In this paper, we study an information-theoretic secret sharing problem, where a dealer distributes shares of a secret among a set of participants under the following constraints: (i) authorized sets of users can recover the secret by pooling their shares, and (ii) non-authorized sets of colluding users cannot learn any information about the secret. We assume that the dealer and participants observe the realizations of correlated Gaussian random variables and that the dealer can communicate with participants through a one-way, authenticated, rate-limited, and public channel. Unlike traditional secret sharing protocols, in our setting, no perfectly secure channel is needed between the dealer and the participants. Our main result is a closed-form characterization of the fundamental trade-off between secret rate and public communication rate.

We study a secret sharing problem, where a dealer distributes shares of a secret among a set of participants under the constraints that (i) authorized sets of users can recover the secret by pooling their shares, (ii) non-authorized sets of colluding users cannot learn any information about the secret. We assume that the dealer and the participants observe the realizations of correlated Gaussian random variables and that the dealer can communicate with the participants through a one-way, authenticated, rate-limited, and public channel. Our main result is a closed-form characterization of the trade-off between secret rate and public communication rate. Unlike traditional secret sharing protocols, in our setting, no perfectly secure channel is needed between the dealer and the participants, and the size of the shares does not depend exponentially but rather linearly on the number of participants and the size of the secret for arbitrary access structures.

Current state-of-the-art in global positioning system (GPS) anti-jam technology has relied on a phase array antenna that consists of N antenna elements and a processing unit that performs a phase-destructive sum of any intentional and unintentional jamming up to N-1 signals. If this limitation is exceeded, then the GPS signal will degrade rapidly and become buried in the noise. Hence, alternative anti-jamming technologies have been sought recently. This paper describes an anti-jam method that can suppress more than N-1 jamming signals with a significant reduction in size, weight, and power (SWaP) and no degradation under additive white Gaussian noise (AWGN).

Cell association is a critical aspect of cellular network operation wherein mobile terminals (MTs) connect to optimal base stations before commencing data transmission and reception. This paper investigates a novel physical layer security problem wherein malicious base stations (MBSs) seek to subvert the cell association process by spoofing the common reference signals of legitimate base stations (LBSs). Since these signals are used by MTs to measure signal strength, the MBSs thus attempt to increase the likelihood of MT radio link failure (RLF). A stochastic geometry approach using a Poisson point process (PPP) to model the random locations of LBSs and MBSs is used to analyze the impact of this attack. We analytically derive the conditional probability of the RLF given a suboptimal association triggered by MBSs and verify the theoretical results using simulations. This paper also presents insights on the appropriate ranges of thresholds for MTs seeking association with LBSs and claiming RLF using the conditional RLF probability triggered by MBS attacks.

Taking advantage of information and communication technologies, the power industry is moving towards the next generation power grid, the smart grid. This information-based power grid is expected to change the way electricity is generated, distributed, and transmitted to the consumers by enhancing the reliability, efficiency, sustainability, and economics of the grid. However, due to the high volume and high granularity of the data generated by smart electricity meters, careful planning and management of this communication network is necessary. Given the large scale future deployment of smart grid, utility companies face possible network capacity constraints. Due to this scarcity, an efficient spectrum allocation is often difficult, thus resulting in low overall bandwidth utilization in Smart Grid Networks (SGN). Hence, an efficient utilization of this communication network should be studied. Cognitive Radio Networks (CRN) enable Secondary Users (SU) to coexist with existing network infrastructures. Cognitive Smart Grid Networks (CSGN) use CRN to optimize resource allocation in SGNs. However, efficient utilization of available channel bandwidth by SUs, without interfering with the Primary Users (PU), remains an important open problem in CSGN. In this paper, we focus on CSGN as the Secondary Network (SN), coexisting with a Primary Network, and outlining the applicability of Code Division Multiple Access for overcoming the low Number of SUs (NSU) in SN. We propose a novel resource allocation technique to improve NSU in CSGN by using a specific kind of Orthogonal Chip Sequence (OCS) allocation in spread spectrum communications for SU transmissions. By means of extensive simulations and analysis, we show that our technique improves NSU on SN (or CSGNs) significantly.

In this work, we proposed user selection strategies for downlink of multiple input and multiple output (MIMO) cognitive radio (CR) network. Underlay CR secondary users (SUs) are selected by cognitive base station (CBS) to share subchannel with primary users (PUs). It is assumed that the cross interference channel from cognitive radio base station to PUs is not known. CBS selects underlay SUs based on the knowledge of SUs transmission channels in order to reduce the interference from base station to PUs. We propose and evaluate user selection schemes with low computational complexity and best-effort interference mitigation to PUs.

This paper proposes minimum mean square error (MMSE)-based amplify-and-forward (AF) relay amplifying matrices under perfectly and imperfectly known channel state information by imposing a constraint on the transmit power of the relays. The main objective of this paper is to determine optimal relay amplifying matrices with and without channel uncertainty under the transmit power constraint at the relays. Additionally, by using the derived optimal relay amplifying matrices, it is proven that the better BER performance is observed when power is constrained at the relays during data transmission, compared to the no-power constraint case in [6]. Finally, simulation results show that the MMSE cost function values with and without channel uncertainty are always less than the number of sources and destinations (M), regardless of the number of relays (N).

This paper considers a downlink relay network where source communicates with the receivers through relays under frequency-selective fading channels. A spreading sequence design scheme, which is subjected to maximizing the signal-to-interference- plus-noise ratio (SINR) is proposed. It is shown through simulations that a better bit error rate (BER) can be achieved using this proposed scheme. The sensitivity of the proposed scheme to channel uncertainty and broadband noise jamming is also examined.

Millimeter wave (mmWave) signals experience a significant path-loss in free space. To overcome this weakness, a large number of antennas are needed to obtain a high beamforming gain. Although a large number of antennas can be implemented in small area due to the short wavelength, the digital beamforming techniques cannot be implemented easily due to the high complexity of hardwares. To solve this problem, the hybrid beamforming systems which have smaller number of radio frequency (RF) chains are proposed in the literature. Although the hybrid beamforming systems may achieve the spectral efficiencies of the digital beamforming systems closely, the spectral efficiency cannot be monotonically increase along with the number of data streams due to the limited scattering in mmWave channel. In this paper, we provide a guide for the design of mmWave hybrid beamforming systems. We find the optimal number of streams, and present the spectral efficiency achievable region in which the system guarantees the reliable communications with the lowest cost.

