The problem of decision fusion for cooperative spectrum sensing in cognitive radio networks is studied when noisy fading channels are present between the cognitive radios (CRs) and the fusion center (FC). The CRs perform spectrum sensing using energy detection and transmit their binary decisions to the FC for a final decision on the absence or presence of the primary user activity. Considering the limited resources in cognitive radio networks, which makes it difficult to acquire the instantaneous channel state information, noncoherent transmission schemes with on-off keying (OOK) and binary frequency shift keying (BFSK) are employed to transmit the binary decisions to the fusion center. The aim is to optimize the detection performance in terms of the achievable secondary throughput in the cognitive radio network. Toward this end, for each of the transmission schemes considered, first a weighted energy-detector is obtained. Then the detection threshold at the CR nodes as well as at the FC, the sensing weights and the sensing time are optimized to maximize the secondary throughput.

Abstract-Given the ever growing demand for radio spectrum,cognitive radio has recently emerged as an attractive wireless technology. Since orthogonal frequency division multiplexing (OFDM) is one of the major wideband transmission techniques, detection of OFDM signals in low signal-to-noise-ratio (SNR)scenario is an important research problem. In this paper, it is shown that the cyclic prefix correlation coefficient (CPCC) algorithm, which has been introduced as a simple and computationally efficient spectrum sensing test for OFDM signals, is a special case of the constrained generalized likelihood ratio test(GLRT) in the absence of multipath. As such, the performance of this algorithm degrades in a multipath scenario where OFDM is usually implemented. Moreover, by considering the multipath correlation in the GLRT algorithm and employing the inherent structure of OFDM signals, a simple and low complexity algorithm, called multipath-based constrained-GLRT (MP-based CGLRT)algorithm is obtained. The MP-based C-GLRT algorithm is shown to outperform the CPCC-based algorithm in a rich multipath environment. Further performance improvement can be achieved by simply combining both the CPCC-based and MPbased C-GLRT algorithms.

Synchronous CDMA systems whose transmission bandwidth is quantified through the fractional out-of-band energy (FOBE) constraint are considered. Either a conventional matched filter (MF) receiver or a minimum mean-square error (MMSE) receiver is employed for users' data detection. The total squared correlation (TSC) and the total mean-square error (TMSE) are proposed as the performance parameters for the MF and MMSE receivers respectively. These parameters need to be minimized in order to maximize the signal-to-interference ratios (SIRs) at the receivers' outputs. For a given FOBE bandwidth constraint, the sets of signature waveforms that minimize either TSC or TMSE are obtained from the prolate spheroidal wave functions (PSWFs). Furthermore, if the number of users is the size of a Hadamard matrix, then optimal signature waveforms can be obtained to maximize the individual SIR for every user. Due to the complicated nature of the PSWFs, simplified MF and MMSE receivers based on the Walsh signal space are developed.

Synchronous code-division multiple-access systems where each receiver is a minimum mean-squared-error receiver and each user has the same received power, signaling rate, and required signal-to-interference ratio are considered. Based on the results Viswanath, Anantharam and Tse (see IEEE Trans. Inform. Theory, vol.45, p.1968-83, 1999), the optimal signature waveforms under both fractional out-of-band energy and root-mean-square bandwidth constraints that maximize the network capacity are determined. Comparison to various suboptimal signature waveforms, including the ones constructed from rectangular pulses, is also made to quantify the gain achieved by the optimal signature waveforms.

An algorithm to estimate jointly the symbol timing and carrier phase for continuous-phase modulation (CPM) is described. It is designed to optimize the steady-state performance of the CPM synchronizer and exhibits excellent performance, very close to the optimum maximum-likelihood estimate. The algorithm is simple and practical and may be employed with any CPM scheme. It is based on a signal space decomposition of the CPM signal in the Walsh signal space.

