This paper develops a design methodology for constructing protomatrix-based low-density parity-check (LDPC) codes that are paired with (matched to) continuous phase modulation (CPM) waveforms. We show how a protomatrix extrinsic information transfer (PEXIT) based search can yield lower decoding thresholds than previously reported, and how a single constraint added to this search is effective at preserving the linear minimum distance growth property while remaining within one dB of capacity. We show that a two-stage lifting procedure plays an essential role in completely eliminating error floors at very low error rates. Our high-throughput joint LDPC–CPM decoder is demonstrated to be practical with execution speeds comparable to a standalone LDPC decoder. The global iterations of the joint decoder are shown to provide natural protection against undetected errors due to small minimum distance, and this protection is further enhanced by a novel check node “splitting” technique. The diverse family of three CPM waveforms that are used in aeronautical telemetry are considered as design examples.

The minimum mean-squared error (MMSE) estimator is recognized as the best estimator for measuring transmission channel distortion in orthogonal frequency division multiplexing (OFDM) using pilot-symbol assisted modulation (PSAM) in the presence of noise. In practice, however, the estimator suffers from high complexity and relies on the estimation of second-order statistics which may change rapidly within small-scale fading environments in a high-mobility wireless transmission system. We propose using machine learning (ML) with Gaussian Process Regression (GPR) to adaptively learn the hyperparameters of a channel model, which then can be used to calculate the MMSE estimates. Moreover, GPR can be used to more accurately interpolate the channel estimates in between pilot symbols compared to linear interpolation techniques. After describing the learning process and its equivalency to MMSE, we derive the BER for a receiver using GPR for time-domain interpolation, then use BER to find a practical bound on the number of training points needed to achieve best performance. We show that the performance of GPR-based ML is comparable to that of more complex neural network-based ML.

We investigate the problem of delay-efficient and reliable data delivery in ultra-dense networks (UDNs) that constitute macro base stations (MBSs), small base stations (SBSs), and mobile users. Considering a two-hop data delivery system, we propose a partial decode-and-forward (PDF) relaying strategy together with a simple and intuitive amicable encoding scheme for rateless codes to significantly improve user experience in terms of end-to-end delay. Simulation results verify that our amicable encoding scheme is efficient in improving the intermediate performance of rateless codes. It also verifies that our proposed PDF significantly improves the performance of the decode-and-forward (DF) strategy, and that PDF is much more robust against channel degradation. Overall, the proposed strategy and encoding scheme are efficient towards delay-sensitive data delivery in the UDN scenarios.

With the growing popularity of delay-sensitive applications (e.g., real-time conversational video, online gaming, and augmented reality) and future trends toward ultra-reliable low-latency communications such as the tactile Internet, performance analysis of wireless systems under the finite code blocklength constraint becomes extremely important. In this paper, we investigate the maximum achievable throughput of incremental redundancy-hybrid automatic repeat request (IR-HARQ) over the (correlated) Rayleigh fading channel under finite blocklength and delay-violation probability constraints as a function of the modulation scheme. The maximum number of HARQ rounds together with the transport block size specifies the underlying coding latency of the IR-HARQ scheme. A framework, namely the HARQ Markov model (HARQ-MM), is introduced to track the throughput and the probability of error of IR-HARQ over the Rayleigh fading channel as a function of the modulation scheme. The dispersion of parallel additive white Gaussian noise channels with finite input alphabets (e.g., pulse amplitude modulation) is analytically characterized. It is used to identify the state transition probabilities of the underlying HARQ-MM. An algorithm is developed to efficiently compute the steady-state distribution of the HARQ-MM. Extensive performance evaluation is conducted, which shows a good match between the throughput performance characterized by the theoretical framework and that achieved by the practical channel codes.

A structured random matrix ensemble that maintains constant modulus entries and unit-norm columns, often called a random phase-rotated (RPR) matrix, is considered in this letter. We analyze the coherence statistics of RPR measurement matrices and apply them to acquire probabilistic performance guarantees of orthogonal matching pursuit (OMP) for support detection (SD). It is revealed via numerical simulations that the SD performance guarantee provides a tight characterization, especially when the signal is sparse.

