Performance study of suboptimum maximum-likelihood receivers for FFH/MFSK systems with multitone jamming over fading channels

We derive two suboptimum maximum-likelihood (ML) receivers for fast frequency-hopped M-ary frequency-shift-keying (FSK) spread-spectrum (SS) communication systems. These two receiver structures attempt to countermeasure the effects of the worst case multitone jamming (MTJ) and additive white Gaussian noise over Rayleigh- and Rician-fading channels, respectively. In addition, analytical bit-error-rate (BER) expressions for the two proposed suboptimum structures are derived and validated by simulation results. Performance comparisons among various receivers show that the proposed suboptimum receivers significantly outperform the other existing receivers over fading channels. The optimum diversity level of the suboptimum ML receiver for the Rayleigh-fading case is found to be higher than that of the Rician-fading case. In addition, the proposed suboptimum ML receivers with optimum diversity levels can effectively remove the effect of MTJ, even under very low signal-to-jamming ratio conditions.     

A covariance shaping framework for linear multiuser detection

A new class of linear multiuser receivers, referred to as the covariance shaping multiuser (CSMU) receiver, is proposed, for suppression of interference in multiuser wireless communication systems. This class of receivers is based on the recently proposed covariance shaping least-squares estimator, and is designed to minimize the total variance of the weighted error between the receiver output and the observed signal, subject to the constraint that the covariance of the noise component in the receiver output is proportional to a given covariance matrix, so that we control the dynamic range and spectral shape of the output noise. Some of the well-known linear multiuser receivers are shown to be special cases of the CSMU receiver. This allows us to interpret these receivers as the receivers that minimize the total error variance in the observations, among all linear receivers with the same output noise covariance, and to analyze their performance in a unified way. We derive exact and approximate expressions for the probability of bit error, as well as the asymptotic signal-to-interference+noise ratio in the large system limit. We also characterize the spectral efficiency versus energy-per-information bit of the CSMU receiver in the wideband regime. Finally, we consider a special case of the CSMU receiver, equivalent to a mismatched minimum mean-squared error (MMSE) receiver, in which the channel signal-to-noise ratio (SNR) is not known precisely. Using our general performance analysis results, we characterize the performance of the mismatched MMSE receiver. We then treat the case in which the SNR is known to lie in a given uncertainty range, and develop a robust mismatched MMSE receiver whose performance is very close to that of the MMSE receiver over the entire uncertainty range.     

A Comparative Analysis of Optimum and Suboptimum Rake Receivers in Impulsive UWB Environment

In this paper, the performance of rake receivers in the presence of fading and impulsive noise is addressed. The optimum maximum likelihood (ML) rake receiver for impulsive fading channel is derived, and a suboptimum rake receiver with a reduced complexity is obtained for practical purposes. Numerical results show that the suboptimum rake receiver exhibits almost the same performance as the optimum rake receiver. It is also observed that, as the number of fingers of a rake receiver increases, the performance of the rake receiver designed for impulsive environment improves, while the rake receiver optimized for Gaussian environment experiences performance degradation in an impulsive environment     

Error probability analysis of FFH/MFSK receivers over frequency-selective Rician-fading channels with partial-band-noise jamming

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.     

Continuous Phase Chirp (CPC) Signals for Binary Data Communication-Part I: Coherent Detection

Chirp (linear FM) signals provide an attractive wideband digital modulation scheme in applications where interference rejection is important. This paper evaluates the error rate (performance) of coherent binary continuous phase chirp (CPC) receivers operating on the additive white Gaussian noise (AWGN) channel and determines the improvement in performance made possible by multiple bit observation. In particular, it is shown that a receiver with two bit observation, giving up to 1.75 dB signal-to-noise ratio (SNR) improvement over the optimum single bit chirp receiver, provides a good compromise between SNR gain and system complexity. Furthermore, a simple, suboptimum, average matched filter (AMF) receiver is analyzed, and it is shown that a two-bit observation is optimum, giving a performance equivalent to that of antipodal phaseshift keying (PSK). An implementation of this receiver in the form of in-phase and quadrature demodulators is also derived.     