This paper addresses optimum nondiagonal and diagonal amplifying relay matrices for the amplify- and-forward (AF) wireless relay networks. Single- input multiple-output (SIMO) nondistributed and distributed relaying system strategies with the relay power constraint are applied, based on the signal-to-noise ratio (SNR) criterion. By adopting the optimum amplifying relay matrices derived, the SNRs at the destinations are analytically and numerically investigated in order to evaluate the proposed system. In particular, using the SNR values, it can be predicted which scheme would yield a better system performance than the others.

Two different two-way amplify-and-forward (AF) wireless relay systems with transmit power constraints at the relay(s) are studied: one- relay system with multiple N antennas between two sources, and multiple N-relay system with one antenna per relay between two sources. The iterative and explicit relay amplifying matrices (or vectors) with perfect cancelation of self- interference under channel uncertainty are determined based on the minimum mean square error (MMSE) criterion. Both iterative and explicit relay amplifying matrices are numerically investigated through the simulation. Simulation results show that the gain of diversity order with channel uncertainty can occur as N increases, while the loss of diversity order can occur as channel estimation error powers increase.

This paper proposes amplify-and-forward (AF) relay strategies for two-way wireless distributed relay networks consisting of two sources with a single antenna per source and multiple N relays with a single antenna per relay. The objective of this paper is to determine optimal relay amplifying matrices (or vectors) under global and local power constraints at the relays based on the minimum mean square error (MMSE) criterion with/without the perfect cancelation of self-interference. With the derived optimal relay amplifying vectors, performances of the proposed two-way AF distributed relay system are investigated by presenting average bit error rate (BER), average MMSE behavior, and the sum of the achievable rate.

This paper presents optimum relay amplifying matrices (or vectors) using the minimum mean square error (MMSE), maximum signal-to-noise ratio (SNR), zero-forcing (ZF), and matched-filter (MF) criteria for an amplify-and-forward (AF) wireless distributed relay network with a one-source-one-destination pair and iV-relay under the global power constraint (GPC) at the relays in a channel uncertainty (CU) environment. In addition, the local power constraint (LPC) at the relays is also considered for the MMSE criterion. With the derived optimum amplifying relay matrices, cost function and SNR behaviors, achievable rate, and relay selection scheme in the CU environment will be investigated theoretically and evaluated numerically.

An aggregate medium access control (MAC) service data unit (A-MSDU) contains multiple subframes with a single sequence number. Hence, it has a major drawback in environments with high error rates because if any subframes are corrupted, then the entire A-MSDU will be lost. In addition, performance of the A-MSDU depends strongly on the choice of parameters, such as frame size, modulation level, coding rate, and spatial mode. In this paper, a novel link-adaptation mechanism, dubbed physical (PHY)supported frame aggregation (PSFA), is proposed over IEEE 802.11 networks, and its performance is analyzed. The proposed PSFA technique is based on a cross-layer interaction that enables joint optimization of various parameters between the PHY and MAC layers. This paper derives a new packet error rate (PER) expression for convolutionally coded multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems as an example. Then, this PER expression is used to efficiently estimate the link quality, given the channel conditions and system parameters, and most importantly, it is able to facilitate a parametric study of the cross-layer interaction. In the proposed PSFA algorithm, we present a rule for selecting the parameters so that MAC throughput is maximized. It is shown analytically and verified using Monte Carlo simulations that this choice of parameters can improve throughput performance significantly and also ensure quality of service (QoS) requirements compared to existing conventional algorithms.

This paper presents a closed form of an optimal cooperative amplify-and-forward (AF) relay amplifying matrix for a distributed relay network of M-source-M-destination pairs and N relays, called a cooperative distributed AF relay network. The objective of this paper is to derive closed forms of minimum mean square error (MMSE)-based and zero-forcing (ZF)-based optimal AF relay amplifying matrices for the cooperative distributed AF relay network under the transmitter power constraint (TPC) at the relays, the receiver power constraint (RPC) at the destinations, and the no-power constraint (NPC) condition. Additionally, by substituting the derived optimum AF relay amplifying matrices into the original cost functions (CFs), the behavior of the optimum CFs and the total optimum signal component power (SCP) at the destinations are compared to each other for different cases. Finally, using the MMSE criterion, a novel relay selection scheme is proposed for the cooperative distributed AF relay network.

This paper proposes a cooperative wireless relay network consisting of a one-source-one-destination node pair and N relay nodes in three wireless communication environments, i.e., jamming, node geometry, and channel uncertainty. The main objective of this paper is to analytically derive the optimal cooperative amplify-and-forward (AF) wireless relay matrix under three conditions with the relay power constraint based on the minimum mean square error (MMSE) criterion. Using the derived amplifying relay matrix, the MMSE cost function and achievable rate will be investigated numerically and analytically.

A method for a spreading sequence design based on signal-to-interference-plus-noise ratio (SINR) is presented in this paper. It considers the relay channel where sources communicate with the receiver via relays under frequency selective fading. We examine the design of the user spreading sequences based on exploiting channel state information. We also examine the sensitivity of the proposed schemes to broadband noise jamming at the destination.

A cooperative amplify-and-forward (AF) wireless relay scheme consisting of M sources, N relays, and L destinations all equipped with a single antenna is studied in this paper. The main objective is to design jointly and iteratively the closed-form of minimum mean square error (MMSE)-based source precode and relay amplifying matrices under a jamming environment with transmit power constraints and aggregate power constraints. With the derived optimal source precode and relay amplifying matrices, the jamming influence on system performance with both transmit and aggregate power constraints is examined numerically by using Monte-Carlo simulations.

This paper studies amplify-and-forward (AF) relay strategies for two-way wireless relay networks consisting of two sources with a single antenna and multiple relays with a single antenna. The closed form of relay amplifying matrices (vectors) with the perfect cancelation of self-interference under both no channel uncertainty and channel uncertainty is presented based on the minimum mean square error (MMSE) criterion. With the derived optimal relay amplifying matrices, the MMSE cost function behavior, the relay power usage, and the sum of the achievable rate are analyzed. Additionally, a filter for each destination will be provided to remove the influences of noises at the receivers.

An amplify-and-forward (AF) relay network has been studied extensively, but a closed form of an optimal AF relaying matrix is not available yet for the distributed AF relay network with the destination power constraint (DPC) and the following adverse environments: (a) partial-band noise jamming (PBNJ), (b) node geometry (NG), and (c) channel uncertainty (CU). Hence, this paper presents a closed form of an optimum AF relaying matrix consisting of a one-source-one-destination pair and N relay nodes under such adverse PBNJ, NG, CU, and DPC environments, based on the minimum mean square error (MMSE). By adopting the optimal relay amplifying matrix, the MMSE cost function behaviors are analytically and numerically studied.