High-speed data communication over channels with limited bandwidth gives rise to intersymbol interference at the receiver usually resulting in a poor receiver error performance. An important parameter that determines the receiver error performance is the minimum Euclidean distance between two received sequences. Channel properties that maximize this distance are investigated. It is shown that maximum distance channels exist for any length of interference.

A simple receiver structure for any continuous phase modulation (CPM) scheme is introduced. Its front end is just the ordinary linear receiver followed by a subinterval sampler, eliminating the need for the standard analog matched filters. Its design is based on the decomposition of the CPM signal in the Walsh signal space. This brings the hardware requirement to a minimum, and near-optimum performance can be easily obtained.

Various turbo codes together with /spl pi//4 DQPSK modulation are investigated for frequency-selective Rayleigh fading channels. The soft output Viterbi algorithm (SOVA) is selected for equalising multipath fading channels so that both reliability information can be available for turbo decoding and the channel impulse response can be effectively estimated. To keep the receiver's complexity low, turbo codes are, built from a simple recursive systematic convolutional code with constraint length K=3. The number of channel estimators in the SOVA and the number of iterations to be performed in turbo decoders are also kept small. Simulation results for different mobile speeds and different frame lengths are obtained and it is shown that when the frame size is long enough, turbo codes can significantly outperform a convolutional code of constraint length K=6.

Fading in a multipath channel is modelled as a Markov process. Based on this, maximum a posteriori (MAP) estimation is developed for fading channels with intersymbol interference (ISI).>

Presents sequence estimation for the frequency selective Rayleigh fading channel. Maximum likelihood estimation using the Viterbi algorithm (MLSE-VA) and sequential sequence estimation (SSE) are developed. Both MLSE-VA and SSE consist of a set of Kalman filters which estimate the fading channel as time evolves. Computer simulations for two different channel models show that the error performance of the two approaches is essentially the same. SSE however has considerably less computational complexity than MLSE-VA. To improve the error performance, diversity is combined with both MLSE-VA and SSE. The simulations show that diversity results in a signal to noise ratio gain of greater than 10 dB.>

The computational complexity of a sequential algorithm (SA) developed for intersymbol interference (ISI) channels is analyzed. To determine the computational complexity, the finite-state machine that models the channel and white matched filter system, of which the SA is a part, is interpreted as a special convolutional encoder followed by a binary symbol to Q-ary symbol mapping. It follows that the computational distribution is Pareto, and that there exists a computational cutoff rate R/sub comp/. For the uncoded data considered, the rate is fixed and the R/sub comp/ criterion translates into a signal-to-noise ratio (SNR) criterion. An upper bound on SNR/sub comp/ is found analytically by assuming a uniform input distribution. Iteration equations developed by S. Arimoto (1976) are adapted to find the true SNR/sub comp/ numerically.>

A vector sequential sequence estimator is proposed for multiple-channel systems with both intersymbol interference (ISI) and interchannel interference (ICI). Both finite ISI-ICI and infinite ISI-ICI are considered. The estimator consists of a multiple-dimensional whitened matched filter and a vector sequential decoder. The metric of the sequential algorithm is derived, and the algorithm's performance is analyzed. Computer simulation results for a two-dimensional finite ISI-ICI channel and a two-dimensional infinite ISI-ICI channel are presented. Analysis and simulation show that the symbol error probability of the vector sequential algorithm is essentially the same as for maximum-likelihood sequence estimation using the vector Viterbi algorithm, while its average computational complexity is much less, although computation per symbol is a random variable with the Pareto distribution. There exists a signal-to-noise ratio above which the ensemble average computation is bounded. An upper bound on this ratio is found.>

Communication systems such as mobile radio and indoor wireless communication typically are modelled as frequency selective fading channels. This paper develops a sequential sequence estimator (SSE), which is essentially maximum likelihood, of the bandlimited signals with a convolutional coded sequence. Simulations show that the SSE with convolutional coded input sequence improves the performance significantly compared with that of SSE with diversity.>

