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In this paper, we investigate multi user chirp spread spectrum with noncoherent detection as a continuation of our work on coherent detection in [1]. We derive the analytical bit error ratio (BER) expression for binary chirp spread spectrum (BCSS) in the presence of multiple access interference (MAI) caused by correlation with other user signals because of either asynchronism or Doppler shifts, or both, and validate with simulations. To achieve this we analyze the signal cross correlations, and compare traditional linear chirps with our recently-proposed nonlinear chirps introduced in [1] and with other nonlinear chirps from the literature. In doing so we illustrate the superior performance of our new nonlinear chirp designs in these practical conditions, for the noncoherent counterpart of [1]., Chirp spread spectrum, Noncoherent detection, Asynchronism, Doppler, Chirp, FMCW, Analysis, BER derivation

We are interested in a communication system that operates under stringent power constraints, but is flexible with bandwidth constraints. Our approach is to consider some of the key elements in a transceiver and optimize them for low power consumption, as opposed to optimizing them to minimize, say, average probability of error. An obvious consequence of this is that high complexity components of the system, such as matched filters, forward error correction that employs iterative decoders, coherent demodulators, and bandwidth-efficient modulation formats, are not feasible for this research. Rather, our system is designed using $M$ -ary FSK with non-coherent detection, optimized two-pole bandpass filters (BPF), and Reed-Solomon (RS) codes with hard-decision decoding. Among other things, we show that by properly optimizing the key parameters of the BPFs and RS codes, we can design the system to be significantly less complex than an optimal one, and only lose about 1.2 ( $M$ =16) to 1.5 ( $M$ =2) dB in terms of performance.

In this article, we propose an index modulation system suitable for optical communications, where the intensity of the light is modulated along the time, space and frequency dimensions, building a Frequency-Hopping Spatial Multi-Pulse Position Modulation (FH-SMPPM). We analyze its performance from the point of view of its efficiency in power and spectrum, and its implementation complexity and required receiver latency. We analyze its error probability in the case of the non-turbulent free-space optical (FSO) channel. We derive formulas for the average symbol and bit error probabilities, and the simulation results show that they are tight enough for a wide range of signal-to-noise ratios and system parameters. We compare FH-SMPPM with other proposed index modulated systems of the same nature, and we highlight its distinctive advantages, like the flexibility to build an appropriate waveform under different constraints and objectives. Moreover, FH-SMPPM shows to be better performing in BER/SER and/or offer advantages in efficiency with respect to those alternatives, thus offering the possibility to be adopted for a variety of contexts., 14 pages, 8 figures, accepted for publication at IEEE Transactions on Communications

This paper is focused on the optimal design and performance analysis of a novel class of no-hit-zone frequency-hopping sequences (NHZ-FHSs) in quasi-synchronous FH multiple-access (QS-FHMA) systems. Although traditional NHZ-FHSs can offer interference-free FHMA performance when the signal arrival delay ( $\tau $ ) does not exceed the width of NHZ ( $Z_{\mathrm{ nh}}$ ), i.e., $|\tau |\leq Z_{\mathrm{ nh}}$ , the same performance cannot be guaranteed for $|\tau |>Z_{\mathrm{ nh}}$ in which traditional NHZ-FHZs may have large Hamming correlation (which denotes the total number of frequency hits of sequences) and consequently poor error probability performance. Since the strict quasi-synchronization (i.e., $|\tau |\leq Z_{\mathrm{ nh}}$ ) may be hard to maintain at all times in practical FHMA networks (e.g., infrastructureless ad hoc networks), it is also important to minimize the Hamming correlation for time-shifts outside of the NHZ. Such FHSs are called strong NHZ-FHSs (SNHZ-FHSs) in this paper. We derive a lower bound on the maximum Hamming correlation outside of the NHZ and then present a design algorithm for the optimal SNHZ-FHS set meeting our proposed lower bound with equality. We analyze the bit-error-rate (BER) performance of the FHMA system employing the proposed SNHZ-FHS sets using the average Hamming correlation function. The theoretical analysis and simulation results show that the proposed optimal SNHZ-FHS sets are feasible for practical FHMA networks with relaxed timing requirement and enhanced BER performance.