This paper studies both cooperative and noncooperative amplify-and-forward (AF) wireless relay strategies with power constraints at the source and at the relays. The main objective is to design jointly and iteratively the closed form of a source scaling factor and a relay amplifying matrix, based on the minimum mean square error (MMSE) criterion under the conditions of both no-channel and channel phase misalignments. With the derived optimal source scaling factors and relay amplifying matrices, impacts on the system performance of both no-channel and channel phase misalignment are investigated by presenting the bit error rate and cost function behavior. Finally, this paper presents the iterative algorithm to solve the constrained Lagrangian optimization problem with a low computational complexity.

This paper addresses a more practical relay network consisting of a mobile source, multiple distributed mobile amplify-and-forward (AF) relays, and a mobile destination node. It considers an appropriate channel model between nodes, which is a cascaded Rayleigh fading channel. The objective of this paper is to determine an optimum AF relay vector (or matrix) using the minimum mean square error (MMSE) criteria for these distributed AF relay networks. The effects of jamming and imperfect channel state information (ICSI) on network performance are included in the analysis. Additionally, by substituting the derived amplifying relay vectors into the MMSE cost functions, it can be predicted which case will yield a better BER performance.

This paper presents both cooperative and noncooperative amplify-and-forward (AF) relay networks consisting of a one-source-one-destination pair and N-relays under receiver power constraint (RPC) at the destination. The optimal AF relay amplifying matrices for the relays by minimizing the mean square error are analytically derived. This paper also shows that the performance of the optimum cooperative relay network is identical to that of the optimum noncooperative network, as long as the same receiver power constraint is applied. The purpose of the RPC is to reduce the interference level for users located in neighboring cells. Finally, using the derived optimal relay amplifying matrices, the achievable rate, the pairwise error probability, and the outage probability are investigated.

This paper proposes amplify-and-forward (AF) relay matrices for a one-source-one-destination pair and cooperative distributed N relay nodes under three adverse wireless relay communication environments: (1) broadband noise jamming (BNJ), (2) node geometry (NG), and (3) channel uncertainty (CU). The main objective of this paper is to analytically derive the minimum mean square error (MMSE)-based optimal relay amplifying matrix. Another objective of this paper is to analyze the MMSE cost function, relay power usage, and signal component power of the received signal at the destination using the derived optimal relay amplifying matrix. Finally, the impacts on these three wireless communication environments for the wireless relay networks will be observed by presenting bit error rate (BER) performance.

This paper assumes a practical channel model, called a cascaded Rayleigh fading channel, for a noncooperative distributed mobile relay network, which consists of one mobile source and one mobile destination, and multiple mobile amplify-and-forward (AF) relays. Then, an optimum AF relay amplifying vector (or matrix) is analytically designed using the minimum mean square error (MMSE) criteria and uses it for an efficient mobile relay selection. Power is intentionally not constrained. Instead, this paper presents a scaling factor scheme to meet a target signal-to-noise ratio (SNRTGT) at the destination. This SNRTGTstrategy can implicitly embrace the power constraint problems and be a more practical implementation.

This paper proposes an optimal power allocation method for two-way decode-and-forward (DF) relay networks when transmit power values at source nodes are the same. In this paper we consider the multiple access (MAC) capacity for DF relaying scheme. Using case studies, it analytically determines the optimal power values for the two source nodes and one relay node. The achievable sum rate is maximized under a sum power constraint for given squared magnitude of the channel coefficients. Finally, numerical results show that the achievable sum rate for proposed optimum power allocation is greater than or equal to that for equal power allocation.

Inter-carrier interference (ICI) and multiuser interference (MUI) occur in an uplink orthogonal frequency division multiple access system if a channel between a mobile user and a base station is rapidly time-varying. To reduce the ICI and MUI, this letter proposes a subcarrier allocation method. The key idea is to allocate a high-speed user's subcarrier near a low-speed user's one. Then, a wide Doppler spread of a high-speed user can be spilled over a low-speed user's subcarrier band with insignificant influence, and the signal-to-interference-plus-noise ratio (SINR) at each high-speed user's subcarrier can be maximized. This can provide a significant performance improvement of multiuser detection in an uplink-OFDMA.

This letter is to correct the incorrect optimal relay coefficient at the k-th relay derived in [1] for an amplify-and-forward (AF) wireless relay network under received power constraints. While the trends remain the same, with the correct optimal relay coefficient in this paper, nonnegligible improvement, e.g., about 0.8 dB at BER = 10-7, can be achieved.

In a multiple-input multiple-output (MIMO) system of a large number of antennas, the requirement of an analog to digital converter (ADC) in each antenna string causes high implementation cost and excessive signal processing. Hence, a hybrid beamforming has been proposed in the literature as a solution. However, still quantization errors introduced at the analog beamformer part can lead to performance degradation. This paper is to present a quantization error reduction scheme for a hybrid beamformer in a 2 by 2 MIMO system. The key idea is to sacrifice the data rate from a full rate to a half rate, estimate all user data in a digital baseband, and then restore the received signal at each antenna string. By using the restored received signal and the residual (which is calculated in the estimator), quantization error can be reduced. Simulation results verify that the proposed scheme can improve the bit error rate performance with a resolution of smaller number of bits.

This paper presents an optimal amplify-and-forward (AF) relay scheme for a multiple-input-multiple-output (MIMO) system consisting of M-mobile sources, M-mobile destinations, and N-cooperative distributed mobile relay nodes. A wireless mobile relaying network with channel state information is investigated. The received signals from the mobile sources are ex- changed between mobile relays to achieve optimal performance. The main contribution in this paper is the derivation of mobile relaying amplifying matrices (MARMs) designed for cooperative MIMO networks based on the minimum mean square error (MMSE) criterion. By adopting the new proposed MRAMs, the bite error rate (BER) performance of the system is evaluated using Monte-Carlo simulations.

This paper studies minimum mean square error (MMSE)-based full-duplex relay processing matrices and source/destination beamforming vectors under perfect channel state information by imposing constraints on the transmit power of source, relay, both, separately, and in various combinations. The main contribution of this paper is the derivation of a set of relay processing and source/destination beamforming vectors under diverse conditions of transmit power constraints on the source and relay. By comparing the bit error rate (BER) performance of each case, an efficient design of a full-duplex amplify-and-forward relay system is presented.

