trellis coded differentially coherent tcdc mpsk with carrier phase noise the authors consider trellis coded m ary phase shift keying mpsk when used with differentially coherent demodulation over a carrier phase noise dominated channel a tight upper bound to the probability of error is introduced this bound shows the presence of an irreducible probability of error when compared to coherently demodulated trellis coded mpsk the irreducible probability of error of the differentially coherent scheme is much lower this improved robustness to carrier phase noise is obtained at the expense of signal to noise ratio snr coding gain numerical results for two ungerboeck codes with differentially coherent mpsk demodulation show poor snr coding gain a modification of ungerboeck codes which makes them more suitable for use with differentially coherent demodulation is shown to increase the snr gain while maintaining good robustness to carrier phase noise

signal classification using statistical moments an automatic modulation classification algorithm utilizing the statistical moments of the signal phase is developed and used to classify the modulation type of general m ary psk signals it is shown that the nth moment n even of the phase of the signal is a monotonic increasing function of m on the basis of this property the authors formulate a general hypothesis test develop a decision rule and derive an analytic expression for the probability of misclassification two examples are given to demonstrate the performance of the algorithm the algorithm is compared with the quasi log likelihood radio qllrc square law slc and phase based pbc classifiers the algorithm is outperformed by qllrc at low cnr but is comparable to slc and is better than pbc the qllrc algorithm is only valid at cnr

continuous phase modulation part i full response signaling the continuous phase modulation cpm signaling scheme has gained interest in recent years because of its attractive spectral properties data symbol pulse shaping has previously been studied with regard to spectra for binary data and modulation index 0 5 in this paper these results have been extended to the m ary case where the pulse shaping is over a one symbol interval the so called full response systems results are given for modulation indexes of practical interest concerning both performance and spectrum comparisons are made with minimum shift keying msk and systems have been found which are significantly better in e b n 0 for a large signal to noise ratio snr without expanded bandwidth schemes with the same bit error probability as msk but with considerably smaller bandwidth have also been found significant improvement in both power and bandwidth are obtained by increasing the number of levels m from 2 to 4

bit error rate of binary and quaternary dpsk signals with multiple differential feedback detection a differentially coherent detection scheme with improved bit error rate ber performance is presented for differentially encoded binary and quaternary phase shift keying psk modulation the improvement is based on using l symbol detectors with delays of 1 2 l symbol periods and on feeding back detected psk symbols exact formulas for the bit error probability are derived for the case that correct symbols are fed back the effect of symbol errors in the feedback path on the ber is determined by computer simulations

improving differential detection of mdpsk by nonlinear noise prediction and sequence estimation a new technique is proposed to improve the performance of differential detection dd of m ary differential phase shift keying mdpsk significantly applying sequence estimation in order to obtain an appropriate representation of the received signal a nonlinear time variant finite impulse response or infinite impulse response prediction error filter is used for both filter structures the optimum coefficients are derived assuming transmission over an additive white gaussian noise awgn channel delayed decision feedback sequence estimation ddfse is employed to estimate the transmitted symbol sequence it is shown by simulations that even for decision feedback equalization which is a simple special case of ddfse a significant performance improvement of conventional dd under awgn conditions results in contrast to other noncoherent low complexity receivers proposed in literature this receiver is very robust under flat fading rayleigh and ricean conditions

enhanced multiple bit differential detection of doqpsk in this paper we consider multiple bit differential detection mbdd of differential offset quadrature phase shift keying doqpsk with conventional bit wise differential encoding de we propose two novel mbdd schemes that outperform simon s mbdd and approach the performance of coherent detection cd as the observation window size n increases the first scheme uses the full available detection window spanning n 1 bit intervals and is referred to as f mbdd a careful bit error rate ber analysis shows that a significant performance improvement can be realized by reducing the detection window size to n 3 bit intervals the resulting improved mbdd i mbdd of doqpsk with bit wise de achieves a similar performance as phoel s mbdd of doqpsk with more complex symbol wise de for both f mbdd and i mbdd tight upper bounds and accurate ber approximations are derived in addition since the complexity per bit decision of brute force decoding of mbdd of doqpsk grows exponentially with n we develop optimum and suboptimum fast decoding algorithms with complexities per bit decision of orders log n 1 and n respectively