Scatter radio, i.e., communication by means of reflection, has been recently proposed as a promising technology for low-power wireless sensor networks (WSNs). Specifically, this paper offers noncoherent receivers in scatter radio frequency-shift keying, for either channel-coded or uncoded scatter radio reception, in order to eliminate the need for training bits of coherent schemes (for channel estimation) at the packet preamble. Noncoherent symbol-by-symbol and sequence detectors based on hybrid composite hypothesis test (HCHT) and generalized likelihood-ratio test, for the uncoded case and noncoherent decoders based on HCHT, for small block-length channel codes, are derived. Performance comparison under Rician, Rayleigh, or no fading, taking into account fixed energy budget per packet is presented. It is shown that the performance gap between coherent and noncoherent reception depends on whether channel codes are employed, the fading conditions (e.g., Rayleigh versus Rician versus no fading), as well as the utilized coding interleaving depth; the choice of one coding scheme over the other depends on the wireless fading parameters and the design choice for extra diversity versus extra power gain. Finally, experimental outdoor results at 13-dBm transmission power corroborate the practicality of the proposed noncoherent detection and decoding techniques for scatter radio WSNs.

Orthogonal modulation, for example, frequency-shift keying (FSK) or pulse-position modulation (PPM), is primarily used in relatively-low-rate communication systems that operate in the power-limited regime. Optimal noncoherent detection of orthogonally modulated signals takes the form of sequence detection and has exponential (in the sequence length) complexity when implemented through an exhaustive search among all possible sequences. In this work, for the first time in the literature, we present an algorithm that performs generalized-likelihood-ratio-test (GLRT) optimal noncoherent sequence detection of orthogonally modulated signals in flat fading with log-linear (in the sequence length) complexity. Moreover, for Rayleigh fading channels, the proposed algorithm is equivalent to the maximum-likelihood (ML) noncoherent sequence detector. Simulation studies indicate that the optimal noncoherent FSK detector attains coherent-detection performance when the sequence length is on the order of 100, offering a 3–5 dB gain over the typical energy (single-symbol) detector. While the conventional exhaustive-search approach becomes infeasible for such sequence lengths, the proposed implementation requires a log-linear only number of operations, opening new avenues for practical deployments. Finally, we show that our algorithm also solves efficiently the optimal noncoherent sequence detection problem in contemporary radio frequency identification (RFID) systems.

We develop closed-form generalized likelihood ratio test (GLRT) sequence detectors for multi-relay amplify-and-forward (AF) cooperative networks employing M-ary differential phase-shift keying (M-DPSK) and noncoherent M-ary frequency-shift keying (M-FSK). The proposed detectors achieve robust performance in a wide range of fading environments where prior knowledge of channels, signal powers, noise variances, and relay functionalities is unavailable to the destination. A comprehensive error probability performance analysis is carried out in Rayleigh fading. Specifically, we derive unified pairwise error probability (PEP) expressions for both detectors in a dual-hop network, which are valid for arbitrary modulation order M and arbitrary sequence length Ns. We also derive unified bit-error probability (BEP) expressions for both detectors employing binary signalings in various networks for Ns = 1. It is further shown that both detectors achieve near full diversity orders. Finally, the superiorities of the proposed detectors over the state-of-the-art noncoherent detectors are justified through extensive comparisons in practical scenarios. For example, in a multi-relay network where the relays are uniformly distributed between the source and destination, the proposed detector for noncoherent FSK with Ns = 1 outperforms the well-known maximum energy selector by almost 15 dB in high signal-to-noise ratios.

The rationale of our design is that although much of the literature of cooperative systems assumes perfect coherent detection, the assumption of having any channel estimates at the relays imposes an unreasonable burden on the relay station. Hence, non-coherently detected Reed-Solomon (ReS) coded Slow Frequency Hopping (SFH) assisted M -ary Frequency Shift Keying (FSK) is proposed for cooperative wireless networks, subjected to both partial-band interference and Rayleigh fading. Erasure insertion (EI) assisted ReS decoding based on the joint maximum output-ratio threshold test (MO-RTT) is investigated in order to evaluate the attainable system performance. Compared to the conventional error-correction-only decoder, the EI scheme may achieve an Eb/N0 gain of approximately 3dB at the Codeword Error Probability, Pw , of 10-4 , when employing the ReS (31, 20) code combined with 32-FSK modulation. Additionally, we evaluated the system’s performance, when either equal gain combining (EGC) or selection combining (SC) techniques are employed at the destination’s receiver. The results demonstrated that in the presence of one and two assisting relays, the EGC scheme achieves gains of 1.5 dB and 1.0 dB at the Pw of 10-6 , respectively, compared to the SC arrangement. Furthermore, we demonstrated that for the same coding rate and packet size, the ReS (31, 20) code using EI decoding is capable of outperforming convolutional coding, when 32-FSK modulation is considered, whilst LDPC coding had an edge over the above two schemes.