A sequential sequence estimator for channels with finite or infinite intersymbol interference (ISI) is proposed. It consists of a whitened matched filter followed by a sequential algorithm. A key component of a sequential estimator is a suitable metric that accounts for the unequal search depth. This metric is derived for the ISI channel. Computer simulations for three different channels show that the sequential sequence estimator has considerably less computational complexity than a maximum-likelihood sequence estimator using the Viterbi algorithm (MLSE-VA), while still maintaining the optimum estimation performance of the MLSE-VA, a performance not achievable with any reduced-state Viterbi algorithm.>

A modified sequential procedure for testing binary hypotheses with different means, proposed by C.C. Lee and J.B. Thomas (ibid., vol.IT-30, no.1, p.16-23, Jan. 1984), is generalized for application to the case of multiple hypotheses with different means/variances of the Gaussian distribution. The method constitutes a two-threshold test for fixed-size packages of samples with a sequential procedure of discarding the package for which no decision is reached and subsequently testing a new package. The objective is to find an optimum package size N/sub 0/ which leads to the minimum overall average sample number (ASN) for a given overall error probability. An optimization algorithm is developed to extend the application of the Lee-Thomas procedure to the M-ary case. Performance characteristics of the generalized two-threshold (GTT) test procedure are compared with those of conventional sequential as well as fixed-sample-size (FSS) methods. It is shown for the M-ary different means/variances cases that for low error rates the number of samples required by the GTT test is, on the average, approximately half that needed by a FSS test. However, it is somewhat more than the ASN obtained with a conventional sequential test. With decreasing error probabilities the GTT test performance approaches that of conventional sequential methods.>

A taxonomy of VLSI grid model layouts is presented for the implementation of certain types of digital communication receivers based on the Viterbi algorithm. We deal principally with networks of many simple processors connected to perform the Viterbi algorithm in a highly parallel way. Two interconnection patterns of interest are the "shuffleexchange" and the "cube-connected cycles." The results are generally applicable to the development of area-efficient VLSI circuits for decoding: convolutional codes, coded modulation with multilevel/phase signals, punctured convolutional codes, correlatively encoded MSK signals and for maximum likelihood sequence estimation ofM-ary signals on intersymbol interference channels. In a companion paper, we elaborate on how the concepts presented here can be applied to the problem of building encoded MSK Viterbi receivers. Lower bounds are established on the product (chip area) * (baud rate)-2and on the energy consumption that any VLSI implementation of the Viterbi algorithm must obey, regardless of the architecture employed or the intended application.

As a specific application of the material presented in Part I, this companion paper identifies VLSI layout strategies for realizing correlative encoded MSK-type Viterbi receivers. When the source symbols are correlatively encoded using a first-order polynomial, the appropriate Viterbi receiver takes the form of a cube-connected cycle (CCC) structure. Second-order encoding polynomials give rise to a new type of area-efficient VLSI structure which is a generalization of the CCC structure. The results are important from two perspectives: 1) Isomorphisms between certain concepts in theoretical computer science and digital communications are established, and 2) good practical VLSI layouts are generated, by a structured design methodology, which commercial silicon foundries can fabricate.

A sequential multiple hypotheses test for the unknown parameters of a Gaussian distribution is developed. The case of a known variance but an unknown mean belonging to the set (00,01,''' ,Om_l} is considered as well as that of a known mean but an unknown variance belonging to the set\{\sigma^{2}_{0}, \sigma^{2}_{1},\cdots ,\sigma^{2}_{m-1}\}. Analytical expressions are developed for the algorithm performance, i.e., the average length of the test and the error probability. The results are compared with a Bayes algorithm and show that the new algorithm needs about half as many samples. As far as the authors are aware this is the firstmary sequential algorithm for which the performance has been found analytically. Because of the performance of this algorithm and the fact that it is a natural generalization of the binary sequential test, it is felt that the algorithm may be optimum or close to optimum.