Aeronautical communications are expected to increasingly demand spectrum in the next years. Given the endemic scarcity of spectrum, both the opportunistic use of licensed bands and carrier aggregation enable aeronautical systems to accommodate higher data rates and more aircrafts. We study dynamic spectrum allocation for air-to-ground (A2G) transmissions when carriers can be aggregated to form larger channels with complete and incomplete information: the aircrafts might not reveal their available channels for security reasons as it would expose their location. The single and multiple ground station scenarios are analyzed. Semi-distributed algorithms are proposed to deal with the incomplete information case for both scenarios, exhibiting a very good tradeoff between performance and complexity.

We study achievable information rates for nonlinear channels with memory, in the context of satellite communication with QAM modulation. The complete channel model can be described by a Volterra expansion, but large alphabet size and/or large channel memory length may prohibit optimal soft-output demodulator processing, say with the BCJR algorithm. Thus we focus on reduced-state receivers and their achievable information rates as a function of state complexity, amplifier backoff, and receiver input sampling rate. These achievable rates for mismatched receivers are known to be attainable with powerful error control codes and optimal decoding.

We study rate-compatible (RC) puncturing algorithms for efficiently-encodable (EE) generalized LDPC (GLDPC) codes of short-to-moderate blocklength. EE-GLDPC codes are systematic codes and well-suited for puncturing, thus they are able to address a rate constraint issue, which is an obvious disadvantage of traditional GLDPC codes. In this work, we propose systematic puncturing algorithms for EE-GLDPC codes. Simulation results show that the systematic puncturing has considerable performance improvement over random puncturing. In addition, the punctured codes, like their mother codes, have the advantage of good error floor performance, which can be a very important feature in practical applications. Finally, it is also demonstrated that, compared with LDPC codes, GLDPC codes have a better error floor performance, but suffer from a decoding threshold loss at high puncturing rates; nonetheless the tradeoff between error floor and decoding threshold loss can be conveniently implemented via the method of doping.

We study the performance of amplify-forward (AF) protocols in a three-terminal hub-remote satellite exchange channel, which is an extension of the two-way relay channel. We want to answer two questions: 1) Can non-orthogonal signaling and partial interference cancellation bring as much improvement as what have seen in the two-way relay channel? 2) Which decoding method achieves the largest achievable rate region? Theoretical analysis and numerical plots show that for the three-flow case, three-user simultaneous signalling outperforms a time-shared AF protocol, while for the four-flow case, three-user simultaneous signalling only shows advantage when the hub terminal has much higher SNR than remote terminals.

We present an M-ary spectral amplitude code (SAC) modulation technique to improve the performance of free-space optical (FSO) communication systems. Although this approach can be used in any dispersive FSO system, in this paper we focus on non-line of sight (NLOS) ultraviolet (UV) systems relying on atmospheric scattering. Spectral amplitude encoding is applied on a broadband UV source using the same code families for the M-ary alphabet as used previously in SAC optical code division multiple access (OCDMA) systems. A differential structure using two photomultiplier tubes is utilized in conjunction with various demodulation algorithms to decode the received signal. Intersymbol interference (ISI), received beam divergence and shot noise are considered as the main factors limiting the system performance. An upper bound on the bit error probability is presented and compared with simulation results for various geometries and for different code parameters. The maximum bit rate for a fixed bit error probability is calculated in terms of the link length, and results for different alphabet sizes are shown. By sacrificing spectral efficiency without becoming more susceptible to ISI, the proposed system can support higher rates and longer distances for the same performance compared with on-off keying systems.

In long-haul fiber-optic communication systems, the system performance is affected adversely by both severe physical impairments and amplified spontaneous emission (ASE) noise. Constrained coding, which avoids waveforms in the transmitted signal that are more likely to be detected incorrectly, has been proved to be an effective approach to suppress some physical impairments. However, the constrained coding schemes proposed in the literature are limited to the suppression of only some “resonant” sequences and their performance is evaluated in the absence of ASE noise. Various error correction codes also have been developed to reduce errors due to ASE noise but their performance is very vulnerable to the strong nonlinear impairments. This paper develops a novel concatenation scheme with the inner code being a constrained code based on Total Impairment Extent Rank (TIER) and the outer code being a low-density parity-check (LDPC) code. The TIER code ranks the bit patterns by order of all physical impairments imposed on them and constrains the bit patterns with large physical impairments. It is based on a discrete-time analytical model of physical impairments in long-haul fiber-optic communication systems. Compared with the current constrained codes, the TIER code offers more flexibility and better effectiveness. The TIER-LDPC concatenation scheme combines the strength of the TIER code in correcting errors due to physical impairments and that of the LDPC code in correcting memoryless errors due to ASE noise. Simulation results in the presence of ASE noise show that the TIER-LDPC concatenation scheme performs significantly better than the LDPC code alone in the case of severe impairments.