the statistical performance of some instantaneous frequency estimators the authors examine the class of smoothed central finite difference scfd instantaneous frequency if estimators which are based on finite differencing of the phase of the analytic signal these estimators are closely related to if estimation via the periodic first moment with respect to frequency of discrete time frequency representations tfrs in l cohen s 1966 class the authors determine the distribution of this class of estimators and establish a framework which allows the comparison of several other estimators such as the zero crossing estimator and one based on linear regression on the signal phase it is found that the regression if estimator is biased and exhibits a large threshold for much of the frequency range by replacing the linear convolution operation in the regression estimator with the appropriate convolution operation for circular data the authors obtain the parabolic scfd pscfd estimator which is unbiased and has a frequency independent variance yet retains the optimal performance and simplicity of the original estimator

adaptive noncoherent dfe for mdpsk signals transmitted over isi channels a novel noncoherent decision feedback equalization ndfe scheme for m ary differential phase shift keying signals transmitted over intersymbol interference channels is presented a suboptimum version with lower computational complexity and a noncoherent linear equalizer nle are derived from the original ndfe scheme furthermore the relation of the novel nle to a previously proposed nle is investigated in contrast to known ndfe schemes the novel scheme can approach the performance of coherent minimum mean squared error decision feedback equalization for adaptation of the feedforward and feedback filters efficient novel modified least mean square and recursive least squares algorithms are presented finally it is shown that the proposed adaptive ndfe scheme is robust against frequency offset

multiple symbol differential detection with diversity reception in this letter we first consider the maximum likelihood sequence estimator for multiple symbol differential detection msdd over the slow fading diversity channel since this optimum decision metric results in a complex receiver implementation whose average bit error probability bep performance is difficult if not impossible to obtain analytically we then focus our attention on evaluating the average bep for msdd with diversity reception in the form of postdetection equal gain combining egc giving emphasis to its ability to bridge the gap between egc of conventional differentially detected m psk and maximal ratio combining of coherently detected m psk with differential encoding

noncoherent block demodulation of msk with inherent and enhanced encoding it is shown that there is a close relation between known noncoherent minimum shift keying msk demodulation structures such as envelope and differential receivers and schemes derived from the noncoherent maximum likelihood block estimation n mlbe principle when the observation interval is increased the performance of msk with n mlbe tends to that of binary coherently detected orthogonal binary frequency shift keying a new demodulation strategy reduced block noncoherent estimation rbne is introduced and shown to improve the performance of noncoherent msk beyond that of coherently detected orthogonal fsk when rbne is used with msk and the observation interval is increased the performance approaches that of antipodal signaling the key feature of all these structures is multisymbol noncoherent processing with exploitation of the msk inherent coding properties induced by its phase continuity the use of binary block codes for msk with n mlbe is considered it is shown that simple binary block codes with low bandwidth expansion that exploit the inherent msk memory can give significant gains

noncoherent sequence detection new noncoherent sequence detection algorithms for combined demodulation and decoding of coded linear modulations transmitted over additive white gaussian noise channels possibly affected by intersymbol interference are presented optimal sequence detection in the presence of a random rotation of the signal phase assumed to be constant during the entire transmission requires a receiver complexity exponentially increasing with the duration of the transmission based on proper approximations simple suboptimal detection schemes based on the viterbi algorithm are presented whose performance approaches that of coherent detection in a companion paper by colavolpe and raheli see ibid vol 47 no 9 p 1303 7 1999 noncoherent sequence detection is extended to continuous phase modulations in the proposed schemes the tradeoff between complexity and performance is simply controlled by a parameter referred to as implicit phase memory and the number of states of a trellis diagram besides being realizable these schemes have the convenient feature of allowing us to remove the constant phase assumption and encompass time varying phase models the proposed schemes compare favorably with other solutions previously proposed in the technical literature