This paper considers an amplify-and-forward (AF) relay scheme for M-source-M-destination pairs and N relay nodes. Cooperative minimum mean square error (MMSE) strategies for wireless relay networks under both a jamming environment and channel uncertainty with received power constraints at the destination nodes are studied. The main contribution of this paper is the derivation of the MMSE-based amplifying relay matrices (ARMs) under both a jamming environment and channel uncertainty. With the proposed ARMs, the system performance under study is evaluated by observing bit error rate (BER) using Monte Carlo simulations. In addition, it is proven that the proposed ARM is the global optimal ARM.

This paper shows how to obtain the capacity of modular additive noise of an arbitrary single-input- single-output (SISO) relay network. The arbitrary SISO relay network is a network where the relays are interconnected with each other in various combinations. Its capacity is obtained by using a quantize-and-forward (QAF) strategy at each relay node. This paper considers all channels as discrete memoryless channels. In order to obtain the capacity of an arbitrary SISO relay network, this paper simplifies the network in terms of a parallel and serial relay network and finds the capacity. First, the capacity expression for a parallel relay network is obtained. In a parallel relay network, the source is transmitted to all relays; then each relay, using a QAF strategy, forwards the source to the destination. Second, the capacity expression for a serial relay network where the relays are interconnected serially is obtained. Finally, after expressing the capacities for parallel and serial relay networks, this paper explains how to obtain the capacity for any arbitrary SISO relay network.

As channel time-variation increases, orthogonality among subcarriers in an orthogonal frequency division multiplexing (OFDM) symbol can be destroyed because of the relatively long symbol period, whereupon intercarrier interference (ICI) appears, and hence an irreducible error floor occurs. It was shown recently that grouping pilot tones into a number of equally spaced clusters can yield better channel estimation against the doubly selective channel than placing each pilot tone in an equally spaced manner. However, a random pilot sequence was used in the literature, and an optimal sequence has not yet been studied. This paper presents how to optimize the clustered pilot sequence. First, this paper (a) proves the existence of an optimum pilot sequence and (b) suggests a guideline for finding an optimum sequence. Second, this paper shows that an optimum sequence is independent of the signal-to-noise ratio and Doppler rate, and the sequence is generally optimum for any channels. Third, this paper verifies through analysis and simulation that the coded-OFDM system with an optimized cluster pilot sequence can yield a smaller mean square channel estimation error and lower bit error rate than the system with an equidistance pilot or a random cluster pilot under a rapidly time-varying channel.

This paper derives an optimum relay amplifying matrix for a wireless relay network under channel uncertainty and received power constraints at the destination node. To achieve this objective, an amplify-and-forward strategy is employed at the relay nodes, and the minimum mean square error (MMSE) criteria is applied. And, for simplicity, this paper will assume a one-source-one-destination pair and N multiple relays. Then this paper will compare the bit error rate (BER) performance of the proposed relay network with that of other existing schemes, and also claim that the proposed relay amplifying matrix can improve BER significantly, compared to other existing schemes.

This paper derives analytically an optimum amplifying relay matrix using the minimum mean square error (MMSE) criteria for a noncooperative amplify-and-forward (AF) distributed relay network. Global and local power constraints are included in the analysis. And a one-source-one-destination node pair and N-relay network is considered. Because the relays are noncooperative, this paper exploits the diagonal property in an amplifying relay matrix for the optimum matrix derivation. Then, this paper claims that the bit error rate of the AF network using the proposed amplifying relay matrix is significantly better than that of the AF network with the other existing amplifying matrices.

This paper presents channel capacities of parallel and serial modulo-sum relay networks. A parallel relay network consists of one source, multiple relays in parallel, and one destination node. A serial relay network consists of one source, multiple relays in serial, and one destination node. Each relay employs a quantize-and-forward (QAF) strategy. Each node including source, multiple relays, and destination, employs its own codebook for its own encoding and or decoding. Every node has information of the other nodes codebooks. And every addition in any channel is a modulo-sum. First, this paper presents the capacities for the binary modulo-sum symmetric parallel, and serial relay networks, assuming that the channels are discrete and memoryless. Second, this paper claims that the capacities obtained are strictly below the cut-set bounds except the trivial cases. Third, this paper extends the capacities obtained for the binary modulo-sum relay networks to the m-ary modulo-sum relay networks. Finally, this paper presents the closed form capacities for a worst direct channel which is a binary modulo-sum symmetric channel with a crossover probability of 1/2.

In this paper, a novel four symbols Finite Dimensional Modulation (4FDM) in three dimensional scheme with polarization diversity is presented that seeks to combine the advantageous features of phase shift-keying and conventional orthogonal modulation. Different from QPSK, the four symbols in 4FDM are allocated in three-dimensional Euclidean space to improve the energy efficiency. In addition, the polarization diversity is attached to the proposed system in order to reduce the waste of bandwidth. Analytical results are obtained for the exact symbol and bit error performance of the 4FDM design in additive white Gaussian channels. By computer simulation, the error probability and bandwidth efficiency of the 4FDM scheme are compared with conventional two-dimensional and orthogonal modulation designs such as PSK, QAM, and FSK.

An inter-carrier interference (ICI) occurs in an orthogonal frequency division multiplexing (OFDM) system when a channel is rapidly time-varying. The proposed scheme employs a polynomial cancellation code (PCC) to suppress this ICI, and uses a linear complex field (LCF) code as a transmit-diversity technique to make the transmission rate compatible up to {nT} / {(nT+1)}, where nTis the number of transmit antennas used. The conventional orthogonal code (OC), such as the Alamouti code, with accompanying PCC cannot achieve this rate. Both analysis and simulation results verify that the proposed scheme can achieve higher channel capacity as well as lower bit error rate (BER) than the other schemes in rapidly time-varying channels, even with a linear receiver and inaccurate channel estimation.

In this paper, a cooperative system with two users and one relay is considered. An amplify-and-forward relaying protocol is applied in a half duplex mode. To make the transmission delay as short as possible, the relay forwards for both users simultaneously. We consider transmission schemes with symbol rates 2/3 to demonstrate the tradeoff among performance, delay, and symbol rate. Based on the analysis for the pairwise error probability (PEP), an optimal precoder is proposed to achieve the full diversity and best coding gain. Simulations show that the proposed precoder can provide about one dB improvement over some conventional space-time block codes at bit error rate 10-4.