Two-way satellite communication that simultaneously shares spectrum, with subsequent interference cancellation, is an attractive means of efficiently using satellite resources. Systems may employ this method on full-transponder access, or with lease of a partial transponder. In this case, it is of interest to request bandwidth and power resources that minimize satellite costs. In this paper, we provide a solution to this optimization, using information-theoretic guidelines and a generic cost model, that can be easily translated into real coding and modulation options.

Hybrid free space optical (FSO)/radio frequency (RF) communication systems provide an attractive solution for high-throughput wireless connectivity. Such systems promise high data rates (Gbps) due to the FSO channel, weather permitting. The reliability of these systems is enhanced by the more robust RF channel. A critical question is how to efficiently transmit data using hybrid systems with highly variable channel conditions. In this paper, a hybrid FSO/RF communication system is modeled as two independent parallel channels. Under the assumptions of quasi-static channels and perfect channel knowledge at the transceivers, we propose an adaptive design resulting in a capacity-approaching and seamless joint system. In our design, information bits are jointly encoded and decoded. The encoder rate, modem transmission rate, and modulation scheme of each channel are dynamically adjusted according to the channel state. Analytical and simulation results give insight into the relationship between the adaptive parameters and the performance of the hybrid system.

Power amplifiers, an integral component to most wireless communication systems, are inherently nonlinear devices that introduce out-of-band spectral regrowth and constellation degradation to the amplifier output. One solution is to operate in a highly backed-off state to achieve quasi-linear performance. Operating in this region requires a higher-saturated power rating for a given output power and reduces DC-to-RF efficiency. A more effective solution is to apply digital predistortion which pre-compensates for the harmful nonlinear effects. A common framework for identifying the predistortion system is known as the indirect learning architecture. A single iteration of this architecture, i.e. a one-step approach, demonstrates performance improvement. We propose an multi- iteration approach to the indirect learning architecture that demonstrates additional improvement, as exhibited by three different algorithms shown to be effective at identifying a predistorter.

We propose two classes of efficiently-encodable GLDPC (EE-GLDPC) codes by generalizing the ideas of IRA and EERC codes. These GLDPC codes have performance as good as ordinary GLDPC codes. Moreover, another advantage of these EE-GLDPC codes is that they are naturally suitable for puncturing. Simulation shows that, at code length around 600, the punctured EE-GLDPC codes can outperform optimized irregular LDPC codes by 0.4-0.5 dB at BER=10-6, making them good candidates when designing error correcting codes at short-to-medium code lengths.

We study the relay assignment problem for cooperative diversity using a wireless network setting in which the terminals (nodes) are randomly distributed. Specifically, we develop low-overhead and decentralized relay assignment protocols whose performance is close to the protocols which require more overhead in terms of handshaking and look-up tables or a centralized structure to assign relays to the transmitting nodes.

We consider the impact of carrier frequency offsets arising naturally when multiple relay terminals transmit simultaneously using a space-time code in a cooperative relaying scenario. In such a scenario, we design an adaptive, low-complexity receiver that attempts to eliminate the effect of frequency offsets. The adaptive receiver allows for decoupling of the decisionmaking of transmitted symbols utilizing the orthogonality of the underlying space-time code. In a quasi-static Rayleigh fading channel, we demonstrate the performance of the adaptive receiver over a range of frequency offsets by considering two transmitting relays. We prove that the adaptive receiver achieves full diversity, and using simulation results for two relays we show that the performance greatly improves over a conventional differential receiver that ignores the presence of frequency offsets.

