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.     

Performance analysis of predetection EGC receiver in Weibull fading channel

The predetection equal gain combining (EGC) receiver is generally known to have a performance that is close to the maximal ratio combining (MRC) receiver while having relatively less implementation complexity. The bit error rate (BER) of an EGC receiver for binary, coherent and noncoherent modulations has been analysed for an independent Weibull fading channel. Numerical results have been compared with the available results for selection combining (SC) and MRC diversity receivers.     

Performance of optimum and suboptimum OFDM‐CPM receivers over multipath fading channels

A class of orthogonal frequency division multiplexing‐continuous phase modulation (OFDM‐CPM) signals is introduced in which binary data sequence is mapped to complex symbols using the concept of correlated phase states of a CPM signal. Canonical optimum and suboptimum multiple‐symbol‐observation OFDM‐CPM receivers are derived. Multipath channel with AWGN is assumed. The receivers are analyzed for bit error rate (BER) performance in terms of high‐ and low‐SNR bounds. These bounds are illustrated as a function of parameter h, time delay and attenuation level. It is shown that OFDM‐CPM systems, with h=0.5,0.25 and an observation interval length of two symbols, can outperform conventional OFDM‐PSK system for a two‐ray multipath model. Copyright © 2005 John Wiley & Sons, Ltd.     

Performance of RAKE receivers in Nakagami fading channel witharbitrary fading parameters

A new expression for the bit error rate of RAKE receivers with either coherent or noncoherent/differentially coherent binary demodulation schemes in a Nakagami fading channel is derived. The analysis assumes an arbitrary number of diversity branches with arbitrary fading parameters     

Optimum detection and signal selection for partially coherent binary communication

The optimum detectors for coherent and noncoherent reception of binary signals in additive Gaussian noise and the resuiting error probabilities were obtained by Helstrom [1]. In many practical communication systems a reasonable estimate of the phase of the received signal is available as the result of an auxiliary tracking operation of the carrier signal by a coherent tracking device such as a phase-locked loop. It is shown that the optimum detector for this case, which we refer to as partially coherent reception, is a linear combination of the correlation detector and the squared envelope correlation detector, which are optimum for the coherent and noncoherent cases, respectively. The error probabilities are also obtained as a function of the energy-to-noise ratio of the channel and the variance of the error in the phase estimate, which is a function of the signal-to-noise (SNR) in the tracking loop. The signal selection problem is considered in terms of these parameters.     

The influence of mobile-to-mobile land communication channelspectrum on the error rate of binary DPSK and NFSK matched filterreceivers

The effect of a specific fading correlation function derived for a mobile-to-mobile land communication channel on the performance of differentially coherent PSK and noncoherent FSK matched filter receivers is investigated. The bit error probability, irreducible error rate, and the degradation in signal-to-noise ratio (SNR) are specifically derived for each system. The effect of the fading bandwidth on the performance of the system is also investigated     

Coherent detection of biorthogonal signals over Rayleigh fadingchannels

A practical coherent detection scheme for biorthogonal signals over Rayleigh fading channels is proposed. The proposed scheme improves the bit error rate (BER) performance compared to the noncoherent detection schemes for biorthogonal signals. It also outperforms the coherent and noncoherent detection schemes for orthogonal signals with comparable bandwidth efficiency. The BER performance for a Rayleigh fading channel with two path diversity combining is obtained by computer simulation. The results show that the required average signal-to-noise ratio per bit γ_b can be reduced by as much as 1.4 dB when we use this system in the CDMA cellular reverse link     

DPSK exact bit error rates with unsynchronized slowly fading interferers

We derive a new closed-form expression for the exact bit error probability for the detection of a noncoherent binary phase shift keying signal experiencing a multiple cochannel asynchronous interferers in nonselective Rayleigh-fading channels. The analysis accounts for the effect of the timing offset of the different interfering signals as well as the correlation between two adjacent bit intervals. It is valid for general waveshaping pulses and allows interfering signals to have unequal power levels. The results are used to assess the accuracy of the Gaussian interference approximation for diversity receivers.     

Asymptotical performance of M-ary and binary signals overmultipath/multichannel Rayleigh and Rician fading

This paper presents a general framework for computing the asymptotic error probability (i.e., at high average SNRs) of M-ary and binary signaling schemes over Rician and Rayleigh fading diversity channels. A general theorem (Theorem 1) relates the asymptotic error rate of multipath and multichannel receivers (over AWGN, ISI free channels) to the multidimensional integral of the conditional error probability. Two other theorems are presented for the particular cases where the conditional error probability is a function of the sum of received SNRs (Theorem 2) or received amplitudes (Theorem 3). Theorems 2 and 3 are related for linear coherent systems, and closed form expressions are obtained for equal gain combining systems. Detection structures for typical diversity schemes (coherent/noncoherent maximal ratio and equal gain combining, and quadratic noncoherent combining) are considered. We analyze the asymptotic error rates of some M-ary signaling schemes (MPSK/MPAM with Kth order diversity and orthogonal signals with K=1 and with coherent and noncoherent detection). Binary signaling is also considered in our study     