This paper develops a detection scheme based on the implicit pilot-symbol-assisted architecture of M-ary frequency-shift-keying (FSK) modulation in amplify-and-forward (AF) multiple-relay networks. It is shown that, at the expense of the low spectral efficiency inherent in FSK modulation, every transmitted symbol from the source to the destination can be used as a pilot symbol. In the proposed detection scheme, the destination combines the signals from the source and the relays to perform detection by using the estimated channels obtained from the implicit pilot symbols. Using the Gaussian approximation for the effective noise at the destination, an upper bound of the approximated bit-error-rate (BER) is provided. Simulation results reveal that the proposed scheme can significantly improve the BER performance when compared to previously proposed schemes in a temporally-correlated fading environment. The simulation results also verify the obtained upper bound on the approximated BER.

For communication schemes employing Frequency Hopping/Multiple Frequency Shift Keying modulation, we present an algorithm for finding good non-binary synchronization sequences, which are permutations, to be used with permutation codes to synchronize/resynchronize data in channels with background noise and interference(frequency jamming/fading). For the synchronization sequences, new analytical expressions for the probability of false acquisition are also given. Using simulation results, we show that our synchronization sequences perform better than some conventional non-binary synchronization sequences, in the presence of background noise and interference.

The performance of decode-and-forward multi-hop communication is analyzed in a Rayleigh fading environment. Analytical expressions for the end-to-end symbol error probability are derived in the cases of M-ary phase-shift keying with coherent detection and orthogonal M-ary frequency-shift keying with non-coherent detection using a difference equation approach. When the path loss exponent is greater than one, each node transmits with the same power as that of a direct transmission source, and the relays are equispaced along the line joining the source and the destination, the performance improves with increasing number of hops. Furthermore, for fixed average signal-to-noise ratio per hop, the incremental degradation in performance when adding more hops decreases with each extra hop.

This paper considers how to estimate the average signal-to-noise ratio (SNR) for a communication system employing orthogonal non-coherent M-ARY frequency shift keying (NCMFSK), in white Gaussian noise (AWGN) and over both symbol-by-symbol fading channels and block fading channels. The proposed algorithm finds its application in a variety of applications including a cooperative transmission system, which is the main motivation behind this study. The maximum likelihood estimator and one using data statistics have been derived and simulated for various scenarios including data-aided, non-data aided and joint estimation using both the data and pilot sequences. We also derive the Cramer-Rao bound for the estimators in the case of Rayleigh fading channels. The results show that for a particular region of interest (e.g. high SNR or low SNR) and depending upon the availability of pilot sequence, a particular SNR estimation scheme is suitable.

Two-way cooperative communications are considered to improve the throughput of conventional one-way cooperative communications. For fast Rayleigh fading channels, we propose optimal and suboptimal non-coherent detectors for on-off keying (OOK) and frequency-shift keying (FSK) modulated two-way amplify-and-forward (AF) cooperative communications in this paper. In the proposed system, the relaying node combines the received signals from two nodes, amplifies them and retransmits the conjugate of the combined and amplified signals to the above-mentioned nodes. At the receivers of above-mentioned nodes, the optimal non-coherent detection is employed which is based on maximum likelihood rule. Since it involves integration operation, the optimal detector is simplified to a suboptimal detector which omits the real component of the relayed signal over the frequency which includes interference. The simulation results have shown that compared with the optimal detector, the proposed suboptimal detector reduces the receiver complexity at the expense of acceptable performance degradation. Furthermore, we have analytically studied the bit-error-rate performance upper and lower bounds of proposed non-coherent FSK modulated two-way AF cooperative communications.

A channel-coded physical-layer network coding strategy is refined for practical operation. The system uses frequency-shift keying (FSK) modulation and operates noncoherently, providing advantages over coherent operation: there are no requirements for perfect power control, phase synchronism, or estimates of carrier-phase offset. In contrast with analog network coding, which relays received analog signals plus noise, the system relays digital network codewords, obtained by digital demodulation and channel decoding at the relay. The emphasis of this paper is on the relay receiver formulation. Closed-form expressions are derived that provide bitwise log-likelihood ratios, which may be passed through a standard error-correction decoder. The role of fading-amplitude estimates is investigated, and an effective fading-amplitude estimator is developed. Simulation results are presented for a Rayleigh block-fading channel, and the influence of block length is explored. An example realization of the proposed system demonstrates a 32.4% throughput improvement compared to a similar system that performs network coding at the link layer. By properly selecting the rates of the channel codes, this benefit may be achieved without requiring an increase in transmit power.

