Showing papers on "Continuous phase modulation published in 1999"

Noncoherent sequence detection

Abstract: 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.

A serial concatenation approach to iterative demodulation and decoding

Abstract: Iterative demodulation and decoding of convolutionally encoded data is treated as a special case of the previously proposed serial concatenation of interleaved codes. It is shown that by exploiting the recursive nature of the differential modulation schemes (for example, DBPSK, DQPSK, CPM, etc.), large interleaving gains can be achieved similar to serial concatenation schemes. We also show that when memoryless modulation is used, precoding can be used to create a rate-1 recursive inner code in order to obtain interleaving gains without adding redundancy from the inner code.

Noncoherent sequence detection of continuous phase modulations

Abstract: In this paper, noncoherent sequence detection, proposed in a companion paper by Colavolpe and Raheli (see ibid. vol.47, no.9, p.1376-85, 1999), is extended to the case of continuous phase modulations (CPMs). The results in the companion paper on linear modulations with intersymbol interference (ISI) are used here because a CPM signal is mathematically equivalent to a sum of ISI-affected linearly modulated components, according to the Laurent decomposition. The proposed suboptimal detection schemes have a performance which approaches that of coherent detection with acceptable complexity, allow for time-varying phase models, and compare favorably with previously proposed solutions.

Performance of trellis coded CPM with iterative demodulation and decoding

Abstract: Interleaved trellis coded systems with continuous phase modulation (TCCPM) are considered. Upper bounds and lower bounds on the bit error rate (BER) performance are derived for coherent detection on the additive white Gaussian noise and flat Rayleigh fading channels by considering the trellis code, interleaver and CPM modulator as a serially concatenated convolutional code. A coherent receiver that performs iterative demodulation and decoding is shown to provide performance close to the lower bounds developed.

Hybrid chireix/doherty amplifiers power waveform synthesis

Abstract: Two amplifiers that are driven using outphasing modulation are coupled to one another so that the amplifiers affect each other's effective load line. The two amplifiers can maintain efficiency over a wider dynamic range than in a conventional amplifier. Amplifiers according to the invention amplify an AC input signal of varying amplitude and varying phase using a DC power supply. A converter converts the AC input signal into a first signal having constant amplitude and a first phase angle and into a second signal having constant amplitude and a second phase angle. The first amplifier amplifies the first signal, and the second amplifier amplifies the second signal. A coupler couples the first and second amplifiers to one another and to a load impedance, such that voltages or currents in the first amplifier become linearly related to voltages or currents in the second amplifier. The coupler may include at least one transformer that serially couples the first and second amplifiers to one another and to the load impedance. The coupler may also include first and second quarter wave transmission lines that couple the first and second amplifiers to one another and to the load impedance. The amplifiers preferably use bilateral devices, such that current flows from the first and second amplifiers to the DC power supply during a part of a signal cycle, and thereby returns energy to the DC power supply. Each of the more than two signals of constant amplitude and controlled phase is then separately amplified in separate amplifiers. The separately amplified more than two signals of constant amplitude and controlled phase are then combined to produce an output signal that is an amplification of the input signal at the desired power level. When converting the input signal into more than two signals, the phase of each of the more than two signals of constant amplitude and controlled phase is controlled to produce the output signal that is an amplification of the input signal at the desired power level. According to another aspect, a signal of varying amplitude and varying phase is generated from a plurality of constant amplitude varying phase signals, the sum of which is the signal of varying amplitude and varying phase. An IQ waveform generator generates a cosine carrier modulation waveform I(t) and a sine carrier modulation waveform Q(t) from the signal of varying amplitude and varying phase. A function generator generates a complementary waveform Q'(t) from the cosine carrier modulation waveform I(t) such that the sum of squares of I(t) and Q'(t) is constant. A first modulator modulates a cosine carrier signal with I(t) to obtain a first modulated cosine carrier. A second modulator modulates a sine carrier signal with Q'(t) to obtain a first modulated sine carrier. A circuit such as a butterly circuit forms the sum and difference of the first modulated cosine carrier and the first modulated sine carrier to obtain the constant amplitude varying phase signals.