Performance Analysis of Optimum and Suboptimum Selection Diversity Schemes on Rayleigh Fading Channels With Imperfect Channel Estimates

In this paper, we present a comparative analysis on the effects of channel estimation errors on the performance of optimum and suboptimum selection diversity (SD) receivers on Rayleigh-fading channels. By modeling the estimation errors as independent complex Gaussian random variables, we derive simple closed-form expressions for the average probability of error for both optimum and suboptimum SD schemes with noisy channel estimates. With dual diversity and imperfect estimates, we establish a connection between optimum SD and maximal-ratio combining (MRC), and between suboptimum SD and equal-gain combining diversity schemes. Interestingly, we show that the optimum SD receiver structure and the resulting performance for differential binary coherent phase-shift keying (DBPSK) signaling can be obtained, in a straightforward way, as a special case of the performance of the optimum SD scheme with binary PSK signaling and channel estimation errors. For a fixed average power and bit duration, in conjunction with pilot-assisted minimum mean-square error channel estimation, we show that the optimum coherent SD scheme coincides with that of the optimum noncoherent SD scheme with binary frequency-shift keying (BFSK) signaling, whereas the coherent MRC scheme coincides with the optimum noncoherent receiver (i.e., the square-law combiner) for BFSK. The optimum number of diversity channels, under an energy-sharing mode of operation, is also studied. Finally, we formulate the problem of optimal pilot placement, consider channel estimation with a practical pilot-symbol-assisted modulation technique, and present some numerical results illustrating the comparative performances of various SD receivers     

Examples of Continuous Phase Modulation Using Discriminator Detection

Continuous phase modulation (CPM) techniques for digital communication have been proposed to achieve narrow bandwidth and good bit error rate (BER) performance in coherent systems. These modulation schemes may also be used with noncoherent discriminator detection. However, in this case, the CPM schemes should be designed for noncoherent detection. Using a receiver proposed by Chung for GTFM and "modified GTFM" signals, we show that it is possible to slightly improve BER performance over that of previous GTFM noncoherent schemes. We also show that a form of GMSK can achieve discriminator detectability performance almost equal to that of classical binary FSK (modulation index = 0.7) but with a much narrower bandwidth.     

Performance of a Predetection EGC Receiver in Hoyt Fading Channels for Arbitrary Number of Branches

Simple and accurate expressions for the performance of an L branch equal gain combining receiver in independent Hoyt fading channels are presented. Using an approximate but highly accurate probability density function of the sum of Hoyt random variables, expressions for the average bit error rate for binary, coherent and noncoherent modulations have been obtained. The effect of the number of diversity branches on the normalized average output SNR is examined. The results have been verified against available results.     

Probability of Error Analyses of a BFSK Frequency-Hopping System with Diversity Under Partial-Band Jamming Interference--Part II: Performance of Square-Law Nonlinear Combining Soft Decision Receivers

In this paper, error probability analyses are performed for a binary frequency-shift-keying (BFSK) system employingLhop/bit frequency-hopping (FH) spread-spectrum waveforms transmitted over a partial-band Gaussian noise jamming channel. The performance results for two types of square-law nonlinear combining soft decision receivers under worst-case partial-band jamming are presented. The receivers employ, prior to combining, nonlinear weighting strategies of 1) adaptive gain control and 2) soft limiting (clipping) of the detector output of each channel of the dehopped waveform. Both thermal noise and jamming are included in the analyses. It is shown in the paper that a diversity gain for error rate improvement is realizable for nonlinear combining receivers provided that the noncoherent combining loss is less dominant than the jamming power reduction realized by the weighting strategy. Performance comparisons between linear and nonlinear combining receivers are presented.     

Asymptotic error probability analysis of quadratic receivers inRayleigh-fading channels with applications to a unified analysis ofcoherent and noncoherent space-time receivers

A general, asymptotic (high signal-to-noise (SNR)) error analysis is introduced for quadratic receivers in frequency-flat and multipath Rayleigh-fading channels with multiple transmit and receive antennas. Asymptotically tight expressions for the pairwise error probabilities are obtained for coherent, noncoherent, and differentially coherent space-time receivers. Not only is our unified analysis applicable to more general modulation schemes and/or channel models than previously considered, but it also reveals a hitherto unrecognized eigenvalue structure that is common to all of these problems. In addition to providing an easy recipe for computing the asymptotic pairwise error rates, we make some conclusions regarding criteria for the design of signal constellations and codes such as (a) the same design criteria apply for both correlated and independent and identically distributed (i.i.d.) fading processes and (b) for noncoherent communications, unitary signals are optimal in the sense that they minimize the asymptotic union bound     

