRESH filtering may reduce the number of samples required to achieve a given detection performance by more than 90% in practice, thereby reducing the sensing time in a cognitive radio system. It is also shown that the FRESH filtering before energy detection may reduce the effects of SNR walls caused due to noise uncertainty. The validity of all the derived observations is confirmed via simulations. It has been shown that multi-path fading and shadowing may affect the performance of a single-user spectrum sensing adversely. It is, however, possible to improve the sensing performance in such cases by employing multi-user diversity, that is, collaboration among multiple sensing nodes. It may be argued that if FRESH filtering leads to performance improvement in a single-user, it should also enhance the detection performance of multiple collaborating users. Hence, we consider the problem of spectrum sensing with multiple collaborating users, each equipped with a FRESH filter. In this case, FRESH filtering or Space-Time FRESH filtering may be used to boost the performance of each individual user, thereby improving the overall detection performance of the system. Here, we consider three models of collaboration viz. centralized, distributed and hierarchical. It is argued that the performance of collaborative FRESH filter-based spectrum sensing can be improved further if the collaborating users adapt their filter weights jointly. It is shown using simulations that joint adaptation results in gains of as much as 2 dB over local adaptation in addition to the gains offered by the FRESH filters. Simulation results are also used to compare the performance of the different collaboration schemes and it is observed that there is a slight degradation in the performance of the proposed sensing technique as the system moves from a purely centralized setting to a purely distributed setting. In all the problems discussed above, we assume a perfect knowledge of the cyclic frequency at the spectrum sensor. However, this may not always be true. Phenomena such as Doppler shift and sampling clock offset may cause an offset between the true cyclic frequency of the primary user signal and the cyclic frequency known at the receiver. Cyclic Frequency Offset (CFO) is reported to cause severe degradation in the performance of systems exploiting cyclostationarity. In our proposed FRESH filter-based spectrum sensing systems, CFO may manifest at the adaptation stage as well as the sensing stage. In this thesis, we consider these problems separately. xiv Abstract To study the effect of CFO on the sensing stage, we consider the problem of cyclostatioanry spectrum sensing of an OFDM signal with correlated pilots. Spectrum sensing algorithms for OFDM signals are also important because of the popularity of OFDM as a modulation standard as well as it being the most suitable candidate for cognitive radio networks. A detector for the cyclostationary features introduced due to inter-pilot correlation is developed. The performance of the proposed detector is derived and verified in case of AWGN channels. Following this, the effect of an offset in the value of cyclic frequency known at the spectrum sensor is found out, and it is shown that CFO may cause a substantial performance loss in the system. It is then argued that the true cyclic frequency of the received signal may be estimated using the received samples. The Cramer-Rao bound for the true cyclic frequency estimator is then derived. Based on this bound, it is observed that the true cyclic frequency needs to be determined recursively. Therefore, two recursive algorithms, viz. a gradient ascent algorithm and a greedy-search algorithm, to estimate and compensate for the CFO are proposed. The performance of both these algorithms is then evaluated via simulation techniques. It is observed that the proposed cyclic frequency estimation algorithms may compensate the losses caused due to CFO by as much as 15 dB. Simulation results are also used to study the performance of the proposed detection technique under Rayleigh fading both in the presence and the absence of CFO. A single-branch FRESH filter is considered to study the effects of CFO on the adaptation stage of a FRESH filtering-based spectrum sensor. It is shown that the performances of both the energy detector and the cyclostationarity detector suffer in the presence of a CFO in the adaptation stage. Following this, the greedy search algorithm developed previously is modified to estimate the true cyclic frequency for FRESH filter adaptation. It is observed via simulation techniques that the losses caused due to CFO are reduced by as much as 5 dB for an energy detector and 14 dB for a cyclostationary detector.