Spectrum efficient fast frequency-hopped modem with coherent demodulation

Abstract: A system for increasing data transmission capacity over a wireless mobile link while at the same time providing improved jamming resistance utilizes discrete trellis-coded modulation involving frequency hopping individual symbols, along with encoding the phase of a symbol as a frequency offset to the hopped carrier frequency. This modulation system permits coherent demodulation in which both phase and amplitude of a symbol is robustly decoded and in which each phase of a quadrature amplitude modulated signal is decoded by the detected frequency offset, thus to provide reliable recovery of phase in the demodulation section. The resulting system improves spectrum efficiency and permits fast frequency hopping for improved jamming resistance, with the utilization of frequency offset coding permitting the coherent demodulation that improves the error-rate without the introduction of additional reference bits.

Serially concatenated systems : an iterative coding approach with application to continuous phase modulation

Abstract: Iterative methods for concatenated coding and modulation in digital communication systems are considered. It is assumed that the code and modulation can be described by finite-state machines (FSM). An iterative decoder for such a system typically consists of a posteriori probability (APP) algorithms for the constituent FSMs. Starting with a detailed examination of these algorithms, it is found that their initialization values can be formally justified. Then, possible iterative methods such as fix-point iteration, Jacobi over-relaxation, damped substitution, and Newton’s method are presented and evaluated. The result is that fix-point iteration seems to be the best choice in most situations. As an application of iterative decoding in serially concatenated systems, coded and interleaved continuous phase modulation (CPM) is investigated. An APP algorithm (or maximum APP (MAP) detector) for CPM is derived, based on the classic APP algorithm for channel codes. It is then shown that a good suboptimal algorithm can be obtained using only a small set of receiver filters, which are optimal with respect to the size of the set. The resulting system is analyzed with the aim to determine the main parameters affecting performance. The weight spectrum for coded and interleaved minimum shift keying (MSK) is computed, resulting in a transfer function bound. This is cumbersome for a general CPM system; instead only the most significant error events contributing to the weight spectrum are identified, resulting in a new performance measure. Extensive computer simulations show good coherence with theory, and also remarkably good performance for some simple systems. Finally, the power spectral density and bandwidth are computed, allowing for a bandwidth/performance comparison of different combinations.

An automatic modulation recognition algorithm for spectrum monitoring applications

Abstract: An algorithm based on a decision-tree approach for the automatic modulation recognition of communications signals is presented. This algorithm can discriminate between continuous wave (CW), amplitude modulation (AM), double sideband suppressed carrier (DSB-SC), frequency modulation (FM), frequency shift keying (FSK), binary phase shift keying (BPSK) and quaternary phase shift keying (QPSK) modulations. Requirements for a priori knowledge of the signals are minimized by the inclusion of an efficient carrier frequency estimator and low sensitivity to variations in the sampling epochs. Computer simulations indicate good performance on an AWGN channel, even at signal-to-noise ratios as low as 5 dB. This compares favorably with the performance obtained with most algorithms based on pattern recognition techniques.

Constant-envelope orthogonal frequency division multiplexing modulation

Abstract: A constant-envelope signaling approach for orthogonal frequency division multiplexing (OFDM) modulation is proposed. By splitting the standard OFDM complex signals into real and imaginary sections, the proposed approach employs phase modulation in conjunction with signal clipping to endow the transmitted signal with a constant envelope, without destroying the required transmission characteristic associated with OFDM. The resultant constant-envelope signal enables the operation of the transmitter's power amplifier at the saturation point and thus maximizes the achievable power efficiency. Despite the constant-envelope advantage, half the bandwidth efficiency is traded off by the approach. It is shown by simulation that the bit error performance of the proposed system is only slightly degraded from the conventional OFDM system.

Symbol synchronization in a continuous phase modulation communications receiver

Abstract: Symbol synchronization in a continuous phase modulation receiver is achieved by calculating an arctangent function of a digital sample of the output of a quadrature demodulator. This signal is sampled by integration techniques or filtered to produce signals that represent a complex value whose phase changes at a rate which is half of the symbol rate. The complex value may be squared and rotated by an angle which is related to the symbol phase. The integrated sample or an arctangent function of the filtered sample is used as a controlling input for a numerically controlled oscillator which regulates the digital sampling.