Microdiversity on Rician fading channels

The performance of an L-branch equal gain (EG) combiner on slow and nonselective Rician fading channels is analyzed. Two performance criteria are considered; the probability distribution of signal-to-noise power ratio (SNR) at the output of the EG combiner and the average bit error rate (BER). Matched filter receivers are considered for two binary modulation formats, coherent phase shift keying (CPSK) and noncoherent frequency shift keying (NCFSK). Results using both maximal ratio combining (MRC) and selection diversity combining (SC) are presented for comparison. Our results show that from a feasibility and practical tradeoffs point of view, the performance of an EG combiner may be as good as that of a MR combiner. The effects of gain unbalance between branches of the EG combiner on the probability distribution of SNR and on the bit error rates are also investigated. The Rician fading model may be used to model bath the microcellular environment and the mobile satellite fading channel. Hence, the results of this paper may be useful in both of these areas. Furthermore, in the development of the analysis, we present an efficient method for computing the distribution of sums of Rician random variables. This may be useful for other problems involving Rician fading. The suitability of modeling a Rician fading environment by a properly chosen Nakagami model is examined. A formula for determining the corresponding values of Rician parameter K and Nakagami parameter m is also assessed     

Analysis of equal gain diversity on Nakagami fading channels

An infinite series for the complementary probability distribution function (CDF) of the signal-to-noise ratio (SNR) at the output of L -branch equal-gain (EG) diversity combiners in Nakagami (1960) fading channels is derived. The bit error rate for a matched filter receiver is analyzed for the L-branch EG combiner and different fading parameters. Both coherent phase shift keying (CPSK) and differential coherent phase shift keying (DCPSK) are considered. The effects of gain unbalance between branches on the probability distribution of the SNR and on the bit error rates are investigated. Bit error rate results are also obtained for coherent and noncoherent reception of frequency shift keying (FSK). The effects of gain unbalances on FSK modulations are also investigated. Bit error rates for EG combining on Rayleigh fading channels are obtained for L>2. These results are presented as a special case of the more generalized Nakagami fading model     

Optical preamplifier receiver for spectrum-sliced WDM

Spectrum-slicing provides a low-cost alternative to the use of multiple coherent lasers for wavelength division multiplexing (WDM) applications by utilizing spectral slices of a single broadband noise source for creating the multichannel system. In this paper we analyze the performance of both p-i-n and optical preamplifier receivers for spectrum-sliced WDM using actual noise distributions, and the results are compared with those using the Gaussian approximation. This extends prior results of Marcuse for the detection of deterministic signals in the presence of optical amplifier and receiver noise. Although the methodology is similar, the results are considerably different when the signal is itself noise-like. For the case of noise-like signals, it is shown that when an optical preamplifier receiver is used, there exists an optimum filter bandwidth which minimizes the detection sensitivity for a given error probability. Moreover the evaluated detection sensitivity, in photons/bit, represents an order of magnitude (>10 dB) improvement over conventional detection techniques that employ p-i-n receivers. The Gaussian approximation is shown to be overly conservative when dealing with small ratios of the receiver optical to electrical bandwidth, for both p-i-n and preamplifier receivers     

基于深度学习的抗窄带干扰MSK非相干接收机

窄带干扰(Narrowband Interference,NBI),作为一种敌意的频域干扰,会严重地恶化最小频移键控(Min-imum Shift Keying,MSK)非相干检测的误码率(Bit Error Rate,BER)性能.为降低窄带干扰对BER性能的影响,MSK非相干接收机一般首先对接收信号进行干扰抑制.然...     

Analysis of switched diversity systems on generalized-fadingchannels

The performances of switched diversity systems operating on generalized (Nakagami)-fading channels are analyzed using a discrete-time model. The average bit error rate (BER) of binary noncoherent frequency shift keying (NCFSK) on slow, nonselective Nakagami-fading channels is derived. Closed-form expressions that can be used to determine optimum switching thresholds (in a minimum error rate sense) are also derived. In addition, the use of optimum fixed thresholds is considered. It is found that a considerable amount of diversity gain can be obtained using an optimum fixed (rather than adaptive) switching threshold. Results are obtained for both independent and correlated Nakagami-fading branch signals. The effects of fading severity and the correlation coefficient on both the BER and on the optimum switching threshold are investigated. It is shown that useful diversity gain can be obtained with power correlation coefficients as high as 0.9 when the fading is strong. The results for a Rayleigh channel are obtained and presented as a special case of generalized-fading model     

Pilot symbol aided coherent decorrelating detector for up-link CDMAmobile radio communication

A new decorrelating arrangement for asynchronous up-link direct sequence code division multiple access communication, which employs coherent detection with pilot symbol aided channel estimation, is proposed. The proposed coherent scheme improves the bit error rate (BER) and exhibits no error floor compared to the previous noncoherent schemes. The BER performance for BPSK is obtained by simulations over a frequency-nonselective Rayleigh fading channel