Interception of frequency-hopped spread-spectrum signals

A frequency-hopped spread-spectrum signal is modeled as a sinusoid that has one of N random frequencies. Coherent and noncoherent interception receiver structures based on Neyman-Pearson detection theory are determined. Under the assumption that there is a single hop per detection period, the optimum receiver structure is shown to consist of a bank of matched filters called the average likelihood (AL) receiver. A suboptimum structure called the maximum likelihood (ML) receiver is also analyzed. It is shown that AL and ML receivers have essentially the same performance. Simple formulas that relate the probability of detection, P_D, to the probability of false alarm, P_F, and the signal-to-noise ratio (SNR) for large N are derived. Receiver structures are also derived and analyzed for the case where the signal hops a number of times in one detection interval. This may correspond to the detection of a multihop signal in one symbol interval or to detection based on integration over a number of symbol intervals. The relationships of P_D to P_F, for both coherent and noncoherent multiple-hop receivers, are examined     

Optimum Receiver Design for Broadband Doppler Compensation in Multipath/Doppler Channels With Rational Orthogonal Wavelet Signaling

In this paper, we address the issue of signal transmission and Doppler compensation in multipath/Doppler channels. Based on a wavelet-based broadband Doppler compensation structure, this paper presents the design and performance characterization of optimum receivers for this class of communication systems. The wavelet-based Doppler compensation structure takes account of the coexistence of multiple Doppler scales in a multipath/Doppler channel and captures the information carried by multiple scaled replicas of the transmitted signal rather than an estimation of an average Doppler as in conventional Doppler compensation schemes. The transmitted signal is recovered by the perfect reconstruction (PR) wavelet analysis filter bank (FB). We demonstrate that with rational orthogonal wavelet signaling, the proposed communication structure corresponds to a Lth-order diversity system, where L is the number of dominant transmission paths. Two receiver designs for pulse amplitude modulation (PAM) signal transmission are presented. Both receiver designs are optimal under the maximum-likelihood (ML) criterion for diversity combination and symbol detection. Good performance is achieved for both receivers in combating the Doppler effect and intersymbol interference (ISI) caused by multipath while mitigating the channel noise. In particular, the second receiver design overcomes symbol timing sensitivities present in the first design at reasonable cost to performance.     

Performance of the noncoherent biquadratic and GLRT receivers overtwo-path channels with known amplitudes and Rayleigh fading

Noncoherent detection over Rayleigh fading diversity channels with known or perfectly estimated amplitudes is studied for binary, uniformly orthogonal signaling. The optimum receiver is well known, but is too difficult to implement. Hence, two suboptimal receivers are considered: the “biquadratic” receiver, optimum at low signal-to-noise ratios (SNR's), and the “bilinear” receiver (optimum at high SNR's) which is also a generalized likelihood ratio test (GLRT) receiver for this case. We analyze the performances of the two suboptimal receivers over two-path channels and compare them to the basic quadratic receiver. For this purpose we present a general method for computing the error probability that can be applied to any dual-diversity binary detection problem whenever the method of characteristic functions fails. We present the exact analytical expressions for the biquadratic receiver, and the numerically computed results for the GLRT receiver, in terms of the conditional, average and asymptotic error probabilities. It is shown that the two receivers are rather close in performance in most of the SNR ranges of interest     

Continuous Phase Chirp (CPC) Signals for Binary Data Communication--Part II: Noncoherent Detection

Previous work has shown that coherent multiple bit observation of binary continuous phase chirp (CPC) signals gives improved error rate performance compared to the conventional bit-by-bit detection scheme. This paper determines bounds on the error rate improvement made possible by multiple bit observation for optimum and suboptimum [average matched filter (AMF)] noncoherent detection of binary CPC signals in additive white Gaussian noise (AWGN). For the same observation interval, it is shown that noncoherent CPC receivers provide higher signal-to-noise (SNR) gain than coherent receivers compared to the respective optimum single bit schemes. In particular, the three-bit noncoherent AMF receiver is shown to yield 3 dB SNR gain over a wide range of signal parameters.     

Optical Wireless Systems Employing Adaptive Collaborative Transmitters in an Indoor Channel

We propose a novel optical wireless (OW) system based on a power adaptive multibeam spot-diffusing transmitter serving multiple seven-segment maximum ratio combining (MRC) angle diversity receivers. A feedback link is assumed between the transceivers so that each receiver conveys to the multibeam transmitter the new beams transmit power weights to be used to achieve the best signal quality at a given receiver location. Two cases involving three and five receivers are considered. Four different configurations for the placement of the three-receiver case in the room are also examined. The system's performance in each case is evaluated in terms of signal-to-noise ratio (SNR) and is compared with the single receiver scenario with and without power adaptation. In the presence of one receiver, the transmit spot powers can be adjusted for optimum performance at that receiver location. For multiple receivers, there is conflict, and we propose spot power adaptation based on the average requirements (power distribution in spots), i.e., transmit equal gain combining (EGC) of spot power or MRC of transmit spot powers. The results show that the three receivers benefit most from an adaptive transmitter when each is placed at a corner of the room. In this case, an SNR increase of as much as 2.6 dB is achieved for all three receivers at the corners by both MRC and EGC. Moreover, when all receivers are placed away from the line of diffusing spots, our proposed MRC collaborative approach is 1 dB better than the noncollaborative system. This gain reduces the difference from the upper bound set by the single receiver adaptation, which is 3 dB. For a mobile transmitter, MRC also significantly improved the SNR for the farthest receivers at the opposite end from the transmitter located near one room corner.      