Optimum precompensation filters for IQ modulation systems

Abstract: We present a technique for digitally precompensating for shortcomings in signal reconstruction filters in an IQ modulation system. Optimum digital precompensation filters are found using least squares (LS) techniques. The optimization problem is formulated in the frequency-domain, and the optimum LS solution is characterized using an eigenanalysis approach.

Data-aided linear prediction receiver for coherent DPSK and CPM transmitted over Rayleigh flat-fading channels

Abstract: In this paper, a new data-aided linear prediction receiver for coherent differentially encoded phase-shift keying (DPSK) and coherent continuous phase modulation (CPM) over Rayleigh flat-fading channels is presented, This receiver uses the previously detected symbols to estimate the carrier-phase reference and predict the channel gain continuously and therefore makes the optimal coherent detection of DPSK and CPM. The receiver has a simple structure and can be implemented easily. This is due partly to the fact that the linear predictors used for channel estimation do not depend on the autocorrelation function of the fading process. Simulation results on the bit error performance of QDPSK and minimum-shift keying (MSK) with the new receiver are given for both the additive white Gaussian noise (AWGN) and the Rayleigh flat-fading channels. The results show that the proposed receiver provides almost the same bit error rate (BER) performance as the ideal coherent receiver in an AWGN channel, is very robust against large carrier frequency offset between transmitter and receiver, and can provide a reasonably good BER performance in a fast Rayleigh fading channel. Finally, a multisample receiver is discussed and its error rate performance is evaluated by means of computer simulations. The results show that the multisample receiver provides good BER performance for higher fading rate.

Performance characterization of digital transmission systems with cochannel interference

Abstract: This paper presents a general methodology for performance characterization of digital transmission systems in the presence of cochannel interference, as a function of the actual number of interferers (ranging from zero to infinity). The bit error probability in time-invariant channels and outage probability in time-varying quasi-stationary channels are discussed. More precisely, a general approach to an outage probability definition based on the concept of the outage domain is introduced. This allows the discussion of the relation to the other definitions which have appeared in the literature and the proposal of some new more accurate methods for the evaluation of outage probability. A suitable comparison between exact evaluation, the well-known Gaussian approximation, and the other new approaches proposed in this paper, is carried out to evaluate performance, bit error probability is suitably obtained for linearly modulated signals by adopting a semianalytical approach, and for nonlinear (e.g., continuous phase) modulation signals, by means of simulation. Finally, as an example, the different approaches to derive performance discussed in the paper have been applied to a linear microcellular scenario.

Satellite navigation receiver for precise relative positioning in real time

Abstract: A navigation receiver system provides real-time precise relative positioning in cooperation with an associated carrier phase receiver. The navigation receiver system and the associated carrier phase receiver both sample signals during a single epoch, and the associated carrier phase receiver processes the received signals to provide and transmit first carrier phase measurement data. The navigation receiver system comprises a data link receiver that receives the first carrier phase measurement data from the associated carrier phase receiver, and a carrier phase receiver that receives carrier phase signals during the sampling epoch, and processes the carrier phase signals to provide a second carrier phase measurement data. The navigation system receiver also includes a processing unit that receives the first carrier phase measurement data and the second carrier phase measurement data and computes carrier phase difference measurements. The processing unit applies a local-minima search technique to the carrier phase difference measurements to resolve carrier phase integer ambiguities within the subspace of local minima, wherein the resolved carrier phase integers are subsequently used to determine a precise relative position of the navigation receiver system with respect to the associated carrier phase receiver. The present invention provides high precision, real-time position data from a signal time epoch. That is, the present invention resolves the integer ambiguities in carrier phase measurements with a single snap shot of the measurements. In addition, the system recovers very quickly following a signal interruption.

Chromatic dispersion measurement scheme having high frequency resolution

Abstract: A measurement scheme measures dispersive characteristics of optical components. The scheme includes modulation phase shift measurements performed on modulated optical carriers where the carrier frequency and the modulation frequency of the modulated optical carriers are adjusted to maintain a reference modulation sideband. A reference phase term is established by the reference modulation sideband in each of the modulation phase shift measurements. Phase indices of refraction at discrete optical frequencies of non-reference modulation sidebands are extracted from the modulation phase shift measurements. The extracted phase indices are used to calculate relative group delay and chromatic dispersion as measures of dispersive characteristics of the optical component. High timing resolution and high frequency resolution are achieved simultaneously through independent adjustment of the carrier frequency and the modulation frequency enabling optical components, including those having dispersive characteristics that are highly dependent on optical frequency, to be accurately characterized.