data aided noncoherent demodulation of dpsk considers noncoherent demodulation of dpsk when the receiver has partial knowledge of the information being transmitted this partial knowledge represents preamble symbols pilot symbols or past decisions when operating in a decision feedback mode the maximum likelihood ml noncoherent receiver for this case is derived it is shown that known demodulation schemes such as multi symbol differentially coherent receivers and decision feedback differential receivers can be considered as special cases of this data aided noncoherent dpsk demodulator a simple recursive structure for this receiver is introduced and its performance analyzed

on the generation of tikhonov variates a novel simple and efficient method for the generation of tikhonov a k a von mises random variates is proposed in the proposed method circular variates of a prescribed tikhonov distribution pt x alpha xi are generated via the transformation of variates selected randomly on a one for one basis from a bank of k distinct cauchy and gaussian generators the mutually exclusive probabilities of sampling from each of the cauchy or gaussian generators as well as the variance and half width parameters that specify the latter are derived directly from the cauchy gaussian and tikhonov characteristic functions all of which are either known or given in closed form the proposed random mixture technique is extremely efficient in that a single pair of uniform random numbers is consumed in the generation of each tikhonov or von mises sample regardless of the prescribed concentration and centrality parameters alpha xi all requiring neither the rejection of samples nor the repetitive evaluation of computationally demanding functions additional attractive features of the method are as follows by construction the first dominant n circular moments of tikhonov variates generated with the proposed random mixture technique are the ones that best approximate their corresponding theoretical values with errors measured exactly the exact distribution of generated tikhonov variates is determined analytically and its kullback leibler divergence to the exact tikhonov pdf is shown also analytically to be negligible finally the technique establishes a connection between tikhonov and gaussian variates which can be exploited e g in the generation of piecewise continuous pseudo random functions with tikhonov distributed outcomes

viterbi decoding of differentially encoded psk signals transmitted over rayleigh frequency flat fading channels maximum likelihood bit detection of differentially encoded m psk signals on rayleigh fading channels is investigated it is shown that the solution to this problem can be related to previous results vitetta and taylor 1994 and leads to the implementation of a receiver structure based on the viterbi algorithm and employing per survivor processing the error rate performance of this receiver is evaluated by means of computer simulations for both trellis coded and uncoded systems

differential phase detection using recursively generated phase references we show that decision feedback differential phase detection dfdpd is equivalent to a technique which generates a phase reference by averaging several primitive phase references we then modify the dfdpd into a differential phase detection dpd technique which generates the phase reference using a simple recursive form the proposed technique can be easily implemented and has satisfactory error performance

fast multiple symbol detection for free space optical communications in this paper we investigate noncoherent detection i e detection assuming the absence of channel state information at the receiver of on off keying in an intensity modulation and direct detection im dd free space optical fso system to partially recover the performance loss associated with symbol by symbol noncoherent detection we consider the application of multiple symbol detection msd in which block wise decisions are made using an observation window of several bit intervals specifically we develop a fast search algorithm for optimal msd and propose a reduced complexity decision metric suitable for suboptimal msd performance results confirm that the optimal and suboptimal metrics perform comparably well significantly the complexity of our receiver on a per bit decision basis is only logarithmically dependent on the observation window size we also present the framework for a decision feedback receiver and obtain performance expressions for the ideal case of error free feedback these expressions serve as an upper bound to the performance of msd analytical and simulation results indicate that as the observation window size increases the performance of the msd receiver approaches that of detection with channel state information the conclusion is reached that the proposed implementation provides an attractive low complexity mechanism for performing noncoherent msd in fso systems

the phase of a vector perturbed by gaussian noise and differentially coherent receivers some results are presented regarding the asymptotic distribution of the phase of a vector perturbed by gaussian noise it is shown that for large signal to noise ratio the asymptotic distribution of the phase is of the tikhonov type this framework is then used for the synthesis of differentially coherent receiver structures one for m ary phase shift keying mpsk and the other for minimum shift keying msk the first structure bridges the performance gap between coherent and differentially coherent demodulation of mpsk the msk receiver uses matched filtering with differential demodulation