Performance bounds of free space optical (FSO) systems with multiple laser transmitters and multiple avalanche photodetectors (APDs) are evaluated for terrestrial, line-of- sight communication. Specifically, analytical upper bounds on average uncoded error rate in turbulent multiple-input multiple- output (MIMO) channels with Q-ary pulse position modulation (PPM) are derived for arbitrary observable densities, and are used to quantify APD-based performance improvements over pin detector arrays in non-fading, lognormal, and negative exponential channels. Moreover, it is shown that despite the high complexity of APD array statistics, these performance gains can be accurately predicted using a jointly-Gaussian model for APD array outputs. Both maximum likelihood (ML) and sub-optimal combining rules are derived, and a simple equal gain combiner (EGC) that performs close to optimum is demonstrated. Finally, APD gain selection is discussed.

The use of an optical preamplifier in a two laser system for atmospheric line-of-sight optical communication is investigated. Using orthogonal repetition coding is shown to provide diversity. Two different intensity modulation methods, on-off keying (OOK) and binary pulse position modulation (PPM) are analyzed for systems corrupted by background radiation and amplified spontaneous emission noise. Using an optical preamplifier in a MISO channel results in better performance than using an electrical amplifier.

A novel high-throughput (6 Gb/s), fully-parallel FPGA-based 1200-bit rate-1/2 Low Density Parity Check (LDPC) decoder design is presented. The decoder features a PEG- based regular (6,3) code and a modified min-sum algorithm that improves performance without any additional hardware overhead.

Multiple transmitter and receivers can be used to combat link outage due to the atmosphere turbulence and scattering in an urban 'last-mile' free space optical communication system. We investigate the use of an optical preamplifier in the resulting multiple-input-multiple-output (MIMO) system for atmospheric line-of-sight optical communication, with signal repetition across the laser array. The optically preamplified system has better performance than previous MIMO system relying on electronic amplification. Our focus is on determining symbol error probability for uncoded transmission.

The overarching goal of this work is to assess optical wireless technology with heterodyne detection as a potential distributor of WiMAX traffic in metro/access networks. At the transmitter, we consider optical wireless communication via orthogonal frequency division multiplexing (OFDM) as a form of multi-subcarrier modulation (MSM). At the receiver, heterodyne detection is used to produce an output signal at a carrier frequency specified by the WiMAX standard. We incorporate adaptive modulation, atmospheric turbulence, laser linearity and receiver noise to derive symbol error and outage probability expressions, and compare the findings to an analogous direct-detection (DD) system. Results indicate that with local oscillator power Pl = -10 dBm, heterodyne detection (HD) outperforms DD by over 10 dB at error probability Ps = 10 9 for all modulation formats, in both non-fading and fading channels. This translates to a 3-fold increase in link length over analogous DD systems. Outage probability analysis reveals a similar trend, with HD outperforming DD by 7-15 dB for all cases considered.

We study the use of multiple laser transmitters combined with multiple photodetectors for atmospheric, line-of-sight optical communication, and focus upon the use of multiple-pulse-position-modulation as a power-efficient transmission format, with signal repetition across the laser array. Ideal (photon counting) photodetectors are assumed, with and without background radiation. The resulting multiple-input/multiple-output channel has the potential for combating fading effects on turbulent optical channels, for which both log-normal and Rayleigh-fading models are treated. Our focus is upon symbol error probability for uncoded transmission, and on capacity for coded transmission. Full spatial diversity is obtained naturally in this application.

Space-time encoders exploiting concatenated coding structures are efficient in attaining the high rates available to large-dimensional multiple-transmitter, multiple-receiver wireless systems under fading conditions, while also providing maximal diversity benefits. We present a multistage iterative decoding structure that takes full advantage of the concatenated nature of the transmission path, treating the modulator and channel stages as an additional encoder in serial concatenation. This iterative decoder architecture allows an encoder employing decoupled coding and modulation to reach the performance of coded modulation systems. It also admits reduced-complexity decoding with a computational load that is nonexponential in the number of antennas or the transmission bit rate, and makes practical decoding for large transmitter arrays possible. The performance curves for these methods follow the shape of the Fano bound, with only a modest power penalty.

The use of multiple laser transmitters combined with multiple photodetectors (PDs) is studied for terrestrial, line-of-sight optical communication. The resulting multiple-input/multiple-output channel has the potential for combatting fading effects on turbulent optical channels. In this paper, the modulation format is repetition Q-ary PPM across lasers, with intensity modulation. Ideal PDs are assumed, with and without background radiation. Both Rayleigh and log-normal fading models are treated. The focus is upon both symbol-/bit-error probability for uncoded transmission, and on constrained channel capacity.