Sensitivity enhancement of optical receivers by impulsive coding

A theory for the signal-to-noise ratio (SNR) of optical direct-detection receivers employing return-to-zero (RZ) coding (and possibly optical preamplification) is developed. The results are valid for both signal-independent noise limited and signal-dependent noise limited receivers, as well as for arbitrary optical pulse shapes and receiver filter characteristics. Even if the same receiver bandwidth is used, RZ coding is seen to perform better than nonreturn-to-zero (NRZ) coding. Asymptotic expressions for the SNR in case of very high and very low receiver bandwidths show that the full sensitivity enhancement potential of RZ coding is exhausted at fairly moderate duty cycles. A realistic example taking into account intersymbol interference (ISI) shows that a receiver sensitivity gain (compared to NRZ coding) of, e.g., 3.2 dB can be obtained in a signal-independent noise limited receiver with a bandwidth of 80% of the data rate, using a duty cycle of three     

Maximum likelihood carrier phase recovery for coherently orthogonalCPFSK signals

ML estimation of carrier phase for coherently orthogonal continuous-phase frequency-shift-keying (COCPFSK) signals is considered. Although the estimator, in general is nonimplementable, its high and low signal-to-noise-ratio approximations both lead to linear readily implementable receiver structures. The high SNR approximation yields a DA receiver, whereas the low SNR approximation yields an NDA receiver. The performance of both receivers in term of bit error probability is analyzed. The existence of an unmodulated component in the sufficient statistical representation of a COCPFSK signal is pointed out, and it is shown how this component enters directly into maximum-like carrier recovery. This leads to interpretation of the NDA receiver as a generalization of the conventional matched-filter envelope-detector receiver. The insights gained here are useful to the problem of ML carrier recovery for Viterbi decoding of continuous phase modulation signals     

Analysis of phase noise effects in OFDM modems

The effects of the phase noise (PN) on orthogonal frequency-division multiplex modems are evaluated. Three receivers are studied: a coherent receiver, a common phase error correction receiver (which is a receiver specially designed to combat PN) and a differential receiver. The impact of the PN on the decision signal-to-noise ratio (SNR) of each of these receivers is computed as a function of the PN spectrum. The resulting formulas are extremely simple. The theory is applicable to a wide range of PN models, and unifies and extends previous results on the topic. The conditions under which the decision SNR yields correct symbol error rate predictions are discussed. Simulations are reported that confirm the results.     

PN code-aided ranging for optical satellite communication systems

A model for the pseudonoise (PN) code-aided estimation of the transmission path delay and ranging for direct-detection on-off-keying (OOK) optical intersatellite channels is suggested in which the intensity of the optical field is modulated by a PN code and random binary data symbols. A closed-loop code-tracking loop model, motivated by the maximum-likelihood (ML) estimation of the phase difference between the received PN code and a locally generated one, is obtained. The maximum-likelihood model is approximated and, consequently, receiver models for the high and low signal-to-noise ratio (SNR) are suggested. The resulting code tracking loop S-curves of the receivers are that of the S-curves of a noncoherent delay-locked loop (NCDLL). The performance of the two receivers under the influence of background noise, signal count and PN code length is obtained     

The impact of frequency-flat fading on the spectral efficiency ofCDMA

The capacity of the randomly spread synchronous code-division multiple-access (CDMA) channel subject to frequency-flat fading is studied in the wide-band limit of large number of users. We find the spectral efficiency as a function of the number of users per chip, the distribution of the flat fading, and the signal-to-noise ratio (SNR), for the optimum receiver as well as linear receivers (single-user matched filter, decorrelator, and minimum mean-square error (MMSE)). The potential improvements due to both decentralized transmitter power control and multi-antenna receivers are also analyzed     

BER evaluation for phase and polarization diversity opticalhomodyne receivers using noncoherent ASK and DPSK demodulation

An analysis of the performance of phase diversity receivers using amplitude-shift keying (ASK) and differential phase-shift keying (DPSK) is presented. Both {2×2} and {3×3} multiport receivers are investigated. Asymptotic methods are used to estimate the bit error rate (BER) and signal-to-noise power ratio (SNR) dependence for each type of the receiver. The analysis favors the squarers as the demodulators for ASK whose performance approaches that of the ideal heterodyne detector in the limit of large SNR. A modification of the ASK ({3×3}) receiver which cancels the local oscillator intensity noise is proposed. Receivers which comprise polarization and phase diversity techniques are also investigated for both ASK and DPSK. Their performance is independent of the polarization state of the received signal, and the value of SNR required to obtain the BER of 10^-9 is only a few tenths of a decibel greater than that needed by the phase diversity receivers     