This paper proposes an annular-ring microstrip antenna for a 2×2 MIMO communication system. A single annular-ring microstrip antenna with two feed probes is used to generate two orthogonal radiation patterns. Radiation pattern associated with each probe is generated by FEKO simulations and shown that the patterns are orthogonal to each other. Orthogonal radiation patterns are needed to exploit pattern diversity instead of space diversity. Miniaturization is achieved by using a ferrite substrate instead of using a pure dielectric substrate. A ferrite annular-ring antenna with a single feed probe was manufactured and tested. Also a ferrite single circular patch antenna was manufactured and measurement results are presented.

This paper proposes a novel multi-dimensional modulation (MDM) scheme that achieves better performance than conventional modulation without any diversity or coding gain. We exploit the additional degrees of freedom offered by higher dimensional Euclidean space to construct the proposed constellation design. Analytical results are obtained for the exact symbol and bit error performance of the MDM design over Gaussian and Rayleigh fading channels. Through simulation, we compare the error performance of the MDM scheme with conventional orthogonal modulation.

It is unrealistic to assume that all nodes in an ad hoc wireless network would be willing to participate in cooperative communication, especially if their desired Quality-of-Service (QoS) is achievable via direct transmission. An incentive-based auction mechanism is presented to induce cooperative behavior in wireless networks with emphasis on users with asymmetrical channel fading conditions. A single-object second-price auction is studied for cooperative partner selection in single-carrier networks. In addition, a multiple-object bundled auction is analyzed for the selection of multiple simultaneous partners in a cooperative orthogonal frequency-division multiplexing (OFDM) setting. For both cases, we characterize equilibrium outage probability performance, seller revenue, and feedback bounds. The auction-based partner selection allows winning bidders to achieve their desired QoS while compensating the seller who assists them. At the local level sellers aim for revenue maximization, while connections are drawn to min-max fairness at the network level. The proposed strategies for partner selection in self-configuring cooperative wireless networks are shown to be robust under conditions of uncertainty in the number of users requesting cooperation, as well as minimal topology and channel link information available to individual users.

In this paper, we describe direct-sequence code-division multiple-access (DS-CDMA) systems with quadriphase-shift keying in which channel estimation, coherent demodulation, and decoding are iteratively performed without the use of any training or pilot symbols. An expectation-maximization channel-estimation algorithm for the fading amplitude, phase, and the interference power spectral density (PSD) due to the combined interference and thermal noise is proposed for DS-CDMA systems with irregular repeat-accumulate codes. After initial estimates of the fading amplitude, phase, and interference PSD are obtained from the received symbols, subsequent values of these parameters are iteratively updated by using the soft feedback from the channel decoder. The updated estimates are combined with the received symbols and iteratively passed to the decoder. The elimination of pilot symbols simplifies the system design and allows either an enhanced information throughput, an improved bit error rate, or greater spectral efficiency. The interference-PSD estimation enables DS-CDMA systems to significantly suppress interference.

This paper presents one miniaturized circular patch antenna (1-CPA) instead of two CPAs to generate multimode patterns for multiple-input multiple-output (MIMO) communication systems. A suitable material composition using ferrite substrate materials is proposed. The proposed ferrite 1-CPA is tested using the FEKO simulator, and it is found that the size of the proposed ferrite 1-CPA can be significantly smaller, e.g., 25.7 times, than that of the recently developed dielectric two-CPAs stacked. However, the bandwidth of the proposed ferrite 1-CPA should be sacrificed by one quarter.

Multiuser diversity has been extensively studied to enhance wireless system capacity by always scheduling the strongest user for transmission. In this extended abstract, we propose an extension of this concept termed as 'group diversity', applied to a large coded cooperation network. Specifically, we examine the problem of partner selection, and which cooperative group to schedule for cooperation with a fixed common destination, when there are multiple groups competing for a cooperative time slot. A coalitional game theory approach is formulated to examine how cooperative groups can form in a distributed manner, as well as possible group scheduling methods. Simulation results are presented for the case of self-interested, rational users with an utility function based on the coded-cooperation capacity.

This paper proposes a novel orthogonal frequency- division multiplexing (OFDM)-based iterative channel estimation and irregular repeat-accumulate (IRA) decoding scheme where the pilot symbols are encoded along with the input data and are used for both channel estimation and decoding. To achieve the objective of minimizing the bit error rate, this paper employs systematic IRA codes so that pilot symbols can be encoded as part of the data. In this way, initial channel estimation can be performed using the systematic encoded pilot symbols before channel decoding. In addition, the known pilot symbol positions have higher reliability than data and can significantly improve the initial decoding. The availability of channel state information (CSI) at the transmitter via feedback from the receiver is also exploited by introducing a second pilot permutation that adapts to the receiver channel conditions, which is shown to outperform the conventional uniform pilot spacing within the OFDM symbol. Simulation results verify the improvement in performance compared to iterative OFDM receivers with either un-encoded or encoded uniformly-spaced pilot symbols without CSI feedback.

Coalitional game theory is a promising tool for analyzing the dynamics of networks that implement cooperative protocols. In this paper, we examine the stable outcomes of a self-organizing cooperative network based on decode-and-forward relaying, namely, orthogonal (ODF) and non-orthogonal decode-and-forward (NDF) relay networks. A coalitional game theory approach is formulated to examine how cooperative groups would form in a distributed manner, as well as possible resource allocation methods within groups. Numerical results are presented with a utility function based on the ergodic capacity, which reveal a trade-off between sum-rate and diversity for the ODF system. For the NDF network, it is shown that it is always beneficial for all users to cooperate as a single group.

This paper considers a novel approach to multicarrier orthogonal frequency division multiplexing-based interleave-division multiple-access (OFDM-IDMA) that facilitates both channel estimation and multi-user detection. Specifically, users employ interleavers based upon their channel state information (CSI) to optimize pilot symbol locations, instead of random interleavers as in conventional IDMA. Two variants of this approach are considered: pilot symbols time-multiplexed into the transmit signal after channel encoding, and pilot symbols encoded along with the information bits prior to CSI-based relocation. The encoding of pilot symbols is shown to offer an additional performance benefit at the channel decoders. Simulation results are presented to verify the advantages of the proposed methods with respect to conventional IDMA with uniform and/or uncoded pilot symbols.

This paper proposes a novel joint source coding and modulation scheme. The modulation constellation points are selected according to their prior symbol probabilities for better bandwidth as well as better bit error rate performance. Both the analysis and simulation results are presented to verify that the proposed scheme can achieve better performance than the conventional disjoint source coding and modulation schemes if the modulation and source coding are designed jointly and efficiently.