Fading due to atmospheric turbulence is a primary problem in free-space-optical links, and to address this, we consider the use of (noncoherent) optical arrays, analogous to the use of antenna array technology for microwave systems. Specifically, we envision M separate lasers, assumed to be intensity-modulated only, together with N photodetectors, assumed to be ideal noncoherent (direct detection) receivers. The sources and detectors are physically situated so that the fading experienced between source-detector pairs is statistically independent, and thus diversity benefits can accrue from the MIMO channel. Whereas classic single pulse PPM is known to be efficient from an average power perspective, the required peak power from the lasers must become arbitrarily large in this process. This motivates study of multipulse modulation.

This work considers the design and performance of a stream-oriented approach to turbo codes which avoids the need for data framing. The stream paradigm applies to both serial and parallel turbo codes using continuous, free-running constituent encoders along with continuous, periodic interleavers. A stream-oriented turbo code based on parallel concatenated convolutional codes (PCCC) is considered and interleaver design criteria are developed for both block and nonblock periodic interleavers. Specifically, several nonblock interleavers, including convolutional interleavers, are considered. Interleaver design rules are verified using simulations where it is shown that nonblock interleavers with small-to-moderate delay and small synchronization ambiguity can outperform block interleavers of comparable delay. For large-delay designs, nonblock interleavers are found which perform within 0.8 dB of the capacity limit with a synchronization ambiguity of N=11.

This paper examines the synchronization of turbo coded modulation systems at low SNR where these systems are designed to operate. Maximum likelihood estimation theory is used to derive a causal, discrete-time synchronization structure for estimating the carrier phase and symbol timing of a general QAM signal, using a decision-directed structure which is known to be superior at low SNR. Simulation shows that efficient joint carrier phase and symbol timing estimates can be acquired using our synchronizer for turbo codes. Bit error performance for selected loop bandwidths is presented.

In a high-speed wireless communications network with mobile terminals, an appealing way to off-load hardware complexity to the base station is to use transmitter precoding in the downlink direction. A modification to the conventional DQPSK receiver is presented for processing the extended precoded constellations without requiring good phase synchronization. To avoid the related severe noise multiplication effect, an alternative receiver is developed, incorporating a discrete-time phase tracker so that the constellation size can be reduced before the differential detection operation. With a 2nd-order estimator filter, this receiver approaches the performance of coherent detection for transmitter precoding.

The performance and design of turbo codes using coherent BPSK signaling on the Rayleigh fading channel is considered. In low signal-to-noise regions, performance analysis uses simulations of typical turbo coding systems. For higher signal-to-noise regions beyond simulation capabilities, an average upper bound is used in which the average is over all possible interleaving schemes. Fully interleaved and exponentially correlated Rayleigh channels are explored. Furthermore, the design issues relevant to turbo codes are examined for the correlated fading channel. Turbo interleaver design criteria are developed and architectural modifications are proposed for improved performance.

Iterative decoding of turbo codes, as well as other concatenated coding schemes of similar nature, requires knowledge of the signal-to-noise ratio (SNR) of the channel so that proper blending of the a posteriori information of the separate decoders is achieved. We study the sensitivity of decoder performance to misestimation of the SNR, and propose a simple online scheme that estimates the unknown SNR from each code block, prior to decoding. We show that this scheme is sufficiently adequate in accuracy to not appreciably degrade the performance.

The optimal multiuser sequence estimator is formulated for an asynchronous direct-sequence code-division multiple-access (DS-CDMA) system where each user employs convolutional coding to improve its performance on a nondispersive additive white Gaussian noise (AWGN) channel. It is shown that the decoder may be implemented efficiently using a Viterbi algorithm which operates on a time-varying trellis with a number of states which is exponential in the product of the number of users in the system and the constraint length of the codes used (for the rate 1/2 code case). The asymptotic efficiency of this receiver relative to an uncoded coherent binary phase shift keying (BPSK) receiver (termed asymptotic multiuser coding gain, or AMCG) is then upper and lower bounded. The AMCG parameter unifies the asymptotic coding gain parameter and the asymptotic multiuser efficiency parameter which are traditional figure of merit parameters for single-user coded systems and multiuser uncoded systems, respectively. Finally, some simulations are presented to illustrate the performance of the maximum likelihood sequence estimator (MLSE) at moderate and low bit error rates.