Linearization of receivers using envelope signal injection

This paper presents a new linearization method for receivers employing envelope signal injection. In this technique, the third-order intermodulation distortion (IM3), at the output of a mixer in IF band, is cancelled by injecting the envelope of the RF input signal to both the low noise amplifier (LNA) and the mixer. By properly adjusting the amplitude and polarity of the injected envelope signal, up to 40-dB improvement of the IM3 and 11-dB improvement of the IM5 is obtained in a two tone test with 100-kHz separation at 1.9GHz. This method operates very well over a wide range of power up to the 1-dB compression point of the receiver. The noise performance of the receiver under this linearization technique is also investigated. The noise floor at the output of the receiver is increased by 0.8 dB only when the system is optimized for linearity.     

Performance of UWB Receivers with Partial CSI Using a Simple Body Area Network Channel Model

Ultra wideband (UWB) communication is a very promising candidate for the use in wireless body area networks (BAN). The high UWB peak data rate allows for medium average data rates in combination with a very low duty cycle, which is the key for a very low power consumption. Devices in a wireless BAN require low complexity. Hence, mainly non-coherent receivers such as energy detector and transmitted-reference receiver are suited. In this paper, the symbol-wise maximum-likelihood (ML) detectors for pulse position modulation (PPM) and transmitted reference pulse amplitude modulation (TR PAM) are derived assuming partial channel state information (CSI) at the receiver. Additionally, also the ML detectors for a combination of PPM and TR PAM are presented. The performance of the derived receiver structures is evaluated using a novel BAN channel model not distinguishing line-of-sight and non line-of-sight situations. This simple channel model is based on 1100 channel measurements in the frequency range between 2 and 8 GHz, which were measured in an anechoic chamber. Using the BAN channel model, performance of the derived receiver structures is evaluated showing that the knowledge of the average power delay profile (APDP) at the receiver improves performance substantially. Requiring only slightly more complexity such receivers are a well suited alternative to non-coherent receivers for the use in a BAN.     

Phase noise in coherent analog AM-WIRNA optical links

Coherent analog amplitude modulated-wideband rectifier narrowband (AM-WIRNA) systems have been the focus of many recent studies because of their high performance and relative immunity to phase noise compared to angle modulated systems. Despite their natural advantages over angle modulated systems, AM-WIRNA receivers are still vulnerable to phase noise because of distortion of their phase broadened signals in a finite bandwidth system. We present the first numerical analysis of the effects of this distortion on the performance of AM-WIRNA systems. The analysis accurately models the power spectral density of the phase-to-intensity noise with a root-mean-square deviation from the averaged experimental noise spectrum of 1.2 dB and a maximum deviation of 3.8 dB in the modulation range of <2 GHz. The accuracy of the analysis is limited primarily by nonidealities in the AM-WIRNA receiver and the accuracy of the analytical intermediate frequency (IF) filter model. Optimal link designs are presented which minimize the impact of phase-to-distortion noise in AM-WIRNA systems. We present experimental data from AM-WIRNA links which use both external cavity and distributed feedback lasers for the signal and local oscillator sources. The numerical analysis predicts the link signal-to-noise ratio (SNR) for different signal laser powers to within 1.4 dB of experiment. We find that systems requiring high SNR such as phased array antennas and AM-CATV are significantly affected by this noise     

Optimum diversity detection over fading dispersive channels withnon-Gaussian noise

We consider the problem of M-ary signal detection over a single-input-multiple-output (SIMO) channel affected by frequency-dispersive Rayleigh-distributed fading and corrupted by additive non-Gaussian noise, modeled as a spherically invariant random process. We derive both the optimum detection structure and a suboptimal, reduced-complexity receiver, based on the low-energy-coherence approach. Interestingly, both detection structures are canonical, i.e., they are independent of the actual noise statistics. We also carry out a performance analysis of both receivers, with reference to the case that the channel is affected by a frequency-selective fading and for a binary frequency-shift-keying signaling format. The results obtained through both a Chernoff-bounding technique and Monte Carlo simulations reveal that the adoption of diversity also represents a suitable means to restore performance in the presence of dispersive fading and impulsive non-Gaussian noise. Interestingly, it is also shown that the suboptimal receiver incurs a limited loss with respect to the optimum (unrealizable) receiving structure