Linear MMSE Channel Estimation for Underlay Cognitive Radio Networks

We study the effect of imperfect channel estimation (ICE) on the error probability performance of M-level quadrature amplitude modulation ( M-QAM) with maximal-ratio combining and equal-gain combining diversity formats in Nakagami fading channels. We provide a novel formulation of the bit-error rate (BER) of M-QAM with ICE in terms of the signal constellation-dependent effective signal-to-noise ratios (SNRs) or amplitudes, which allows us to derive the general, accurate, and easy-to-evaluate BER formulas for square and rectangular diversity M-QAM with channel estimation errors. Our result shows that the performance loss caused by ICE may be manifested by the signal decision space distortion and a scaling of the effective SNR. Using our analytical result, we evaluate the performance of M-QAM with pilot-symbol assisted modulation and present some insightful findings

In this paper, we study the effect of imperfect channel estimation (ICE) on the performance of M-ary phase shift keying (M-PSK) with maximum ratio combining (MRC) in generalized Rician fading channels. Using decision variable (DV)-based and signal-to-noise ratio (SNR)-based moment generating function (MGF) approaches, error and outage probability formulas, and SNR statistics for the M-PSK MRC receiver are derived, taking into account the effects of ICE and all relevant system and channel parameters. We analytically quantify the average SNR (ASNR) loss of M-PSK caused by ICE, and provided a unified MGF expression for ICE and different M's. In addition, we point out a major approximation for a popular approach used in the literature to evaluate the adverse effect of Gaussian weighting errors.

In recent years, an Ultra Wideband (UWB) system has attracted much attention in short range high speed wireless communications. Meanwhile, the single-carrier transmission with frequency domain equalization (SC-FDE) is also attracting much attention. It is reported that the SC-FDE system obtains an excellent performance as well as orthogonal frequency division multiplexing (OFDM), because the SC-FDE system has the advantage of frequency diversity gain even in strong frequency selective channels. However, in the SC-FDE system, cyclic extension reduces the bandwidth efficiency. To improve the bandwidth efficiency, we proposed UWB-IR and DS-UWB with Frequency-Domain Equalization (FDE) and Cyclic Prefix (CP) reconstruction, and showed that when the channel estimation is ideal, the proposed system achieves the good performance. Both FDE and CP reconstruction use channel gains and thus the performance is expected to depend largely on the channel estimation accuracy. In this paper, we evaluate the effect of imperfect channel estimation on the performance of UWB-IR with MMSE-FDE and CP Reconstruction. We show that CP reconstruction is effective for UWB-IR with MMSE-FDE in the IEEE UWB multipath channels, CM3, CM4.

Channel estimation is critical to coherent RAKE receiver performance. This paper deals with channel estimation based on the standard algorithm suggested for UTRA-TDD by 3GPP. It proposes a spatial pre-combination technique that exploits the spatial structure of the received multipath signal to improve the channel estimator performance. Self and multiple access interference is partially cancelled before the channel estimation algorithm. The performance of the estimation algorithm is assessed by resorting to simulations in typical UMTS-TDD scenarios and the correlation coefficients between the complex channel and the estimates are computed. The effect of imperfect channel estimation on the performance of RAKE1D and RAKE2D receivers is analyzed in a multiuser scenario.

In this paper, the performance of asecondary user (SU) in an underlay cognitive radio (CR) network over ageneralized-gamma (GG) fading channel in terms of three performance metrics,namely, outage probability, ergodic capacity, and bit error rate (BER), isinvestigated. According to the underlay approach, the transmit power of the SUshould be limited to avoid interference to primary users (PUs). The performancemetrics of the SU in the underlay CR network are theoretically derived and alsoobtained with Monte Carlo simulations for a GG fading channel with different fadingparameters. To demonstrate the effect of limited power on the performancemetrics, three different maximum transmit power levels (Pmax), namely, 10, 20,and 30 dB, are used. The simulation results lead to three conclusions: First,when high values are chosen for the fading parameters (α, c), the fadingchannel gets less distorted and the performance metrics improve. The secondconclusion is that the BER performance gets better as the limited powerincreases. The final conclusion is that the BER performance of SUs improves asthe interference power that PUs can tolerate increases. Cite this article as: Aldırmaz Çolak S.Performance Analysis of a Secondary User in Cognitive Radio overGeneralized-Gamma Fading Channels. Electrica, 2019; 19(2): 166-172.