differential detection with iir filter for improving dpsk detection performance this paper presents a method for improving the performance of differential detection of differentially encoded phase shift keying dpsk the structure of the proposed detection scheme consists of a conventional differential detection circuit equipped with an infinite impulse response iir filter combined with decision feedback the results of theoretical analysis and computer simulation show that performance of the proposed detection method can approach that of coherent detection of dpsk under additive white gaussian noise awgn conditions without any increase in architectural complexity furthermore a parameter of the proposed detector can be varied to optimize performance for static or fading conditions an adaptive scheme suitable for time varying rician fading channel conditions is presented and performance results obtained by computer simulation are given

df dd for channels with phase noise in this letter we design decision feedback differential detection df dd schemes for channels with phase noise if the df dd feedback filter is properly optimized a performance similar to that of a more complex scheme recently reported by chiavaccini and vitetta based on expectation maximization can be achieved however it is also shown that an error floor is unavoidable for channels with phase noise if a constraint is introduced the df dd receiver can be made robust against unknown frequency offsets

decision feedback differential detection of mdpsk for flat rayleigh fading channels in this paper decision feedback differential detection df dd of m ary differential phase shift keying mdpsk signals which has been introduced previously for the additive white gaussian noise awgn channel by leib et al 1988 and edbauer 1992 is extended to flat rayleigh fading channels the corresponding df dd metric is derived from the multiple symbol detection msd metric and for genie aided df dd an exact expression for the bit error rate ber of qdpsk m 4 is calculated furthermore the dependence of ber on the power spectrum of the fading process is investigated for feedback filters of infinite order it is shown that in this case for ideally bandlimited fading processes the error floor of conventional differential detection dd can be removed entirely simulation results confirm that both msd and df dd with feedback filters of finite order can reduce the error floor of conventional dd significantly df dd thereby causes considerably less computational load

pilot symbol assisted coded transmission over the block noncoherent awgn channel in this paper pilot symbol assisted transmission in conjunction with high performance coding over the block independent noncoherent additive white gaussian noise channel is investigated several approximate iterative receivers are proposed which either perform carrier phase estimation separately from detection or joint carrier phase estimation decoding in an iterative fashion the performance of the proposed receivers is analyzed using density evolution the power allocation to the pilot symbol is quantified and it is shown that an optimal allocation scheme exists that minimizes the overall information bit signal to noise ratio required for error free communication this optimal power allocation which could be utilized in code design is found to be sensitive to the channel coherence interval as well as to the particular receiver used in addition a simple upper bound on the performance of any receiver that performs joint iterative carrier phase estimation and detection is derived the obtained results are compared with the simulated performance of the proposed receivers

multiple bit differential detection of shaped offset qpsk we consider multiple bit differential detection mbdd of differentially encoded shaped offset quadrature phase shift keying soqpsk a highly bandwidth efficient and popular constant envelope modulation we propose two mbdd schemes that are based on a recent continuous phase modulation interpretation of soqpsk we show that the performance of these mbdd schemes approaches that of coherent detection cd as the multiple bit observation n window increases the first scheme uses a detection window that spans the full bit observation window f mbdd and is shown to require very large values of n to approach the performance of cd this presents a practical problem since the complexity of mbdd grows exponentially with n the second scheme is an improved version i mbdd with a detection window that is shortened to n 2 bit intervals although the complexity of i mbdd also increases exponentially with n it represents a significant improvement since only modest values of n are needed for high performance these performance characteristics are identified via a detailed performance analysis which provides asymptotic formulas for the bit error probability that are confirmed with computer simulations the analysis is also used to find the symmetric frequency pulse shapes with the best and worst error performance finally we develop a simplified and practical decision feedback differential detection algorithm that achieves near optimal performance with complexity that grows only linearly with n