Multilevel coding (MLC) is the main contender to the celebrated bit-interleaved coded modulation (BICM) technique for combining binary error-control codes with multilevel constellations. Although MLC has a more complex encoding-decoding structure, it can achieve a larger rate in a number of important scenarios such as multiple-input multiple-output (MIMO) and orthogonal modulation transmission. In this paper, we consider two issues related to the application of MLC. First, we examine the use of general decoding metrics in MLC, including mismatched metrics that arise from approximations to reduce detection complexity. We make use of recent advances in the analysis of BICM and apply those techniques to individual MLC transmission layers. Our contributions include rate analysis and metric-mismatch correction to improve throughput performance of MLC. Second, we consider the combination of MLC with binary rateless codes. Such a combination eliminates the need to carefully design code rate for each MLC layer. In slow fading environments, rateless coding can also seamlessly adapt to the instantaneous channel quality and achieve an increased average throughput compared to a fixed-rate MLC transmission. However, due to the MLC structure, we show that a naive combination of MLC and rateless coding can cause a significant rate loss. Thus, we propose a novel rotation rateless scheme which preserves the rate advantage of MLC over BICM. We provide relevant examples with MIMO, frequency-shift keying (FSK), and pulse-position modulation (PPM) signaling to demonstrate that our scheme can achieve throughput gains compared to BICM in a variety of transmission scenarios.

Gaussian frequency shift keying (GFSK) is a promising digital modulation scheme. The design of simple and high-performance receivers for GFSK systems is a challenging task. In this letter, we develop an optimized differential GFSK demodulator and investigate the phase wrapping issue in its implementation. Simulation results show bit-error-rate (BER) performance improvement in comparison with conventional differential demodulators in both AWGN and flat fading channels. We also compare our proposed demodulator with other existing alternatives in terms of BER performance.

In this paper, we analyze the performance of soft decision decoded, synchronous, fast frequency-hopping spread-spectrum multiple-access networks using M-ary frequency shift keying in Rayleigh fading channels under the assumption that the number of frequency hopping slots is sufficiently large. The joint probability density function (pdf) of the absolute values of the correlator outputs is derived to compute the channel capacity and evaluate the soft decision decoding performance of the 3GPP Turbo and convolutional codes. Results indicate that soft decision decoding based on the derived pdf drastically outperforms traditional decoders based on the Gaussian approximation of the effect of the multiple access interference (MAI). The sensitivity of the derived soft decision decoder to estimation errors in system parameters and the required computational complexities of the derived soft decision decoding metrics are also investigated.

A very simple design rule for parallel concatenated Turbo codes over GF(q) with q-ary orthogonal modulation is proposed. Unlike previously proposed exhaustive search methods, the proposed design rule allows straightforward and systematic code designs for any value of q ≥ 2 and any constraint length greater than 2.

A maximum-likelihood (ML) receiver structure is proposed for fast frequency-hopped M-ary frequency-shift keying communication systems over Rayleigh-fading channels with the composite effects of multitone jamming (MTJ) and partial-band noise jamming (PBNJ). The corresponding semi-analytical bit-error rate (BER) expressions of the proposed ML receiver are also presented and validated by simulation results. Numerical results show that the BER performance with both MTJ and PBNJ is bounded by the two extreme cases, where only MTJ or PBNJ is present. It is also found that the proposed ML receiver can better counteract MTJ than PBNJ.

In this paper, we analyze the error probability of equal gain combining with quantized channel phase compensation for binary phase shift keying signalling over Rayleigh fading channels. The probability density and characteristic functions of the combined signal amplitude are derived and used to compute the analytic expressions for the bit error probability in dependance of the number of quantization levels L, the number of diversity branches NR and the average received signal-to-noise ratio. The analysis is utilized to outline the trade-off between NR and L and to compare the performance with non-coherent binary frequency shift keying and differential binary phase shift keying schemes under diversity reception.

In this paper, we propose a "two-level" frequency-hopping code-division multiple-access (FH-CDMA) scheme for wireless communication systems. The new scheme provides flexibility in the selection of modulation codes and FH patterns. By partitioning the modulation codes, our two-level scheme can be modified to support more possible users without increasing the number of FH patterns. The performance and spectral efficiency (SE) of the scheme are analyzed. Our results show that the partitioned two-level FH-CDMA scheme supports higher data rate and greater SE than Goodman's frequency-shift-keying FH-CDMA scheme under some conditions.