A survey about linear channel estimation exploiting slowly varying channel properties is given for receivers with multiple antenna elements. The slowly varying channel properties are described by the channel's second-order statistics. First, a detailed comparison of classical linear pilot-based channel estimators, a novel matched filter, and reduced-rank (RR) approaches is made in a common framework with respect to the model they assume for the channel, their performance (MSE), and complexity. The matched filter channel estimator is introduced, which exploits second-order statistics with quadratic order of complexity. For flat correlated Rayleigh fading channels, an analytical performance comparison of all estimators in terms of the uncoded bit error probability is provided. It is a generalization of previous results and shows that the matched filter is a low complexity alternative with good performance at an interesting signal-to-noise ratio (SNR) range. The effects of these approaches on linear equalization are briefly discussed in the context of direct-sequence code division multiple access (DS-CDMA), where the focus is on a generalization of the rake receiver in space and time, which reduces the channel rank based on its second-order statistics, resulting in a complexity reduction of the equalizer. For this discussion, a new notation for the generalized rake is presented, which allows for its interpretation in the context of channel estimation and reveals alternatives for implementation. We conclude that exploiting second-order channel statistics results in significant performance gains, and RR channel estimation should only be used together with equalization in the reduced signal subspace.

Optimal receiver diversity combining employing linear channel estimation is examined. Based on the statistical properties of least-squares (LS) and minimum mean square error (MMSE) channel estimation, an optimal diversity receiver for wireless systems employing practical linear channel estimation on Rician fading channels is proposed. The new receiver structure includes the conventional maximal ratio combining receiver as a special case. Exact analytical expressions for the symbol error rates (SERs) of LS and MMSE channel estimation aided optimal diversity combining are derived. It is shown that, if an optimal detector is used, an MPSK wireless system with MMSE channel estimation has the same SER when the MMSE channel estimation is replaced by LS estimation. This is an interesting counterexample to the common perception that channel estimation with smaller mean square error leads to smaller SER. Extensive simulation results validate the theoretical results.

After a few decades’ evolution of wireless communication systems, to ensure reliable highspeed communication over unreliable wireless channels is still one of the major challenges facing researchers and engineers. The use of multiple antennas at transmitter and receiver, known as multiple-input multiple-output (MIMO) communications, is one promising technology delivering desired wireless services. The main goal of this thesis is to study two important issues in wireless MIMO communication systems: receiver design for coded MIMO systems, and diversity-multiplexing tradeoff analysis in general fading channels. In the first part of this thesis, we decompose the receiver design problem into two subproblems: MIMO channel estimation and MIMO detection. For the MIMO channel estimation, we develop an expectation-maximization (EM) based semi-blind channel and noise covariance matrix estimation algorithm for space-time coding systems under spatially correlated noise. By incorporating the proposed channel estimator into the iterative receiver structure, both the channel estimation and the error-control decoding are improved significantly. We also derive the modified Cramer-Rao bounds (MCRB) for the unknown parameters as the channel estimation performance metric, and demonstrate that the proposed channel estimation algorithm can achieve the MCRB after several iterations. For the MIMO detection, we propose a novel lowcomplexity MIMO detection algorithm, which has only cubic order computational complexity, but with near-optimal performance. For a 4×4 turbo-coded system, we show that the proposed detector had the same performance as the maximum a posteriori (MAP) detector for BPSK modulation, and 0.1 dB advantage over the approximated MAP detector (list sphere decoding algorithm) for 16-QAM modulation at BER = 10−4. In the second part of this thesis, we derive the optimal diversity-multiplexing tradeoff for

Cooperative communication is regarded as a key technology in wireless networks, including cognitive radio networks (CRNs), which increases the diversity order of the signal to combat the unfavorable effects of the fading channels, by allowing distributed terminals to collaborate through sophisticated signal processing. Underlay CRNs have strict interference constraints towards the secondary users (SUs) active in the frequency band of the primary users (PUs), which limits their transmit power and their coverage area. Relay selection offers a potential solution to the challenges faced by underlay networks, by selecting either single best relay or a subset of potential relay set under different design requirements and assumptions. The best relay selection schemes proposed in the literature for amplify-and-forward (AF) based underlay cognitive relay networks have been very well studied in terms of outage probability (OP) and bit error rate (BER), which is deficient in multiple relay selection schemes. The novelty of this work is to study the outage behavior of multiple relay selection in the underlay CRN and derive the closed-form expressions for the OP and BER through cumulative distribution function (CDF) of the SNR received at the destination. The effectiveness of relay subset selection is shown through simulation results.

In this article, the authors study the convergence of an iterative algorithm for the joint estimation of the signal-to-noise ratio (SNR) and the transmission channel in orthogonal frequency division multiplexing context. At each step of the algorithm, the authors use the minimum-mean-square error (MMSE)-based SNR estimation, which feeds the linear MMSE channel estimation. Reciprocally, this efficient channel estimation is used to perform the SNR estimation. The authors provide a proof of convergence of the algorithm to a single value. Furthermore, we derive an accurate approximation of the bias of the estimation. Simulations show that the algorithm converges quickly and verifies the theoretical results. They also show the efficiency of both SNR and channel estimation. By comparing with the existing methods, the authors show that the tradeoff between the number of required pilots in the preamble and the performance of the SNR estimation were improved. Furthermore, for a fixed bit error rate, the SNR gap between the proposed channel estimation and the perfect one is <0.5 dB.