phase based time domain estimation of the frequency and phase of a single sinusoid in awgn the role and applications of the additive observation phase noise model this paper presents the theoretical foundation for time domain phase based estimation of the frequency and phase of a single sinusoid in additive white gaussian noise awgn analogous to the theoretical foundation provided by rife and boorstyn for frequency domain fourier transform based estimation it is shown from the maximum a posteriori probability map and the maximum likelihood ml estimation principles that with the additive observation phase noise aopn due to the awgn being described by its a posteriori distribution conditioned on the received signal magnitude the received signal phase is a sufficient statistic for estimating the single sinusoid angle parameters using a geometric approach the exact statistical model for the aopn is derived where the a posteriori probability density function pdf and the corresponding a priori pdf are given by explicit closed form expressions that are valid for arbitrary signal to noise ratios snrs the a posteriori pdf is tikhonov and is of particular interest as it establishes the aopn model for phase based frequency phase map ml estimation in the time domain it is further illustrated that the results derived can yield various aopn models as special cases and the underlying physical insights and interconnections that exist among these models are revealed it is shown that the model derived by tretter is an ultimate specialization in the high snr limit of the aopn models developed here for high snr the a posteriori tikhonov pdf can be accurately approximated by a gaussian distribution which leads to the best linearized aopn model the applications of these aopn models to the design of linear estimators including the linear minimum mean square error lmmse estimator the linear minimum variance estimator and the lmmse implementation of the weighted phase averager are presented and their estimation performances are compared through computer simulations with the cramer rao lower bound crlb and the bayesian crlb as the benchmark to facilitate estimator design the a priori statistical models of the frequency and phase are proposed from the information theoretic perspective and an improved phase unwrapping algorithm over that given by fu and kam is presented it is shown that by incorporating all the information available in the aopn the estimation accuracy can be much improved

auditory motivated level crossing approach to instantaneous frequency estimation we address the problem of estimating the instantaneous frequency if of a phase signal using its level crossing lc information based on front end auditory processing motivation we show that the problem of if estimation using lc information can be cast in the framework of estimation from irregularly sampled data the formulation has the generality of estimating different types of if without the need for a quasistationary assumption we consider two types of if polynomial and bandlimited we use polynomial interpolating functions for the former and for the latter we propose a novel line plus sum of sines model the model parameters are estimated by linear regression considering the noisy case lc data for different levels is analyzed and methods for combining different estimators from lcs are discussed theoretical and extensive simulation results show that the performance of the zero crossing zc based if estimator and the level crossing based if estimator with smaller level values is better than those obtained with higher level values or their combinations the new technique reaches the crame spl acute r rao bound crb roughly above 4 db signal to noise ratio snr and its performance does not deteriorate rapidly with mismatch in the if order compared with the other techniques in the literature

theoretical analysis and performance limits of noncoherent sequence detection of coded psk a theoretical performance analysis of noncoherent sequence detection schemes previously proposed by the authors for combined detection and decoding of coded m ary phase shift keying m psk is presented a method for the numerical evaluation of the pairwise error probability for which no closed form expressions exist is described the classical union bound is computed and results are compared with computer simulations an upper bound on this pairwise error probability is also presented this upper bound may be effectively used for the definition of an equivalent distance which may be useful in exhaustive searches for optimal codes using this bound it is proven that in the general coded case the considered noncoherent decoding schemes perform as close as desired to an optimal coherent receiver when a phase memory parameter is sufficiently large in the case of differentially encoded m psk a simple expression of the asymptotic bit error probability is derived which is in agreement with simulations for high as well as low signal to noise ratio snr