Adaptively-equalized digital receiver with carrier tracking

Abstract: A method of carrier tracking in a digital receiver includes adjusting the phase of an equalized signal by a phase correction to compensate for a carrier frequency offset. For a small carrier frequency offset the phase correction is based on a first estimate of phase error and phase velocity of the equalized signal. For a large carrier frequency offset the first phase velocity estimate is controlled by a second phase velocity estimate based on rotation of the data constellation.

Turbo detection of coded continuous-phase modulations

Abstract: Iterative (turbo) decoding of a coded, interleaved continuous-phase modulated (CPM) waveform is presented. The transmitter consists of a rate-2/3 convolutional encoder followed by an interleaver, and an 8-ary continuous phase modulator. At the receiver, soft output a posteriori probability algorithms for the convolutional code and the CPM waveform iteratively refine their probability estimates. Current simulation results show a 2.5 dB SNR improvement (at 10/sup -5/ bit-error rate) over trellis-coded CPM (TCCPM) with a 99% bandwidth efficiency of 1.24 bps/Hz. The detector has a complexity of approximately 4.5 times that of the TCCPM system.

Blind receivers for nonlinearly modulated signals in multipath

Abstract: Classical blind channel equalization methods may not be suitable for systems with nonlinear modulation (e.g., continuous phase-modulated signals) because the input to the channel may not be i.i.d. due to the modulator's memory. Moreover, the nonlinear characteristics of the modulator further complicate the channel estimation task. In this correspondence, we derive blind maximum likelihood channel estimation algorithms for nonlinearly modulated signals using a hidden Markov model (HMM) formulation. The proposed method implements a stochastic maximum likelihood approach and is well suited for short data records appearing in TDMA systems. Cramer-Rao bounds are derived, and some illustrative simulations are presented.

Soft-decision phase detection with Viterbi decoding for CPM signals

Abstract: It is known that continuous phase modulation (CPM) signals can be optimally detected by using coherent demodulation followed by Viterbi decoding. However, such a receiver is generally complicated, particularly at higher numbers of states, as it requires many correlators and many reference signals in the demodulator. In this study, a much simpler receiver, which employs a soft-decision phase detector followed by a Viterbi decoder, is proposed for the detection of CPM signals. The phase detector makes a decision in favor of one of the preselected phase subregions at the end of every interval, which is then used to calculate metrics for decoding. As in optimal detection, the Viterbi decoder decodes according to the trellis structure of CPM signals. The proposed receiver is analyzed in a narrow-band Gaussian channel with 2REC, 2-h, and trellis-coded continuous-phase frequency-shift keying signals. Numerical results show that the proposed receiver performs close to optimal detection with all types of signals considered in this study. The effect of the number of subregions in the phase detector is examined.

Differentiation and subtraction of amplitude and phase images using a photorefractive novelty filter

Abstract: In this article, we demonstrate the capability of a two-beam coupling photorefractive optical novelty filter of detecting changes in the amplitude or phase of optical images. These changes may either be continuous or discrete in time. The performance of the two-beam coupling novelty filter is investigated and expressions for the output contrast corresponding to phase and amplitude changes based on a novel, simple interference model of two-beam coupling are derived. These expressions are verified by experimental results on the novelty contrast, revealing that the amplitude contrast is not described correctly by the commonly accepted coupled-wave theory. The novelty filter was applied to the detection of temporally continuous phase changes provided by a gas flow and moving microscopic objects. A novel scheme for image subtraction is also demonstrated, showing the novelty filter’s ability to detect temporally discrete changes.

Optimized phase quantization for diffractive elements by use of a bias phase

Abstract: Many applications of diffractive phase elements involve the calculation of a continuous phase profile that is subsequently quantized for fabrication. The quantization process maps the continuous range of phase values to a limited number of discrete steps. We report our observation of the influence of this quantization process on the performance of mode-selecting diffractive elements and show that the quantization process produces significantly better results by use of an optimized bias phase. In principle this process can be employed to a greater or lesser extent in any quantization process.