A maximum energy selection (MES) receiver scheme is proposed for noncoherent amplify-and-forward (AF) cooperative diversity systems. An expression for the symbol error probability of this system when deployed with M-ary frequency shift keying (FSK) modulation is derived. It is shown that a noncoherent AF system employing the proposed MES scheme achieves full spatial diversity, while requiring neither instantaneous nor statistical channel gain information at the destination, but only knowledge of the average source-relay link signal-to-noise ratio (SNR) at the corresponding relay. The average source-relay link SNR information can be locally obtained at each relay using conventional practical estimation techniques, which in turn allows fully distributed implementation of the proposed scheme.

In this paper, linear combining receivers with deterministic weights are considered for a communication system employing receive diversity in flat Rician fading. We propose two receiver structures: (1) a modified maximum likelihood (ML) receiver in which detection is performed by maximizing the likelihood function of the combined received signal, (2) a deterministic maximal-ratio combining (MRC) receiver which uses the same structure as that of an MRC receiver but with deterministic weights. The deterministic weight vector is chosen such that it minimizes the union bound on the symbol error probability. Methods of computing this deterministic weight vector are presented. The error performance of the receivers is numerically compared with that of the square-law combining receiver and the equal-gain combining (EGC) receiver (which requires more complex phase estimation rather than using fixed, deterministic weights). Numerical results show that in the case of phase-shift keying, the EGC receiver performs better than the modified ML receiver (which has the same performance as that of the deterministic MRC receiver), but the performance gap decreases with increase of the Rician K-factor. It is also seen that in the case of orthogonal frequency-shift keying, the modified ML and deterministic MRC receivers outperform the square-law combining receiver.

In this paper, coherent detection for multilevel correlated signaling sets in additive white Gaussian noise is addressed. From the decision rule, a general analytical expression for the symbol error probability (SEP) is derived, which is in the form of a single integral. Our new result is not only in agreement with a known equivalent expression, but it also has a much simpler analytical form. The structure of the correlation matrix under consideration of the signaling set is quite generic, including various known signaling sets as special cases. Hence the derived SEP expression is useful for analyzing the performance of various coherent modulation schemes such as multilevel phase-shift and frequency-shift keying. Specific correlation structures which minimize the SEP are also studied. Based on eigendecomposition or LU decomposition, generic methods for constructing a correlated signaling set for any correlation matrix under consideration are also provided.

This paper presents a new unified analytical technique for accurate interference analysis of noncoherent M-ary frequency shift keying (MFSK) wireless communication systems in the presence of additive white Gaussian noise (AWGN) and multiple arbitrary interfering signals. New exact bit error rate expressions are derived for nonorthogonal noncoherent binary FSK in the presence of an arbitrary number of interfering signals having arbitrary spectral shapes at arbitrary frequency offsets. Furthermore, tight upper bounds for the symbol and bit error rates are given for noncoherent MFSK with arbitrary tone spacings. These results are extended to include MFSK signals experiencing Rayleigh, Nakagami-m or Rician fading. Some specific interference scenarios are analyzed in details, including jammers with a given Doppler-spread, direct sequence spread spectrum and orthogonal frequency division multiplexing signals, and a Poisson field of arbitrary interferers.

In this paper, we compare the battery power efficiencies of various pulse-based modulations widely adopted for their low complexity. Taking into account circuit modules and battery imperfectness, we establish simple closed-form analytical formulas which can be used to conveniently determine the relative preference between arbitrary pulse-based modulation pairs in terms of their actual average battery energy consumption.

A system involving the multisymbol noncoherent reception of coded continuous-phase frequency-shift keying is developed, optimized, and analyzed. Unlike coherent systems, the modulation index of the waveform does not need to be rational with a small denominator, and the oscillator only needs to be stable for the duration of a small block of symbols. The achievable performance over AWGN and Rayleigh block-fading channels is determined by computing the average mutual information, which is the capacity of a channel using the given modulation format and receiver architecture under the constraint of uniformly distributed input symbols. The code rate and modulation index are jointly optimized with respect to average mutual information under a bandwidth constraint. For binary and quaternary signaling, the information-theoretic results are corroborated by bit-error-rate curves generated using a standardized turbo code in conjunction with iterative demodulation and decoding. It is shown that, while more robust than a system with coherent reception, the proposed system offers superior energy efficiency compared with conventional single-symbol noncoherent reception.

This letter presents a reduced complexity equalizer for offset quadrature phase-shift keying (OQPSK), Gaussian minimum shift keying (GMSK), or any other staggered modulation format. Due to the relative time offset of the in-phase and quadrature components, the received signal must be sampled at a rate of at least twice the symbol rate of its corresponding nonstaggered signal, where using a symbol-spaced equalizer (SSE) is an option. The conventional approach doubles the number of equalizer coefficients required relative to QPSK. In this work it is shown that also for OQPSK it is possible to implement an equalizer spaced in symbol rate, with about half the complexity required for the linear equalizer (LE). For the decision feedback equalizer (DFE), savings are achieved only in the feed forward filter.