reduced complexity soft decision multiple symbol differential sphere detection unlike a generic psk qam detector which may visit a constellation diagram only once a depth first sphere decoder sd has to re visit the same constellation diagram multiple times therefore in order to prevent the sd from repeating the detection operations the schnorr euchner search strategy of schnorr and euchner may be invoked for optimizing the nodes search order where the ideal case is for the sd to visit the constellation nodes in a zigzag fashion however when the hard decision multiple symbol differential sphere detection msdsd of lampe et al is invoked for using multiple receive antennas n r ge 1 the schnorr euchner search strategy has to visit and sort all the m textrm psk constellation points a similar situation is encountered for the soft decision msdsd of pauli et al when the a priori llrs gleaned from the channel decoder are taken into account in order to tackle these open problems in this paper we propose a correlation process for the hard decision msdsd of lampe et al and a reduced complexity design for the soft decision msdsd of pauli et al so that the schnorr euchner search strategy always opts for visiting the m textrm psk constellation points in a zigzag fashion our simulation results demonstrate that a substantial complexity reduction is achieved by our reduced complexity design without imposing any performance loss explicitly up to 88 7 complexity reduction is attained for msdsd n w 4 aided d16psk this complexity reduction is quite substantial especially when the msdsd is invoked several times during turbo detection furthermore in order to offer an improved solution and a comprehensive study for the soft decision msdsd we also propose to modify the output of the sd to harmonize its operation with the near optimum approx log map then the important subject of coherent versus noncoherent is discussed in the context of coded systems which suggests that msdsd aided dpsk is an eminently suitable candidate for turbo detection assisted coded systems operating at high doppler frequencies

phase noise effects on turbo trellis coded over m ary coherent channels the effect of the phase noise on the performance of bandwidth efficient coded modulation is studied to this end the average mutual information ami for specific constellations such as 8 phase shift keying and 16 quadrature amplitude modulation is calculated in the presence of carrier phase error caused by imperfect carrier tracking over an additive white gaussian noise channel the ami not only quantifies the effect of the phase noise from an information theoretic viewpoint but also serves as an estimate for a permissible amount of the phase noise for a given signal to noise ratio the bit error rate ber performance of a near optimal turbo trellis coded modulation scheme is then investigated over such a channel for this purpose an optimal branch metric which best fits the channel characteristics is derived furthermore simple branch metrics referred to as suboptimal simplified and gaussian metrics are derived which may offer the tradeoff between ber performance and computational complexity numerical analysis shows that a near optimal coded modulation scheme renders a transmission system more robust against phase noise than is the case with a conventional trellis coded modulation scheme

decision feedback differential detection in impulse radio ultra wideband systems in this paper we present decision feedback differential detection df dd schemes for autocorrelation based detection in impulse radio ultra wideband ir uwb systems a signaling scheme regarded as a promising candidate in particular for low complexity wireless sensor networks to this end we first discuss ideal noncoherent sequence estimation and approximations thereof based on block wise multiple symbol differential detection msdd and the viterbi algorithm va from the perspective of tree search trellis decoding exploiting relations well known from tree search decoding we are able to derive the novel decision feedback differential detection df dd schemes a comprehensive comparison with respect to performance and complexity of the presented schemes in a typical ir uwb scenario reveals along with novel insights in techniques for complexity reduction of the sphere decoder applied for msdd that sorted df dd achieves close to optimum performance at very low and in particular constant receiver complexity

a unified performance analysis framework for differential detection in mimo rayleigh fading channels in this paper a unified framework for the analysis of differential detection dd schemes in time variant multiple input multiple output rayleigh fading channels is provided the present results are very general in that they apply to transmission with differential phase shift keying unitary differential space time modulation dstm and block dstm and reception with conventional dd cdd multiple symbol dd msdd decision feedback dd dfdd and differentially coherent detection cd new result for general quadratic forms of gaussian random variables are derived which allows us to obtain elegant closed form expressions for the pairwise error probabilities peps of the dominant error events of the considered detectors furthermore it is shown that a unified treatment of all considered detectors is possible with a properly defined effective signal to noise ratio esnr and a useful connection between msdd and minimum mean squared error mmse interpolation is established interesting novel results obtained from this analysis include i dstm constellations designed for cdd and cd are also optimum for msdd and dfdd ii the error floor entailed by msdd and dfdd in time variant fading decreases exponentially with the observation window size n and iii in time variant fading with effective normalized fading bandwidth bh efft msdd with n rarr infin suffers only from an snr loss of 1 2bh efft compared to cd whereas dfdd suffers from a diversity loss of 1 2bh efft