An application of turbo trellis-coded modulation to tactical communications

Abstract: We present a frequency-hop packet radio system that is compatible with existing SINCGARS radio equipment and provides three times the spectral efficiency of SINCGARS. The system employs parallel concatenated trellis coded modulation, or turbo trellis-coded modulation, a recently proposed modulation scheme that combines the error control capability of turbo decoding with the bandwidth efficiency of trellis-coded modulation. The encoded data symbols are transmitted using continuous-phase modulation, demodulated noncoherently, and decoded with symbol-by-symbol maximum a posteriori decoding. The receiver also obtains channel quality estimates to aid in the decoding process. The turbo decoder and channel estimates provide resistance to jamming, cosite interference, and multiple-access interference. The packet success rate of the system for a variety of channel conditions is to be studied through simulation.

Image rejection in logic-based architecture for FSK modulation and demodulation

Abstract: A cost-effective continuous phase logic-based modulator and demodulator are provided to allow communications using binary frequency shift keying (BFSK) as well as M-ary FSK techniques The modulator of the 1-bit precision modem architecture is based on a 1-bit precision numerically controlled oscillator (NCO), which provides complete programmability with respect to a frequency of the 1-bit precision logic-based modulator and/or demodulator The 1-bit precision NCO includes an adder and a phase accumulator register which is clocked by a master clock signal A two-input multiplexer has a single bit symbol value to generate BFSK, or larger input multiplexers can be implemented to provide M-ary FSK The output of the 1-bit precision NCO is upconverted to an intermediate frequency using a simple logic function, ie, XNOR logic Alternatively, the intermediate frequency may be arrived at without the need for upconversion by directly utilizing a harmonic alias at a desired IF frequency The undesirable portion of the upconverted signal may be suppressed using I/Q image rejection, and/or an appropriate bandpass filter may be used A band limited, hard limited signal at the high IF is presented to the 1-bit precision demodulator as a receive IF signal, which is treated as a 1-bit quantization of the signal The receive IF signal is digitally down-converted to a low IF signal to produce an alias signal at the low IF frequency

Reduced complexity detection of bandwidth efficient partial response CPM

Abstract: A coherent CPM detector based on a reduced filter bank and a reduced state Viterbi decoder is proposed. Bit error probabilities of this detector for some CPM schemes satisfying a specific narrow spectrum requirement mask are simulated for the AWGN channel. The performance for one of the good candidates is then further evaluated for the case when co-channel and adjacent channel interference is present. For the AWGN channel with and without co-channel interference, the detector is found to be robust to complexity reduction both in the number of states in the Viterbi decoder and in the approximate filter bank. The number of states in the decoder and the complexity of the filter bank can be reduced significantly. It is still possible to reduce the complexity for the AWGN channel with adjacent channel interference, but not to the same extent without loosing significantly in performance.

A differential FM detector for low-IF radios

Abstract: This paper describes the implementation of a differential continuous phase FSK (CPFSK) detector suitable for low-IF receiver architectures. By using both in-phase and quadrature channels the double frequency term resulting after differential detection can be avoided. The digital detector assumes limited I/Q input signals which are 16 times oversampled. The proposed defector can be used for CPFSK, with a modulation index in the range 0.28-0.5. Simulation results are given for a worst case situation in which the modulation index is 0.28.

An innovative synchronization preamble for UHF MILSATCOM

Abstract: 4-ary, multi-h continuous phase modulation (CPM) has been added to MIL-STD-188-181B for dedicated mode UHF SATCOM operation to provide greater throughput capacity for this power- and bandwidth-restricted communications network. The physical layer of the waveform is designed to occupy the entire channel bandwidth at all data rates, optimizing power and spectral efficiency, but presenting challenges for acquisition. As an example, at low data rates the waveform has a 4 dB processing gain relative to binary phase shift keying (BPSK). Hence this waveform is expected to be acquired successfully at an E/sub b//N/sub 0/ 4 dB lower than that of BPSK. To acquire the CPM waveform, the modem must be capable of acquiring at low signal-to-noise, in the presence of large unknown frequency and timing offsets, and with the band-limiting and hard-limiting channel impairments introduced by the satellite. To promote interoperability and reliability, the Joint Interoperability and Engineering Organization (JIEO) requested a synchronization method that would provide reliable acquisition at an E/sub b//N/sub 0/ corresponding to a 1/spl times/10/sup -3/ bit-error-rate and also provide automatic data rate and waveform parameter detection. The resulting preamble achieves the aforementioned objectives and, in addition, is short enough in length to allow it be implemented as the burst preamble for future incorporation of the CPM waveform into the MIL-STD-188-182 and -183 demand assigned multiple access modes of operation. In this paper the design philosophy and implementation of the preamble are presented.