This paper introduces a modified UCA- ESPRIT algorithm to estimate the direction of arrival (DOA) of coherent signals using one single snapshot. First, the mode excitation method is used to transform the uniform circular array (UCA) in element space into a virtual uniform linear array (VULA) in mode space. Then, the Hermitian Toeplitz matrix can be reconstructed from the observed data vector as a decorrelated algorithm. The purpose for using the Hermitian Toeplitz matrix is to rearrange the data in order to extend the dimensionality of the noise space. Consequently, signal and noise spaces can be estimated more accurately. The proposed method does not need forward/backward spatial smoothing of the covariance matrix, which would result in reduced computational complexity. Simulation results verify that the proposed algorithm with one snapshot has a close performance to the conventional mode of spatial smoothing with 100 snapshots.

Recent research in multiuser MIMO systems has focused on providing partial channel state information (CSI) at the transmitter as an alternative to full CSI in order to reduce overhead. However, there is an implicit loss in data throughput even due to partial CSI feedback which is not included in conventional sum-rate computations. We introduce a sum-rate distortion model including the implicit loss for a multiuser MIMO downlink with block diagonalization. A distortion function is subsequently presented which accounts for quantization error at the receiver, feedback latency due to non-homogenous receiver channel coherence times and the loss in net capacity due to feedback overhead. This system model is used to derive bounds on the amount of feedback that can be supported under various antenna, channel and signal-to-noise ratio scenarios. Simulation results are presented to show the impact of feedback on the sum- rate for multi-antenna wireless systems with multiple users.

There is an implicit loss in data throughput due to channel state information (CSI) feedback for a multiple- input multiple-output (MIMO) system. This loss has usually not been considered in conventional sum-rate studies. Recently, a duplex model was introduced for a single-user point-to-point MIMO system to calculate the rate loss due to the feedback. This paper extends the duplex system model for a multi-user MIMO downlink with block diagonalization. In other words, this paper will determine the sum-rate loss and show what is the trade-off between user data and CSI overhead rate. In addition, effects of quantization error at the receiver and noisy feedback upon the loss in net system capacity are presented. Finally, simulation results verify the impact of feedback on the sum-rate for multiple user multi-antenna wireless systems.

A complete multiple-input multiple-output (MIMO) communication system with orthogonal frequency-division multiplexing (OFDM) based on multiple excitation modes for a single circular microstrip antenna is introduced. Traditional diversity techniques such as spatial diversity by means of a linear antenna array or polarization diversity by means of a cross-polarized antenna array may prove to be unsuitable in the case of severe restrictions on antenna size and spacing. A microstrip antenna employing multiple modes is found to be comparable to traditional antenna arrays in an urban micro-cell setting as defined by the Third-Generation Partnership Project (3GPP) at a much lower cost in terms of size and spacing. The throughput performance and signal detection of multimode antennas in flat and frequency-selective fading environments is examined subsequently.

The authors of this paper proposed an iterative expectation-maximization (EM) channel estimation based on a low-density parity-check (LDPC) code-division multiple access receiver in their previous work. The receiver algorithm could efficiently estimate both channel coefficients and noise power spectral density (PSD). However, their previous work considered only a single user channel environment, so they tested only for a constant noise PSD. In the current paper, we extend the single user to a more realistic multiuser environment for the testing of a time-varying interference plus noise PSD estimation. Also our proposed adaptive PSD estimation scheme will be compared with a conventional system in which a constant PSD is assumed. It will show that the proposed iterative EM scheme can provide accurate interference plus noise PSD estimates to the LDPC decoder.

This paper proposes a block diagonalization (BD) method, which nullifies the multiuser interference and, hence, increases the sum capacity in a multiuser multiple-input multiple-output (MU-MIMO) downlink system. The proposed BD scheme employs all users' receive processing as well as channel information. In addition, this paper proposes three adaptive mode selection schemes for the proposed BD: namely, an exhaustive mode search (EMS); an up-tree-based mode search (UTMS); and a down-tree-based mode search (DTMS). The EMS is a greedy search, whereas UTMS and DTMS are simplified searches that reduce the EMS computations significantly but have almost the same performance as the EMS. Simulation results show that the proposed BD method with the proposed adaptive mode selection schemes can increase the sum capacity significantly.

In this paper, we propose an algorithm to estimate the one- and two-dimensional direction of arrival angles (DOAs) from the coherent incident sources. We can apply our proposed algorithm for more practical situations even when the unknown noise covariance matrix is in a complex symmetric Toeplitz form; whereas the Prasad's method requires that the unknown noise should be in a real symmetric Toeplitz form. Our proposed method is based on the difference between the forward/backward spatial smoothing for the data covariance matrix and the Hermition of the backward spatial smoothing. This covariance matrix difference is introduced to eliminate the noise components from the array structure. The numerical results verify that the proposed method gives more accurate estimation and superior performance than the conventional root MUSIC of the forward/backward spatial smoothing.

This paper proposes an improved matrix pencil (MP) algorithm for estimation of non- circular, narrow-band, and coherent signal direction of arrival angles (DOAs). The MP method has advantages over the conventional subspace-based algorithms such as MUSIC and ESPRIT. For example, the MP method does not require multiple snapshots and spatial smoothing but rather a single snapshot observation to estimate DOAs. Hence, it is attractive for real-time applications. However, the MP method can estimate DOAs from up to N/2 number of coherent sources when N antenna elements are used. This paper proposes a modified MP method, which can estimate up to (N-l) coherent source DOAs and, furthermore, can improve performance of the MP algorithm significantly.

In this paper, we employ the propagator method (PM) to find the direction of arrival angles (DOAs) from the incident sources without any eigendecomposition. This can reduce complexity when compared to eigensubspace methods such as forward/backward spatial smoothing, which requires eigenvalue decomposition (EVD). Also, we apply our proposed algorithm in the situation when the incident sources are coherent. Our proposed algorithm can be applied for more practical situations when the unknown covariance noise matrix is in a complex symmetric Toeplitz form, whereas in Prasad's model the unknown noise is in a real symmetric Toeplitz form. Moreover, the proposed algorithm, when compared with Prasad's model does, has three advantages: (1) it does not require any EVD to find the DOAs, whereas Prasad's model does, (2) our proposed algorithm requires the number of sensors M to be larger than the number of sources K, i.e., M>K, but Prasad's method requires M>2K, and (3) the proposed method can be applied in the situation when the sources are coherent, but Prasad's method cannot. Our proposed method is based on a covariance matrix difference between the forward/backward spatial smoothing for covariance matrices of the received data and the Hermition of the backward spatial smoothing only. This difference is introduced to eliminate noise components from the array structure. The numerical results verify that the proposed method gives better performance and less computation than forward/backward spatial smoothing.