on the error probability of decision feedback differential detection we give a tight approximation for the bit error rate ber of decision feedback differential detection df dd the influence of error propagation is modeled by a markov chain a simple state reduction method is proposed to limit computational complexity our results show that error propagation strongly depends on the chosen feedback filter in particular the popular assumption that error propagation increases ber by a factor of two is not always justified

adaptive linear equalization combined with noncoherent detection for mdpsk signals a novel noncoherent receiver for m ary differential phase shift keying signals transmitted over intersymbol interference channels is presented the noncoherent receiver consists of a linear equalizer and a decision feedback differential detector a significant performance gain over a previously proposed noncoherent receiver can be observed for an infinite number of feedback symbols the optimum equalizer coefficients can be calculated analytically and the performance of the proposed receiver approaches that of a coherent linear minimum mean squared error equalizer moreover a modified least mean square and a modified recursive least squares algorithm for adaptation of the equalizer coefficients are discussed

iterative decision feedback differential demodulation of bit interleaved coded mdpsk for flat rayleigh fading channels a simple receiver structure previously proposed by the authors for convolutional coded m ary differential phase shift keying transmission over flat rayleigh fading channels without channel state information is analyzed in detail we present a thorough discussion of the iterative decoding procedure which is referred to as iterative decision feedback differential demodulation iterative df dm the convergence behavior of iterative df dm is theoretically examined the analysis supports the observation that the iterative decoding scheme works well for target bit error rates which are usually of interest furthermore the associated cut off rate for error free decision feedback is studied judging from this performance parameter remarkable gains in power efficiency compared to conventional differential demodulation are indicated while the computational complexity of the decoding remains low the results from information theory are in good agreement with the given simulation results

a new method for solving hilbert type singular integral equations abstract a simple method for solving hilbert type singular integral equations is proposed using the reproducing kernel as the basis of w 2 1 0 2 the singularity of the considered equation is removed skillfully since the problem is discussed in space w 2 1 0 2 which only require the absolute continuity of the considered function our method is effective not only for smooth solutions but also for non smooth solutions the final numerical examples show the efficiency of the proposed method

maximum likelihood differential detection of uncoded and trellis coded amplitude phase modulation over awgn and fading channels spl minus metrics and performance this paper derives metrics for maximum likelihood differential detection of uncoded and trellis coded mpsk and qam transmitted over rayleigh and rician fading channels receiver structures based on these metrics are proposed and their error probability performance analyzed and or simulated the results represent a generalization of the notion of multiple symbol differential detection previously introduced by the authors for mpsk over an awgn to the fading channel and other modulations for the coded cases ideal interleaving deinterleaving is assumed and furthermore the presence or absence of channel state information an interesting side result is that for a constant envelope modulation transmitted over a fading channel with unknown but rapidly varying phase error the other extreme to the slowly varying phase error case normally assumed for differential detection under certain practical assumptions it is shown that the optimum receiver is of the limiter discriminator type

differential encoding by a look up table for quadrature amplitude modulation in this paper we propose a novel differential encoder for qam quadrature amplitude modulation by a look up table instead of a rule using a table for differential encoding has the advantages of both low complexity and good error performance we propose algorithms to construct the table for maximizing the minimum noncoherent distance and minimizing the number of different data bits between two codewords with small noncoherent distance for 16qam and 32qam we show that the differential encoders obtained by the proposed algorithms are optimal in terms of minimum noncoherent distance differential detectors for qam including a reduced complexity two symbol detector and multiple symbol detectors are proposed as well simulation results of 16qam show that the proposed differential encoder provides significant gain over existent differential encoders as expected by distance analysis and the proposed low complexity multiple symbol differential detector can further improve the error performance