An optimum maximum-likelihood (ML) receiver structure for a fast frequency-hopped M-ary frequency-shift keying system over frequency-selective Rician-fading channels against partial-band-noise jamming and additive white Gaussian noise is proposed. In addition, we propose two suboptimum ML receivers and derive their corresponding analytical bit-error rate expressions.

We analyze the error performance of two-hop relay networks adopting frequency shift keying (FSK) over frequency flat Rayleigh fading channels. It is assumed that relay networks consist of a source, a relay, and a destination without a direct path signal from the source to the destination and the relay adopts the amplify-and-forward protocol with a fixed gain. Firstly, considering imperfect frequency and phase synchronization, we obtain the exact error probability expressions for noncoherent and coherent binary FSK (BFSK). Secondly, assuming perfect frequency and phase synchronization, we derive a closed-form error probability approximation for coherent M-ary FSK (MFSK). The proposed methods can also be used for the error performance analysis of classical one-hop FSK systems with perfect/imperfect frequency and phase synchronization. The obtained error probability expressions will help the design of two-hop relay networks adopting FSK in determining the system parameters such as the transmission power at the source, the amplifying coefficient at the relay, and the maximum affordable frequency and phase offsets to satisfy the required error performance.

Space-time trellis coding is an established diversity technique that reduces the effects of multipath fading over wireless communication channels. Here, we consider high rate space-time trellis codes (STTC) with continuous phase frequency shift keying (CPFSK). We present optimized rate-2/3 STTC implemented with 3 transmit antennas. These codes provide system throughputs of 4 and 6 bits per channel use with 4-ary and 8-ary CPFSK respectively. Simulated error rate performance of the optimized codes with receive diversity is presented. We show that although the schemes do not achieve full transmit diversity, they provide excellent coding gains compared to full rank schemes that have equivalent throughput, but higher order modulations and greater complexity.

Optimum selection combining using the maximum energy (OSC-ME) criterion for M-ary noncoherent frequency shift keying signaling in independent and nonidentically distributed fading channels is examined. A weighted maximum energy selection combining (WMESC) scheme is proposed and found to provide virtually the same symbol error probability as OSC-ME in Rician fading channels. The WMESC always provides power gain over the classical selection combining regardless of diversity order and signal-to-noise ratio.

The jamming robustness of frequency hopping (FH) systems with M-ary frequency shift keying (MFSK) modulation may be potentially neutralized by a follower partial-band jammer. In this paper, a maximum likelihood (ML)-based algorithm that uses a two-element array is proposed for joint follower jamming rejection and symbol detection in slow FH/MFSK systems over quasi-static flat Rayleigh fading channels. The algorithm is derived by treating both the received jamming components and the unknown data symbols as deterministic quantities to be jointly estimated in an integrated ML operation. In addition, an approximate expression for the symbol error rate (SER) of the proposed scheme is derived when BFSK signaling is employed in a jamming dominant scenario. Analytical and simulated results show that the proposed approach is able to remove jamming and outperform the conventional and sample matrix inversion (SMI)-based beam-formers in the presence of a follower partial-band jammer.

A robust frequency-hopping system with noncoherent detection, iterative turbo decoding and demodulation, and channel estimation is presented. The data modulation is the spectrally compact nonorthogonal continuous-phase frequency-shift keying, which strengthens the frequency-hopping system against multiple-access interference and multitone jamming. An analysis based on information theory provides the optimal values of the modulation index when there is a bandwidth constraint. The channel estimator, which is derived by applying the expectation- maximization algorithm, accommodates both frequency-selective fading and interference. Simulation experiments demonstrate the excellent system performance against both partial-band and multiple-access interference.

In this paper, we propose the use of Reed-Solomon (RS) code sequences for modulation on top of a frequency-hopping code-division multiple access (FH-CDMA). Our analysis shows that this RS/FH-CDMA scheme supports higher data rate but worse performance than the conventional -ary frequency-shift-keying FH-CDMA scheme. These two schemes provide a tradeoff between the data rate and the performance.