In this paper, a new direction-of-arrival (DOA) tracking algorithm, direction lock loop (DiLL), is proposed for wireless direct-sequence code-division multiple-access systems. It has a similar concept to the delay lock loop that is used for timing synchronization. It may track the DOA of sources by iterations. Its computational requirements are NK+O(K) for coherent DiLL and 2NK+O(K) for noncoherent DiLL, where N is the number of antenna elements and K is the number of signal sources, which is less than that of the projection approximation subspace tracking with deflation algorithm. The DOA tracking accuracy is demonstrated by analysis and computer simulations.

We propose a novel algorithm to perform jointly the azimuthal direction-of-arrival (DOA) estimation and the multiuser detection (MUD) of signals impinging on an array of antennas. We treat the DOA estimation as an inverse problem of identifying a specific set of parameters that explains the received signal for a suitable physical model. We reformulate the estimation problem as a highly underdetermined linear system and solve the resulting least squares problem using the well-known conjugate gradients (CG) iterations on the normal equations (NE). Unlike methods such as MUSIC, our method does not require any a priori information concerning the number of sources and also it is independent of the. type of modulation employed. Simulation results confirm the robustness of our algorithm in the regimes of perfect correlation and low signal-to-noise ratios (SNRs). We also propose a MUD algorithm using the least squares solution obtained during the DOA estimation.

For pt. I see IEEE Trans. Veh. Technol. A smart antenna, i.e., a blind adaptive antenna array, has attracted much attention to improve the capacity of a future code-division multiple-access wireless communications system. It has been demonstrated that there is significant improvement in data demodulation through lab simulations and field experiments by employing a smart antenna of multiple elements. However, only one element is used for the pseudonoise (PN) code acquisition process, which is a coarse PN code synchronization prior to data demodulation. This paper proposes a simple and practical PN code acquisition scheme, which employs all elements in the smart antenna. Also, this paper uses an adaptive threshold for the PN code acquisition. Simulation results demonstrate that the proposed scheme can significantly improve the PN code acquisition performance, e.g., the PN code acquisition time will be half as long by employing five elements rather than the single element at a given bit-energy-to-interference power spectral density ratio.

This paper employs a smart antenna algorithm to improve pseudonoise (PN) code chip time tracking loop (PNCTL), and analyzes its root-mean-square-chip-time-jitter (RMS) for a third generation (3G) wideband code division multiple access wireless communications system (W-CDMA). The edge effect may happen frequently in a mobile environment and causes a sudden change in the direction of arrival angle (DOA) at a receiver when a transmitter moves around a building corner. The objective of this paper is to analyze the edge effect on the RMS performance of the PNCTL with a smart antenna. This paper concludes that the smart antenna can still significantly improve the PNCTL performance even under realistic edge effect and mobile fading environments.

Theoretically, turbo codes must be implemented with large block sizes. To reduce delay and complexity in practical communications systems, we need to utilize small block sizes. In these cases, interleaving and puncturing play important roles in the code performance. In this paper, we introduce an algorithm, called interleaver trellis, to analyze a specific interleaver. This will enable us to select the best interleaver among given, designed, or randomly generated interleavers when the bit error rate (BER) is considered as the performance criterion. Then we will design a good puncturing pattern for the selected interleaver to increase the code rate with the minimum degradation or even performance improvement.

This paper proposes to employ a smart antenna to improve pseudonoise (PN) code chip time tracking loop (PNCTL), and analyzes its performance in the third generation (3G) wideband code division multiple access wireless communications channel (W-CDMA). Since a smart antenna can improve the signal-to-interference-plus-noise power ratio (SINR), the smart antenna may also improve the PNCTL performance as well as the bit error rate (BER) and capacity of the CDMA system. We consider the mean-time-to-lose-lock (MTLL) as the performance criteria. The PNCTL takes the smart antenna array output as its input. We examine both the first and second order PNCTLs, and employ a normalized least mean square (NLMS) algorithm to update the weight vector for the smart antenna. A flat Rayleigh Jakes fading multipath is taken as the channel model, and independent additive white Gaussian noise (AWGN) is added at each antenna element. Through both analysis and simulation, we demonstrate that the MTLL can be significantly improved under fading and AWGN environments, compared to a single antenna element, e.g., a 6 dB improvement in SINR with four antenna elements.

An efficient PN code acquisition scheme with an adaptive antenna array and adaptive threshold is proposed. The basic structure is the combination of a conventional PN correlation searcher, an adaptive beamformer and an adaptive threshold setting circuit. The proposed scheme employs all the array element outputs in the PN correlation searcher and also uses an adaptive threshold for each PN code phase hypothesis testing by estimating the instantaneous power prior to PN code despreading. The performance of the proposed scheme is theoretically analyzed and also simulated in terms of the false alarm probability P/sub f/, detection probability P/sub d/ and average acquisition time T/sub acq/ under a Rayleigh mobile fading environment. Theoretical and simulation results show that the proposed scheme is robust against received signal power variations and can significantly improve the PN code acquisition performance.

A digital baseband receiver called zero-intermediate frequency zero-crossing demodulator (ZIFZCD) was developed for digital FM signal detection. ZIFZCD is applicable to many worldwide mobile and personal communications systems. In addition, ZIFZCD offers lower power consumption and simpler implementation, compared to the conventional analog implementation [e.g., a limiter-discriminator integrator and dump (LDI)] and the conventional digital implementation [e.g., the cross-differentiate-multiply demodulator (CDM)]. This paper introduces the ZIFZCD and reports the bit-error rate (BER) of the ZIFZCD under both static and fading environments. The analyzed and simulated BER results show that the ZIFZCD is comparable to the conventional CDM for narrowband digital FM with a modulation index of 0.5, and the ZIFZCD is significantly better than the CDM for wideband digital FM with a modulation index larger than 1.5.