Memory-based LT encoders (MBLTEs) have been shown to have better performance than the regular LT encoder in terms of bit error rate (BER) and decoding convergence speed. In this paper, we explore the entire family of MBLTEs for finite block-length codes over the binary erasure channel (BEC). We propose an algorithm to extend the first and second order MBLTE approach to an arbitrary i-th order MBLTE. We analyze the performance of such encoders mathematically by characterizing the expected accumulated number of recovered variable nodes at each decoding round. We define the threshold of the memory-based encoding method (MBEM) and show that the performance of MBLTEs increases as the memory order increases up to the point where this threshold is achieved. Beyond this point, we show that the performance of MBLTEs saturates if the channel erasure probability is zero and degrades otherwise. We formulate an optimization problem to solve for the optimal memory order based on whether or not the MBEM threshold is achieved. We present an extensive set of numerical results. These show agreement between our analysis and computer simulations. They also show that our optimization problem is efficient in determining the optimal memory order of MBLTEs in terms of decoding convergence speed, BER/frame-error-rate, and error floor.

In this paper, we investigate memory based Luby transform (LT) encoders (MBLTEs) over binary input additive white Gaussian noise (BIAWGN) channels. We analyze the performance of MBLTEs by characterizing the expected probability at each decoding round that a variable node has not yet received any nonzero message. Simulation results verify our analysis and show that MBLTEs outperform the regular LT encoder over BIAWGN channels in terms of bit error rate (BER)/frame error rate (FER) and error floor.

Massive multiple input multiple output (MIMO) systems are a promising technology for next generation wireless communications due to their ability to increase capacity and enhance both spectrum and energy efficiency. To utilize the benefit of massive MIMO systems, accurate downlink channel state information at the transmitter (CSIT) is essential. Conventional approaches to obtain CSIT for frequency-division duplex (FDD) multi-user massive MIMO systems require downlink training and uplink CSI feedback. However, such training results in large overhead for massive MIMO systems because of the large dimensionality of the channel matrix. In this paper, we investigate the channel estimation problem in FDD multi-user massive MIMO systems with spatially correlated channels and develop an efficient channel estimation algorithm that exploits the sparsity structure of the downlink channel matrix. The proposed algorithm selects the best features from the measurement matrix to obtain efficient CSI acquisition that can reduce the downlink training overhead compared with the conventional LS/MMSE channel estimators. We compare the performance of our proposed channel estimation method with traditional ones in terms of normalized mean square error (MSE). Simulation results verify that the proposed algorithm can significantly reduce the pilot overhead and has better performance compared with the traditional channel estimation methods.

Communication at millimeter wave frequencies will be one of the essential new technologies in 5G. Acquiring an accurate channel estimate is the key to facilitate advanced millimeter wave hybrid multiple-input multiple-output (MIMO) precoding techniques. Millimeter wave MIMO channel estimation, however, suffers from a considerably increased channel use overhead. This happens due to the limited number of radio frequency (RF) chains that prevent the digital baseband from directly accessing the signal at each antenna. To address this issue, recent research has focused on adaptive closed-loop and two-way channel estimation techniques. In this paper, unlike the prior approaches, we study a non-adaptive, hence rather simple, open-loop millimeter wave MIMO channel estimation technique. We present a random phase rotation design of channel subspace sampling signals and show that they obey the restricted isometry property (RIP) with high probability. We then formulate the channel estimation as a low-rank subspace decomposition problem and, based on the RIP, show that the proposed framework reveals resilience to a low signal-to-noise ratio. It is revealed that the required number of channel uses ensuring a bounded estimation error is linearly proportional to the degrees of freedom of the channel, whereas it converges to a constant value if the number of RF chains can grow proportionally to the channel dimension while keeping the channel rank fixed. In particular, we show that the tighter the RIP characterization the lower the channel estimation error is. We also devise an iterative technique that effectively finds a suboptimal, but stationary, solution to the formulated problem. The proposed technique is shown to have improved channel estimation accuracy with a substantially low channel use overhead as compared to that of previous closed-loop and two-way adaptation techniques.