Symbol and superbaud timing recovery in multi-h continuous-phase modulation

Abstract: This paper is concerned with the estimation of two synchronization parameters that play a key role in multi-h continuous-phase modulation receivers-the ordinary symbol timing phase and the so-called superbaud timing phase. The recovery of symbol and superbaud timing is implemented by means of feedforward nondata-aided algorithms. The novelty of the proposed method is that it can be applied to any modulation format, either full or partial response, with binary or multilevel symbols and with arbitrary modulation indices.

Variable-interval pilot symbol aided modulation and demodulation

Abstract: The signaling overhead required for pilot symbol aided modulation is significantly reduced by recognizing that the residual uncertainty in the carrier frequency decreases after an initial carrier frequency estimate is made during an initial signal interval. This allows a commensurate reduction in channel process sampling rate during the remainder of the message; i.e., the frequency uncertainty of the pilot symbols can be decreased. This technique may be particularly effective when the rate of change of the received carrier frequency and phase is low as in fixed satellite terminal equipment. The resultant increase in spectral efficiency makes reduced-overhead pilot symbol aided modulation attractive for applications in low-cost/low-complexity terminal equipment.

High IF frequencies with a lower frequency logic based FSK modulation selecting a harmonic alias and demodulation using sub-sampling techniques

Abstract: A cost-effective continuous phase logic-based modulator and demodulator are provided to allow communications using binary frequency shift keying (BFSK) as well as M-ary FSK techniques. The modulator of the 1-bit precision modem architecture is based on a 1-bit precision numerically controlled oscillator (NCO), which provides complete programmability with respect to a frequency of the 1-bit precision logic-based modulator and/or demodulator. The 1-bit precision NCO includes an adder and a phase accumulator register which is clocked by a master clock signal. A two-input multiplexer has a single bit symbol value to generate BFSK, or larger input multiplexers can be implemented to provide M-ary FSK. The output of the 1-bit precision NCO is upconverted to an intermediate frequency using a simple logic function, i.e., XNOR logic. Alternatively, the intermediate frequency may be arrived at without the need for upconversion by directly utilizing a harmonic alias at a desired IF frequency. The undesirable portion of the upconverted signal may be suppressed using I/Q image rejection, and/or an appropriate bandpass filter may be used. A band limited, hard limited signal at the high IF is presented to the 1-bit precision demodulator as a receive IF signal, which is treated as a 1-bit quantization of the signal. The receive IF signal is digitally down-converted to a low IF signal to produce an alias signal at the low IF frequency. In the case where a sub-sampler in the 1-bit precision demodulator is not capable of operating at a required frequency (e.g., above 100 MHz or so), a harmonic sub-sampling mixer may be employed, with the resulting low IF signals being hard limited and lowpass filtered directly to the desired low IF. The received symbols are correlated with expected local frequencies representing a mark and a space. The correlation is integrated in an oversampled manner relative to the symbol interval. A decision is made as to which symbol was received using, e.g., a magnitude comparator.

Noncoherent sequence detection in frequency nonselective slowly fading channels

Abstract: A new class of noncoherent sequence detection (NSD) algorithms for combined demodulation and decoding of coded linear and continuous phase modulations, transmitted over additive white Gaussian noise (AWGN) channels, has been previously presented by the authors. In this paper, this class is generalized to the case of frequency nonselective Rayleigh and Rice slowly fading channels. Coded linear modulations, namely M-ary phase shift keying (M-PSK) and quadrature amplitude modulation (M-QAM), are explicitly considered.