This paper computes the probabilities of detection and false alarm for a pseudonoise (PN) sequence code lock detector when a strong radio frequency interference (RFI) hits the communications link. A soft-limiter, a hard-limiter, and no limiter at the front-end of the receiver are considered. Both continuous wave (CW) type RFI and pulse type RFI are analyzed. It is shown that a soft-limiter or a hard-limiter can protect the PN-code lock detector against a typical pulse RFI, but in a CW RFI environment, the PN-code lock detector performance with a soft-limiter or a hard-limiter will be worse than that with no limiter.>

This paper analyzes the probabilities of data packet loss for both an encrypted channel in self-synchronous cipher feedback mode and a nonencrypted channel, in the space data systems. Simulation results show reasonable agreement with analytical results. When channel bit error probability is 10/sup -5/ and the total number of packets per frame is 3, the analytical model gives 0.39% packet loss while the simulation gives 0.22% packet loss due to encryption. Although the analysis is performed for the space data systems, the resulting derived equations with minor change will be useful in many packet communication applications.>

In an optical multiple-access system, overall system throughput efficiency add significant implementation cost-reduction would be achieved if many users could access a common optical channel at any time without control among users. Recently one such scheme, an optical orthogonal code division multiple-access system (OOCDMA), was introduced by Salehi et al. (1982) for the case of no noise. In this paper, some extensions of that work are presented, including the effects of avalanche photodiode (APD) noise and thermal noise as well as interference for the OOCDMA direct-detection receiver. Since it has been shown that an optical hard-limiter before the receiver correlator can reduce the interference effect for the OOCDMA system in the absence of noise, the hard-limiter role in the presence of thermal and APD noise is also examined.>

For part I see ibid. vol.42, no.7, p.2470 (1994). In a recently proposed optical orthogonal code division multiple-access (OOCDMA) system, one bit of user's data is transmitted per sequence-period, and a threshold is employed for the final bit decision. In this paper, a system that can transmit multibits per sequence-period is introduced, and avalanche photodiode (APD) noise, thermal noise, and interference, are included. This system, derived by exploiting orthogonal properties of the OOCDMA code sequence and using a maximum search (instead of a threshold) in the final decision, is log/sub 2/ F times higher in throughput, where F is sequence-period. For example, four orders of magnitude are better in bit error probability at -56 dBW received laser power, with F=1000 chips, 10 "marks" in a sequence, and 10 users of 30 Mb/s data rate for one-bit/sequence-period and 270 Mb/s data rate for multibits/sequence-period system. Furthermore, an exact analysis is performed for the log/sub 2/F bits/sequence-period system with a hard-limiter placed before the receiver, and its performance is compared to the performance without hard-limiter, for the chip-synchronous case. The improvement from using a hard-limiter is significant in the log/sub 2/F bits/sequence-period OCCDMA system (while it is not in a one-bit/sequence-period OOCDMA system proposed in Part I).>

A known jamming state information (JSI) scheme for a coded frequency-hopped M-ary frequency-shift-keying (FH/MFSK) system under partial-band noise jamming, plus additive white Gaussian noise, utilizes the maximum a posteriori (MAP) rule based on the total energy received in the M-tone signaling bands. It is assumed that the knowledge of partial-band noise jamming fraction is available to the JSI generator. Because this scheme reduces the M-dimensional information into one dimension, i.e., the total energy, the generated JSI may not be the best. In this paper, a neural network approach to the JSI generation is presented. The efficiency of the new JSI generator with known partial-band noise jamming fraction is compared with the MAP generator. The neural network scheme is then generalized to increase its robustness by allowing for an unknown partial-band noise jamming fraction. The neural network JSI generator with or even without knowledge of jamming fraction offers significantly better performance for a coded FH/MFSK communication system than the MAP JSI generator for high code rate.

The Space Shuttle orbiter (SSO) Ku-band single access return (KSAR) link and the Space Station Freedom (SSF) KSAR link via the tracking and data relay satellite system (TDRSS) use the same carrier frequency. The interference between spacecraft is minimized by opposite antenna polarizations and by TDRSS antenna beam pointing, but if the SSF and SSO are in close proximity, it is expected that mutual interference will be significant. It is shown that a simplified analytical approach will yield adequate accuracy for the expected range of operating conditions. Relative degradation in bit-energy-to-thermal-noise power spectral density ratio to achieve a 10/sup -5/ coded bit-error probability is determined to be 4 dB for the Ku-band SSO-to-TDRS I-channel return link with a 4.5-dB effective signal-to-interference total power ratio (S/I) when the Ku-band SSF-to-TDRS return link interferes. For the Ku-band SSF-to-TDRS return link, both analysis and simulation results yield a relative signal degradation of 0.4 dB at the effective S/I=21.6 dB.>

The error probability achieved by a differential detector with a bandpass limiter preceding the receiver is analyzed for a slow-frequency-hopped CPFSK diversity waveform transmitted over a partial-band noise jamming channel, and is compared to the system's performance without the bandpass limiter. The system's thermal noise is not neglected in the analysis. In principle, each bit is repeated on L different hops, and for the FH/CPFSK system analyzed, these repetitions are combined to yield a soft decision. The main result is that a diversity gain for error rate improvement in worst-case partial-band jamming is realized with the detector preceded by a limiter, but not without the limiter. This is shown by considering the error probability for L=2 in comparison with that for L=1.>

The authors conjecture that a proper combination of partial-band tone jamming (PBTJ) and full-band noise jamming (FBNJ) under a given total jamming power constraint may be more effective than PBTJ alone, not only for the case with a low (E/sub s//N/sub J/), but also for the case with high E/sub s//N/sub J/, since the FBNJ can corrupt the jamming state information (JSI). Assuming this combination of PBTJ and FBNJ jamming, they consider three cases of receiver processing-the hard decision (HD) metric without JSI, the HD metric with perfect JSI, and the maximum-likelihood (ML) metric using Viterbi's ratio threshold (VRT) to generate a 1-b symbol decision quality indicator. System performance is evaluated in terms of the Chernoff bound on the probability of symbol error. From extensive numerical analysis the authors conclude that, for the case of the HD metric without JSI, PBTJ-only jamming is the worst form of jamming, as expected, since the receiver does not use JSI at all; for the other cases, a combination of PBTJ and FBNJ is the worst, with the worst ratio of PBTJ power to FBNJ power a function of the values of M and E/sub s//N/sub J/.>

Since a rectangular spectrum is unrealizable, more realistic spectra such as those where a jammer uses a bandpass filter before amplifying the jamming noise are considered. A Gaussian-shaped filter is used to represent a class of bandpass filters. This is a more realistic shape than the ideal rectangular shape. In addition, it can be easily analyzed by a reasonable approximation, i.e. a Gaussian-shaped spectrum that is constant over each hopped M-ary signaling band. Numerical results indicate that such a Gaussian-shaped partial-band noise jammer has nearly the same effects as an ideal rectangular-shaped partial-band noise jammer with an equivalent bandwidth.>