In this paper, we provide a comprehensive study and comparison of the energy consumption and bit-rate of multiple-input multiple-output (MIMO) wireless devices using multilevel quadrature amplitude modulation (MQAM). Both spatial diversity and spatial multiplexing (SM) are examined and compared under the assumption of perfect channel state information (CSI) at the transmitter. The transmit energy is derived under a target probability of error Peb at the receiver. The transmit energy and transceiver circuit energy are then utilized to study energy tradeoffs for MIMO diversity and SM. We observe that the amount of energy savings for diversity orders two and three is steeper than that of higher diversity orders. On the other hand, SM provides a linear increase in the overall bit rate along with receiver diversity due to maximum likelihood detection. Using these results, we create a diversity-SM tradeoff for energy consumption vs. bit-rate. Using these results our proposed scheme can save around 4 dB in energy consumption while achieving the highest bit rate after full SM at Peb= 10-3.

In this paper, a comprehensive model has been provided to study the energy consumption of wireless cellular devices, by analyzing the relationship between the modulation order and energy consumption of the power amplifier (PA) and other circuits in radio frequency transceivers. Two types of energy consumption for PAs are studied in detail: transmitted energy, which is provided to the antenna to transmit data, and energy dissipated as a heat. First, the transmitted energy is studied along with different modulation orders for different distances between the transmitter and receiver. Next, the dissipated energy with all corresponding parameters such as peak to average ratio (PAR) and the drain efficiency of the PA is discussed. Other circuits are examined to show that the energy of these circuits--unlike other models in the literature--change with modulation order. The results reinforce the idea that increasing the modulation order leads to higher energy consumption in the RF transceiver for large distance. The results also show that the energy dissipated due to PAR and drain efficiency is larger than the transmitted energy.

Future wireless communications will face the dual challenge of supporting large traffic volume while providing reliable service for various kinds of delay-sensitive traffic. In the light of this challenge, this paper investigates the throughput performance of hybrid automatic repeat request (HARQ) systems under finite blocklength constraint. We present a framework to compute the maximum achievable rate with HARQ over the Rayleigh fading channel for a given probability of error. In the proposed framework, the operation of HARQ over the Rayleigh fading channel is modeled as a finite-state Markov chain. The state transition probabilities of the proposed Markov model are estimated from the fading characteristics of the wireless channel as well as the dispersion associated with different channel state sequence realizations. With this framework we are able to link the HARQ throughput performance to the characteristics of the underlying physical channel as well as the system design parameters such as modulation and transmit power. Furthermore, we discuss the relationship between the system throughput, and the number of HARQ rounds. The results show that the required number of HARQ rounds to take full advantage of HARQ depends on the choice of modulation, and varies as a function of the signal-to-noise ratio (SNR).

Future wireless communications will face the dual challenge of supporting large traffic volume while providing reliable service for various kinds of delay-sensitive traffic. In the light of this challenge, this paper investigates the throughput performance of wireless systems under channel coding over finite transport blocks (TBs) with the channel state sequence available only at the receiver. We analyze the performance of a communication scheme with feedback, namely early decoding, where for each codeblock the receiver makes a single decoding attempt at a time determined based on the available channel state information. A finite-state Markov channel (FSMC) is introduced to model the TB-based wireless system where the parameters of the model are linked to the characteristics of the underlying physical channel. The FSMC model is then used to assess the maximum achievable throughput of the early decoding strategy. Numerical results suggest that despite its low computational complexity the proposed scheme significantly reduces the coding latency to achieve rates near the channel capacity.

Future wireless communications will face the dual challenge of supporting large traffic volume while providing reliable service for various kinds of delay-sensitive traffic. In light of this challenge, this paper investigates the throughput performance of wireless communication systems under channel coding over finite transport blocks (TBs) with the channel state sequence available only at the receiver. When we apply coding across multiple TBs, the underlying wireless channel can be effectively modeled as a finite-state Markov chain. By linking the characteristics of the underlying physical channel to the parameters of the Markov chain, we characterize the channel dispersion of the corresponding system. The channel dispersion is then used to assess the coding performance of various communication strategies. We also propose a communication scheme where the receiver determines the decoding time based on the available channel state sequence. Numerical results show that the proposed scheme significantly reduces the coding delay to achieve rates near the channel capacity.