Motivated by the high complexity of the optimal sequence estimator for convolutionally coded asynchronous code-division multiple-access (CDMA) systems, developed by Giallorenzi and Wilson (see ibid., vol.44, no.8, p.997, 1996), and the potentially poor performance of the conventional receiver due to multiuser interference and the near-far problem, we examine relatively simple multiuser receivers which perform nearly as well as the optimal receiver. The multiuser receivers discussed are of two types. The first set of approaches are partitioned approaches that treat the multiuser interference equalization problem and the decoding problem separately. The second set of approaches are integrated approaches that perform both the equalization and decoding operations together. We study linear, decision feedback, and trellis/tree-based approaches in each category. The asymptotic efficiency of this receiver relative to an uncoded coherent binary phase shift keying (BPSK) receiver (termed asymptotic multiuser coding gain, or AMCG) is used as a performance criterion throughout. Also, computer simulations are used whenever the computation of the AMCG is not feasible. It is shown that a number of the approaches which are introduced achieve a high performance level with a moderate complexity.

Considers trellis decoding of convolutional codes with selectable effort, as measured by decoder complexity. Decoding is described for single parent codes with a variety of complexities, with performance "near" that of the optimal fixed receiver complexity coding system. Effective free distance is examined. Criteria are proposed for ranking parent codes, and some codes found to be best according to the criteria are tabulated, Several codes with effective free distance better than the best code of comparable complexity were found. Asymptotic (high SNR) performance analysis and error propagation are discussed. Simulation results are also provided.

Detection for the statistically known channel (SKC) is aimed at obtaining good performance in situations where our statistical knowledge of a time-varying channel is good, and where other equalization/detection schemes are either too complex to implement, or their performance is limited due to the rapidity of channel fading, or where we are simply unable to perform channel estimation. By using a statistical characterization of the channel, we develop a new detector that performs maximum-likelihood sequence estimation (MLSE) (given the channel model) on blocks of N symbols. Both symbol-spaced and fractionally spaced samples are used, to obtain two different detectors, that are generalizations of those devised for optimal block schemes on nondispersive channels. The detector that uses fractionally spaced samples is shown to outperform the detector that uses symbol-spaced samples. The performance of both appears to approach that of the corresponding known channel (KC) detector as the block length increases. We also numerically evaluate the SKC detector performance under conditions where the channel parameters (statistics) are incorrectly estimated, and show that the fractionally spaced detector is fairly robust to modeling errors. Finally, we devise a sliding block algorithm, for use when transmitting more than N symbols.

Considers noncoherent decoding of trellis coded M-DPSK transmission, and attempts to unify and contrast the approaches to this problem which have been previously reported. In the second part of the paper, the maximum likelihood block decoders for the AWGN channel are outlined, first assuming that the decoder has no knowledge of the state of the encoder at the beginning of the block, and then assuming that it knows the state. Because these exhaustive decoders suffer from an exponential growth in complexity with block length, two simplified decoders are proposed that approach the performance of the exhaustive decoders with a much more manageable complexity. Through a union bound analysis and computer simulations, it is shown that it is possible to achieve large gains over uncoded systems with a very reasonable decoder complexity.>

A general-purpose modulation and coding implementation that is based on the quadrature amplitude modulation (QAM) family of modulation is described. The technique utilizes the 'superposed' property of certain rectangular QAM constellations, along with the fact that optimal four-state trellis codes for such constellations are essentially identical, to provide a single modem architecture capable of performing over a wide range of power and bandwidth efficient transmission using either an uncoded or a coded modulation scheme. While the specific modulation and coding techniques are not new, the authors believe that their intrinsic compatibility is not well known and provides attractive system flexibility.>