The performance of binary frequency-shift keying (BFSK) and M-ary frequency shift keying (MFSK) with dual-branch postdetection switch-and-stay combining (SSC) in correlated Rayleigh and Rician fading is studied. Two postdetection SSC receivers are considered and the performances of noncoherent BFSK and MFSK are analyzed. Closed-form expressions are derived for the average bit-error rate (BER) of BFSK and MFSK with postdetection SSC in correlated Rayleigh and Rician fading. Optimum switching thresholds that minimize the average BER are obtained. Extensive Monte Carlo simulations are presented to test the validity of the analytical results. The performance of dual-branch postdetection SSC is compared with the performance of dual-branch predetection SSC. The effects of correlation, fading parameter, average fading power imbalance, and switching threshold on the performances of postdetection SSC receivers are examined

We investigate the performance degradation of basic modulation schemes in a rapidly time-varying channel using a first-order autoregressive channel model. Various performance metrics are used to indicate the relative advantages of each modulation scheme. We find that noncoherent frequency-shift keying (FSK) is suitable for operating at very high mobility and high signal-to-noise ratio, ideal for some military applications. We then propose a partially coherent detector for FSK and differential phase-shift keying that exploits partial channel knowledge to enable the receiver to operate effectively in both fast and slow fading. The maximum-likelihood rule obtained for the partially coherent FSK turns out to be a linear combination of coherent and noncoherent detection rules. Results demonstrate that significant performance improvement can be achieved over the best of coherent and noncoherent FSK detection. The detector is robust to estimation errors present in the channel statistics. We also propose a few adaptive schemes that employ various combinations of modulation schemes to increase the robustness of the system in fast fading

This paper presents a new analytical performance analysis of slow frequency-hopped synchronous spread-spectrum multiple-access (FHSS-MA) networks employing nonorthogonal binary frequency-shift keying (BFSK) and having arbitrary spacing between the hopping carriers. Taking into account the crosstalk due to the nonorthogonality of both hopping carriers and BFSK tones, and based on an accurate interference analysis, we derive new expressions for the average probability of error of a reference signal subjected to a number of similar signals in the additive white Gaussian noise Rayleigh-faded channel. These are used to investigate the effect of carrier and tone spacing on the spectral efficiency of an FHSS-MA network. It is shown that the spectral efficiency depends primarily on the shape of the employed pulses, in addition to both carrier and tone spacing. Numerical results show that rectangular pulses give higher spectral efficiency as compared with the half-sine pulses. Furthermore, orthogonal tone spacing is shown to be more efficient in the case of rectangular pulses, whereas half-sine pulses become more efficient with the nonorthogonal signaling

The performances of dual-branch postdetection switch-and-stay combining (SSC) for noncoherent orthogonal binary frequency-shift keying and noncoherent orthogonal M-ary frequency-shift keying operating over slow, flat Rician fading channels are a topic of current interest. It is shown that recently published analyses obtain incorrect final results because some incorrect probability distribution parameters are used in the analyses. The previous results are corrected, and it is seen that the final results change significantly. The revised results are used to obtain optimum switching thresholds that minimize the average bit-error rate (BER) performance of these systems. Monte Carlo simulations are presented to verify the results, and it is shown that for a given BER, the signal-to-noise ratio difference of postdetection SSC and predetection SSC is much less than previously reported

The performances of general M-ary and binary orthogonal noncoherent frequency-shift keying signal-plus-noise (S+N) receiver structures in slow, flat Rician fading channels are examined. The fading on the diversity branches is assumed to be independent, but not necessarily identically distributed. For each receiver, a symbol-error probability expression is derived as a single integral with finite integration limits. Extensive Monte Carlo simulation results are presented to validate the analytical expressions. The results indicate that, unlike previously published results, the performance of S+N selection combining (SC) is not always superior to that of classical SC in fading and is dependent on the value of the signal-to-noise ratio (SNR), the modulation order, the diversity order, the multipath intensity profile, and the fading parameter. It is further shown that increasing the number of diversity branches in a S+N SC receiver does not necessarily decrease the probability of error if the system is operating in the low-SNR region. The performances of S+N SC schemes are also compared with the performances of equal-gain combining and square-law combining receivers.

In two recent papers, the performances of dual-branch postdetection switch-and-stay combining (SSC) for noncoherent orthogonal binary frequency-shift keying (BFSK) and noncoherent orthogonal M-ary frequency-shift keying (MFSK) operating in the presence of slow flat fading modeled by Rayleigh, Nakagami-m, and Rician distributions have been analyzed. In this paper, we show that these previous analyses for the Nakagami-m fading model, which are restricted to integer values of m, are incorrect, and we derive the correct bit-error rate (BER) performances of BFSK and MFSK with dual-branch SSC in Nakagami-m fading for all values of m. Optimum switching thresholds that minimize the BER of BFSK and MFSK with postdetection SSC in Nakagami-m fading are obtained. The performance of postdetection SSC is compared with the performance of predetection SSC, and it is shown that postdetection SSC outperforms predetection SSC for all values of signal-to-noise ratio (SNR). We also show that for a given BER, the performance gain of postdetection SSC over predetection SSC has been overestimated by several decibels in SNR in previous publications.