In this paper, we derive a joint maximum likelihood (ML) algorithm for the estimation of frequency offset, carrier phase and symbol timing for continuous phase modulations (CPMs). We have considered a burst-mode scenario over additive white Gaussian noise (AWGN) channels in which an optimized training sequence is embedded within each burst in order to assist the synchronization task. The proposed data-aided (DA) approach takes advantage of the optimum training sequence structure which can be applied to the entire CPM family. The simulation results show that the estimator performs quite close to the theoretical Cramér-Rao bound (CRB) for all synchronization parameters in terms of their estimation error variances even at low signal-to-noise ratios (SNRs).

In modern wireless systems such as 3GPP LTE/LTE-Advanced, packets are partitioned into multiple transport blocks where each transport block is a group of resource elements with a common modulation and coding scheme. Accordingly, a transport block is the data unit in the physical layer of modern wireless systems. In this paper, we investigate the throughput performance of modern wireless systems under channel coding over finite transport blocks. When we apply coding over multiple transport blocks, the underlying wireless channel can be effectively modeled as a finite-state discrete-time Markov chain. We link the characteristics of the underlying physical channel to the parameters of the Markov chain, and derive the corresponding “channel dispersion.” The “channel dispersion” is then used to assess the throughput performance of various communication strategies. The results show that for a fixed packet size the system throughput increases with transport block size.

Future wireless communications will face the dual challenge of supporting large traffic volume while providing reliable service for various kinds of delay-sensitive traffic. In light of this challenge, this paper investigates the throughput performance of a wireless communication system under channel coding over finite “packets.” When we apply coding over multiple “packets,” the underlying wireless channel can be effectively modeled as a finite-state Markov process. By linking the characteristics of the underlying physical channel to the parameters of the Markov process, we are able to derive the channel dispersion of the corresponding system. The channel dispersion is then used to assess the coding performance of various communication strategies. It is interesting to find that when there is a constraint on the total blocklength, coding over large “packets” will give better performance than that of coding over small “packets”.

In this paper, we study the Cramer-Rao bound (CRB) for continuous phase modulation (CPM) signals where frequency offset, carrier phase, and symbol timing are jointly estimated when transmitted over an additive white Gaussian noise (AWGN) channel. We consider a data-aided (DA) estimation scenario in which the estimator takes advantage of a known training sequence at the start of each burst. Thus, we first derive the joint CRBs as functions of a known training sequence and CPM parameters. By analyzing the CRB expressions, we propose the optimum training sequence for which the CRB is minimized. We show that the same training sequence is optimum for all three estimation parameters. Additionally, we compare the performance of the optimum training sequence with a random one by providing a closed-form expression for the unconditional CRB (UCRB) for symbol timing estimation of CPM signals. Comparing the UCRB and the CRB for the optimum training sequence reveals that a DA estimator with the optimum training sequence leads to significant gains in terms of the mean-square error of the estimation parameter when the underlying CPM scheme is non-binary and/or partial response.

In this paper, we propose a complete synchronization algorithm for continuous phase modulation (CPM) signals in burst-mode transmission over additive white Gaussian noise (AWGN) channels. The timing and carrier recovery are performed through a data-aided (DA) maximum likelihood algorithm, which jointly estimates symbol timing, carrier phase, and frequency offsets based on an optimized synchronization preamble. Our algorithm estimates the frequency offset via a one-dimensional grid search, after which symbol timing and carrier phase are computed via simple closed-form expressions. The mean-square error (MSE) of the algorithm's estimates reveals that it performs very close to the theoretical Cramer-Rao bound (CRB) for various CPMs at signal-to-noise ratios (SNRs) as low as 0 dB. Furthermore, we present a frame synchronization algorithm that detects the arrival of bursts and estimates the start-of-signal. We simulate the performance of the frame synchronization algorithm along with the timing and carrier recovery algorithm. The bit error rate results demonstrate near ideal synchronization performance for low SNRs and short preambles.