Energy efficiency (EE) is an important issue at 60 GHz due to high power consumption of devices working at such high frequency. In this paper, we investigate EE optimization for full-duplex (FD) decode-of-forward (DF) relay-assisted 60 GHz multiuser indoor networks. In contrast to the existing spectral efficiency (SE) optimization, our scheme maximizes system EE for FD relaying system under cross-layer constraints, addressing the typical problems at 60 GHz, such as the effect of imperfect channel estimation due to serious signal blockage. A low-complexity EE-orientated optimization algorithm is proposed, by which the transmission power, subcarriers and throughput are allocated jointly across multiple users. Simulation results verify our analytical results and confirm that the proposed algorithm achieves a higher EE than the SE-oriented approach, while offering a comparable SE. Also, FD relaying with the proposed algorithm outperforms HD relaying in terms of both EE and SE. In addition, a much lower throughput outage probability is guaranteed by the proposed algorithm, showing its robustness against channel estimation errors. A full range of power consumption sources and imperfect self-interference cancellation are considered to rationalize our analysis.

In this paper, we study upper and lower bounds on the achievable sum-rate of an uncorrelated multiple-input multiple-output (MIMO) multiple access channel (MAC) for Gaussian input signals and with channel estimation error at the receiver. We prove that the gap between the mutual information bounds does not exceed a certain value for arbitrary input covariance matrices and at any input transmit power. We also prove that in a MIMO MAC with uniform input power utilization over the transmit antennas, the gap between the mutual information bounds increases monotonically as the input power of each user increases. Furthermore, we show that the gap between the bounds is maximum when beamforming is applied at the transmitters of all users. We also derive the transmit directions that maximize the mutual information lower and upper bounds when delayed feedback is available from the receiver to the transmitters, and characterize the power allocation of this system in terms of its beamforming range. Numerical simulations are conducted to corroborate our theoretical results and quantify the effect of imperfect channel estimation.

A hybrid overlay/underlay cognitive radio network (CRN) is demonstrated to provide high spectrum efficiency and channel capacity. Decision‐making in joining CRNs is one of the major issues of secondary users (SUs). Each SU has the option of joining the spectrum or balking according to the trade‐off between the service profit and the delay cost. In this study, the decision‐making problem in accessing the hybrid overlay/underlay CRN is addressed using queuing models and game theory. An almost unobservable queuing server is used to model hybrid overlay/underlay CRN. The interaction between the cognitive users is treated as a non‐cooperative game. A closed‐form expression for the average number of cognitive users as well as associated expected waiting time in both overlay and underlay CRNs is derived. The strategic behaviour for spectrum access of cognitive users in hybrid overlay/underlay CRN is investigated and the existence of symmetric Nash equilibrium is proved as well. Finally, we provide extensive validation results using a wide range of realistic simulation scenarios. The proposed model gives detailed guidance to the decision makers to deploy the suitable strategy according to the available channel situation.

In the next-generation wireless communication systems, the broadband signal transmission over wireless channel often incurs the frequency-selective channel fading behavior and also results in the channel sparse structure which is dominant by very few large coefficients. To ensure the stable wireless propagation, various linear adaptive channel estimation algorithms, e.g., recursive least square (RLS) and least mean square (LMS), have been developed. However, the traditional algorithms are unable to exploit the channel sparsity. Supporting by the compressive sensing (CS) theory, channel estimation performance can be further improved by taking advantage of the sparsity. In this paper, RLS based fast adaptive sparse channel estimation algorithm is proposed by introducing two sparse constraint functions, L1-norm and L0-norm. To improve the flexibility of the proposed algorithms, this paper introduces a regularization parameter selection method to adaptively exploit the channel sparsity. Finally, Monte Carlo based computer simulations are conducted to validate the effectiveness of the proposed algorithms based robust channel estimation either for sparse or non-sparse channel.

The present contribution investigates the physical layer security in a cognitive radio network (CRN). To this end, we consider an underlay uplink CRN consisting of multiple secondary sources, a single-antenna secondary base station, and multiple eavesdroppers. In addition, we assume that the secondary sources transmit their data sequentially and that a jammer is randomly chosen from the remaining source nodes to send a jamming signal to the eavesdroppers. However, in an uplink underlay CRN, a friendly jammer is not always allowed to use its maximal transmit power as the secondary users are required to continuously adapt their power in order to avoid causing interference to the primary users. As a consequence, enhancing the system security using a jammer with low transmit power in the presence of numerous eavesdroppers turns out to be questionable. In this regard, we derive novel analytic expressions that assist in quantifying the achievable security levels and the corresponding limitations. This leads to the development of useful insights on the impact of network parameters on the performance of the system’s security. The offered analytic results are corroborated through Monte Carlo simulation. It is shown, that for a low transmit power of the friendly jammer, the system’s security can only be enhanced for a small number of eavesdroppers.