The uplink performance of synchronous and asynchronous slow frequency-hop spread-spectrum multiple-access (SFHSS-MA) networks transmitting L bits per hop using binary differential phase shift keying (BDPSK) is analyzed under the additive white Gaussian noise (AWGN) and Rayleigh fading channels. Analytic expressions for the average conditional bit error probabilities given a hop is hit by K' interfering users are derived. Results show that SFHSS-MA networks using BDPSK achieve nearly twice the maximum normalized network throughput compared to networks using BFSK under both AWGN and Rayleigh fading channels.

Analytical bit-error-rate (BER) expressions are derived for various fast frequency-hopped (FFH) M-ary frequency-shift-keying receivers with the worst-case multitone jamming and additive white Gaussian noise. The BER results for different receivers are compared and the effects of the optimum diversity level on BER performance are also presented.

We present the optimum selection-combining (SC) rule for M-ary signals based on the log-likelihood ratio (LLR) in frequency-nonselective, independent and nonidentically distributed fading channels. The motivation for using the LLR in selecting the diversity branch is that it provides the reliability information of the maximum a posteriori probability decision which minimizes the probability of symbol error. We present coherent and noncoherent optimum SC rules with and without fading information that minimize the probability of symbol error. It is shown that the optimum SC rule provides a significant power gain over the conventional signal-to-noise ratio-based SC rule, and the power gain increases with an increasing number of available diversity branches and decreasing alphabet size. We also present suboptimum SC rules that require less computation, but provide a power gain close to that provided by the optimum SC rule.

In this paper, we provide an analytical performance comparison of various selection combining (SC) schemes for binary noncoherent frequency-shift keying (NCFSK) signals operating on independent and nonidentically distributed (i.n.d.) Rayleigh fading channels. With this motivation, we first derive the receiver structure for the optimum SC scheme, which combines one out of the available L diversity branches so as to minimize the probability of bit error. We show that the optimum SC scheme chooses the diversity branch having the largest magnitude of the logarithm of the a posteriori probability ratio (LAPPR) of the transmitted information bit. We also show that: 1) the optimum noncoherent diversity receiver, for binary NCFSK signals, is equivalent to combining the LAPPRs of all the diversity branches; 2) the SC scheme proposed by Neasmith and Beaulieu is a special case of the optimum SC scheme for independent and identically distributed (i.i.d.) Rayleigh fading; and 3) for i.n.d. fading with dual diversity (i.e., L = 2), the performance of the optimum SC scheme is the same as that of the optimum noncoherent diversity receiver, whereas the Neasmith and Beaulieu SC scheme gives the performance of the suboptimum equal gain combining receiver. Bit-error rate (BER) results show that, at 10(-4) BER, for i.i.d. Rayleigh fading, the proposed optimum SC scheme performs better than the existing SC schemes by 0.5-0.9 dB for L = 3 and by 0.8-1.5 dB for L = 5, and performs within 0.3 dB of the optimum noncoherent diversity receiver for L = 3, 5, and for i.n.d. Rayleigh fading with L = 5, the optimum SC scheme gives an additional gain of about 2.0 dB over the Pierce SC scheme. Further, for i.i.d. Rayleigh fading, we derive the bit-error probability expression for a (3, L) selection scheme which combines three branches whose LAPPR magnitudes are the largest among the available L branches Numerical results for this (3, L) selection scheme show that for L = 5 at a BER of 10-4, combining the three branches with the largest LAPPR magnitudes yields almost the full performance of the optimum noncoherent diversity receiver, whereas, for L = 7 it is just about 0.2 dB away from the latter.

In traditional binary frequency-shift keying (BFSK), two distinct carrier frequencies are used to represent binary data. In this letter, we propose transmitting multiple orthogonal, in-phase subcarriers around two distinct carrier frequencies to represent binary information. The envelope of the resulting FSK signal is a carrier interferometry pattern, and hence, the name carrier interferometry (CI/) FSK. We demonstrate that this technique is spectrally efficient when compared to traditional BFSK. Performance and data-rate benefits are also demonstrated with the use of a novel coherent reception technique. Moreover, while it is difficult to employ traditional BFSK in multipath channels, we show how the new CI/FSK scheme exploits frequency-diversity benefits when used in such channels.