This paper focuses on the problem of optimal bit and power allocation in linear periodically time varying (LPTV) channels in broadband (BB) power line communication (PLC). Previous work has demonstrated that improvements in bit loading can be achieved with LPTV channel adaptation via so-called microslots in time for an orthogonal frequency division multiplexing (OFDM) system. In this paper, we present that the application of a power constraint that is averaged over many microslots can be exploited for further performance improvements through loading. Due to the matroid structure of the optimization problem, greedy-type algorithms are proven to be optimal for the new LPTV-aware bit and power loading. Significant gains are attained especially at reduced transmit-power levels, where the energy per bit-transmission is also low, and for poor (i.e. high attenuation) channel conditions. Furthermore, two mechanisms are utilized to reduce the complexity of the optimal LPTV-aware bit loading and peak microslot power levels: (i) employing representative values from microslot transfer functions, and (ii) power clipping. Our results indicate that the reduced complexity LPTV-aware bit loading with power clipping performs very close to the optimal LPTV-aware bit loading, which makes it an attractive option in a practical setting.

In this paper, we study the Cramér-Rao bound (CRB) for continuous phase modulation (CPM) signals. Based on the CRB computations, we propose the optimum training sequence for joint estimation of carrier phase, frequency offset and symbol timing. Our proposed training sequence is optimum in the sense that it minimizes the CRBs for all three estimation parameters simultaneously. The results are useful in the design of training sequences attached to data packets in burst-mode transmissions where data-aided (DA) synchronization is employed.

FPGAs as commodities offer a resource for high-performance computation that is unmatched in flexibility and price/performance. As a lab, we are interested in high-level descriptions of computation and data, and how they may be customized to map effectively on FPGA fabrics. This paper describes our tool-chain, approach and methodology to FPGA utilization. We give a case study of the generation of a low density parity checking forward error correction algorithm, and discuss the specific challenges we faced with using FPGAs as our target.

Low probability of intercept (LPI) communication generally relies on the presence of noise to obfuscate a covert signal through the use of spectral spreading or hopping. In contrast, this paper addresses the use of ambient interference from other man-made emissions as a means to mask the presence of covert communication. Specifically, the high power, wide bandwidth, and repeating structure of pulsed radar systems provide an advantageous framework within which to embed a communication signal. The operating paradigm considered here is that of an RF tag/transponder that is illuminated by the radar and intends to covertly communicate with the radar or some other desired receiver while being masked by the ambient radar backscatter to avoid detection by an intercept receiver. Communication takes place on an intra-pulse (or individual pulse) basis to maximize the data rate. The impact of multipath, and its exploitation using time reversal to achieve spatio-temporal focusing, is considered. The processing gain for the destination receiver and intercept receiver are derived analytically and subsequently used to optimize the parameterization of communication symbol design.

This paper presents a novel multiple-access modulation scheme which combines key characteristics of single carrier frequency division multiple access (SC-FDMA) with continuous phase modulation (CPM) in order to generate a power efficient waveform. CPM-SC-FDMA is developed based upon the observation that the samples from a CPM waveform may be treated as "data symbols" taken from a constant-envelope encoder. As with any encoder output, these samples may be precoded using the Discrete Fourier Transform and transmitted using SC-FDMA. Having originated from a constant envelope CPM waveform, CPM-SC-FDMA can potentially retain much of the power efficiency of CPM-thus resulting in a lower peak-to-average power ratio (PAPR) than conventional SC-FDMA. In this paper, we account for the information rate, memory, power efficiency, bit error rate (BER) performance and spectral occupancy of CPM-SC-FDMA. In addition, we investigate the impact of amplifier nonlinearity on BER performance as the number of users increases. Finally, we provide a detailed numerical comparison with a commensurate convolutionally coded QPSK-SC-FDMA scheme (CC-QPSK-SC-FDMA). We show a CPM-SC-FDMA scheme that provides an overall gain of up to 4 dB relative to the CC-QPSK-SC-FDMA scheme over a frequency-selective channel.