An L-frequency trellis coding scheme designed for fading channels that provides diversity up to order L is described. L-frequency coding is advantageous over channel coding schemes that achieve implicit time-diversity through trellis coding in conjunction with time-interleaving because it requires negligible end-to-end delay. The authors derive an upper-bound for the probability of symbol error of the L-frequency code. Based on this upper-bound, they then deduce the design criteria for optimum L-frequency codes. A numerical approximation to this upper-bound and the design of a two-state and two four-state, two-frequency codes are presented. Through simulations, it was found that relative to the traditional dual frequency diversity approach, the two-state and four-state codes achieve 3- and 4-dB coding gains, respectively. This energy efficiency gain can be translated into a spectral efficiency gain. A brief discussion on the difference in code design techniques for the Gaussian channel and the fading channel is also presented.>

Two classes of nonbinary convolutional codes for error control in communication systems employing q-ary orthogonal signaling are discussed. These classes include as special cases, the dual-k codes and the codes treated by B.D. Trumpis (1975). The types of code, extensions of previous bounds on free distance, the noncatastrophic condition for these codes, and conditions for catastrophic error propagation are described. Codes obtained by a computer search, optimal in that the truncated transfer function bound on the probability of symbol error is minimized, are presented. It is shown how good convolutional codes can be constructed from cyclic block codes. The performance of some of these codes over additive white Gaussian noise channels, Rayleigh channels, and partial-band interference channels is also discussed.>

The issue of demodulator quantization prior to decoding in error control systems employing M-ary phase-shift keying (PSK) as a modulation technique is considered. The use of angle-only, or polar, quantization with J>or=M levels, which is an easily implemented alternative to rectangular quantization, is described. The R/sub 0/ parameter is presented as an effective indicator of coding potential for quantized M-ary PSK channels, and different designs in the R/sub 0/ context are discussed. The principal results are that for J=2M, a polar quantizer satisfies the necessary condition for optimality, and it is conjectured that the design is in fact optimal. The corresponding performance closes about half the gap (in decibels) between the hard-decision demodulator and the unquantized demodulator. Angle-only quantization, in the limit of fine precision, costs only a fraction of a decibel in performance for typically operated coded 8-PSK and 16-PSK. Numerical results for quantizers with J=2M and J=4M are presented, and the case of an added erasure zone is considered.>

For binary continuous-phase modulation with modulation indexh = 1/2(MSK being a rather familiar example), quadrature matched-filter reception is possible with only minor degradation relative to the maximum likelihood (trellis-based) receiver. Thus this class of modulations provides good spectral attributes together with reception techniques capable of being implemented simply at high speeds. As usual, the constant-envelope property is also present. We study here the effects of interfering signals with the same modulation format, located at the same frequency (cochannel interference), or at a nearby frequency (adjacent channel interference). Coherent reception is assumed, and we analyze two channel situations: both signals nonfading with additive Gaussian noise; and both signals independently Rayleigh fading, with additive Gaussian noise. As one would expect, the smoothed phase modulation schemes have larger tolerable adjacent channel levels, while there is little differentiation in the cochannel case. We also find that MSK filters are usable for other formats with negligible loss in performance relative to the optimal linear filters, provided the filter parameters are rescaled appropriately.

Some new short constraint length codes are described for satellite channels which are constant-envelope and which have spectral and energy efficiencies intermediate to other recent coded techniques, namelyr = 2/3coded 8-PSK andr = 3/4coded 16-PSK. We use two intervals of 8-PSK transmission to form a modulation base forr = 5/6trellis codes. A particularly attractive design is an eight-state code, producing 6.2 dB gain on the Gaussian channel over uncoded 8-PSK, yet sacrificing only 16 percent in spectral efficiency.

Background theory and specific coding designs for combined coding/modulation schemes utilizing convolutional codes and continuous-phase modulation (CPM) are presented. In this paper the case ofr = 1/2coding onto a 4-ary CPM is emphasized, with short-constraint length codes presented for continuous-phase FSK, double-raised-cosine, and triple-raised-cosine modulation. Coding buys several decibels of coding gain over the Gaussian channel, with an attendant increase of bandwidth. Performance comparisons in the power-bandwidth tradeoff with other approaches are made.

Convolutional coding coupled with 16-PSK modulation is investigated for bandwidth efficient transmission. Rate 3/4, small memory codes are found which are optimized in the free-distance sense on the Gaussian channel. These codes provide up to 4.8 dB of coding gain with 32 states over uncoded 8-PSK, a scheme having the same spectral efficiency as the codes described. The performance is compared with earlier findings of Ungerboeck and some recent results onR = 2/3coded 8-PSK. In addition, we present results of a channel transmission study to assess the performance of the four-state code on the band-limited nonlinear channel, and find that performance of the coded scheme degrades comparably with uncoded 8-PSK, i.e., coding gain is roughly preserved.

A method is described for evaluating the minimum distance parameters of trellis-phase codes, including continuous phase frequency shift keying (CPFSK), partial-response FM, and, more importantly, coded continuous-phase modulation (CPM) schemes. The algorithm provides dramatically faster execution times and smaller memory requirements than previous algorithms. Results of sample calculations and timing comparisons are included.

This paper investigates the performance of chain code quantization of general curves using a hexagonal lattice structure, as a means of improving efficiency over the standard square lattice. Performance is first computed theoretically, assuming a generalization of grid-intersect quantization, and the curve to be quantized is assumed to be a straight line. An algorithm is then developed to perform chain coding using the hex lattice. Computer simulations were performed to evaluate hexagonal chain coding for a variety of curves, including circles of various curva-ture, straight lines, and a stochastic curve model. We find that the straight-line theory is substantiated for curves whose radius of curvature is roughly twice the lattice constant. For a given peak error in quanti-zation, hexagonal coding reduces the bit rate about 15 percent relative to the square lattice codes, and exhibits qualitative improvements in fidelity as well.

Upper and lower bounds for the probability of a decoding error event and for symbol error probability are developed for the class of time-varying phase codes known as multi-hcodes. The effect of finite decoder memory is also treated. The analysis is illustrated with numerical examples, and simulation results are compared.

A procedure is presented for calculating the power spectrum of the class of digital continuous-phase signals known as multi-hphase codes. These signals have been shown to have attractive power advantages over other uncoded digital schemes such as QPSK, and represent a bandwidth-efficient alternative to other coding. techniques. The method is general, handlingM-ary signaling, various frequency pulse shapes, and arbitrary sets of modulation indices. Numerical results are shown for several specific codes. In addition, the issue of spectral lines is resolved, and simple spectral approximations are developed.

The performance of two-dimensional polar quantization of independent Gaussian variates is evaluated as a possible improvement over one-dimensional quantizers. The distortion measure is assumed to be squared error. The quantizers are a generalization of more restrictive polar quantizers analyzed previously, admitting a differing number of phase positions in each magnitude sector. Results are provided for several bit rates up to 2.5 bits/sample. The optimal design always performs as well or better than the restricted polar quantizer, and, in the cases analyzed, slightly outperforms the Max (single-sample) quantizers for a fixed number of levels.

The multipath tree-encoding of speech at 8 kbits/s is investigated. Tree coding proceeds along the lines of Anderson, et al, but at this lower bit rate, frequency weighting of the error process and adaptation of the coding process are found to be beneficial. Coding results for a stationary speech-like source are found to agree well with rate-distortion theoretic ideas, and when applied to speech, tree coding at 8000 bits/s yielded frequency-weighted SNR's of 15-20 dB.

Trellis coding of analog memoryless sources with respect to the squared-error distortion criterion is investigated via simulation. Sources treated are the Gaussian, uniform, Laplacian, and Gaussian mixture models, and the encoding algorithms studied are the Viterbi andMalgorithms. Performance versus complexity trade-offs are presented for these source models, and practical aspects of finite encoder memory and unknown source statistics are examined.

The problem of communicating binary information from ground to aircraft viaL-band aeronautical satellite channels is addressed, with particular attention given to the effect of and means of combating diffuse-scattered multipath interference. Differential phase-shift keying (DPSK) is considered throughout. Test results of a recent flight-test program are summarized and compared to theory for uncoded DPSK. We then discuss and evaluate the use of diffuse convolutional codes in conjunction with threshold decoding to improve error probability on the fading channel. Simulation has shown that a power saving of 8 dB may be gained at 10-5error rate for typical channel conditions with very little complexity.

Results of a flight test program involving a KC-135 jet airplane, the synchronous ATS-5L-band satellite, and a ground station are presented. Tests included over-ocean multipath measurements and one-way tone ranging within the 1545-1655 MHz frequency band. Amplitude characteristics, polarization, power spectral density, and selective fading properties were measured for sea-reflected and composite signal channels. CW tone-ranging performance was determined in both the thermal noise and multipath environments. Comparison of experimental results with theoretical expectation is given.