In this paper, we investigate the power efficiency and bit error rate performance of two spectrally efficient CPM-SCFDMA (Continuous Phase Modulated Single Carrier Frequency Division Multiple Access) waveforms. CPM-SC-FDMA is derived by sampling a Continuous Phase Modulated (CPM) waveform and then DFT-precoding the resulting signal samples for transmission using SC-FDMA. Having originated from a constant envelope CPM waveform, CPM-SC-FDMA can potentially retain much of the power efficiency of CPM-thus resulting in a lower peak-to-average power ratio than conventional SC-FDMA. As we show in this paper, when taking the difference in power amplifier backoff requirements into account, CPM-SC-FDMA can provide an overall gain of up to 4 dB relative to convolutionally encoded QPSK-SC-FDMA over a frequency-selective channel.

We consider symbol timing recovery for continuous phase modulations (CPMs) with correlated data symbols. A popular example of such a scheme is shaped offset quadrature phase-shift keying (SOQPSK). We propose an extension to an existing non-data-aided (blind) timing error detector (TED) to make it compatible with such modulation schemes. The merits of the modified TED are demonstrated by comparing its performance with and without taking the data correlation into account. As a further modification, we show that a quantization scheme can be used to yield an extremely low-complexity version of the system with only negligible performance losses. The S-curve of the proposed quantized TED is given, which rules out the existence of false lock points. The proposed scheme shows great promise in a wide range of applications due to its low complexity, its lack of false lock points, and its blind nature; such applications include timing recovery for noncoherent detection schemes and false lock detectors.

We consider highly-simplified decision feedback detectors for shaped-offset quadrature phase-shift keying (SOQPSK), a highly bandwidth-efficient and popular constant-envelope modulation. In particular, we show that the state complexity can be reduced to a minimal level - two states - with asymptotically optimum performance, as demonstrated by performance analysis and confirmed by computer simulations. The complexity reduction is achieved by a novel manipulation of the differential encoder and the SOQPSK precoder, which are both part of the transmission model for SOQPSK. We give two possible architectures for achieving this complexity reduction: the pulse amplitude modulation (PAM) technique and the pulse truncation (PT) technique. We also formulate these detectors for coherent and noncoherent detection. The resulting family of detectors makes use of recent advances in SOQPSK technology based on a continuous phase modulation (CPM) interpretation of SOQPSK. The proposed simplifications are significant because they minimize the complexity of trellis-based SOQPSK detectors, which have become available only in recent years. Because trellis-based SOQPSK detectors are 1-2 dB superior to the widely-deployed family of symbol-by-symbol SOQPSK detectors, the proposed two-state detectors offer the simplest means of achieving these performance gains. Thus, these simple detection schemes are applicable in settings where high performance and low complexity are needed to meet restrictions on power consumption and cost.

Multicarrier orthogonal frequency division multiplexing (OFDM) supports high data rate wireless communication using orthogonal frequency channel transmissions and offers excellent immunity against fading and intersymbol interference. However, it is characterized by a high peak-to-average power ratio (PAPR), which presents a major challenge for battery- driven terminals requiring efficient power amplification. Single carrier FDMA (SC-FDMA) is a variant of OFDM in which the data symbols are modulated in the time domain, which results in a more power efficient scheme. Continuous phase modulation (CPM) forms a class of single carrier constant amplitude waveforms which are known to be power efficient since the PAPR is always 0 dB. In this paper, we present a novel CPM-SC-FDMA modulation scheme which combines key characteristics of SC-FDMA and CPM to produce a constant envelope waveform which is transmitted over a set of OFDM subcarriers. Thus, this new scheme embodies the power efficiency of single-carrier CPM and the low implementation complexity of SC-FDMA. The basis of our approach is found in the observation that the discrete-time samples from the CPM waveform constitute a set of constant envelope time domain "symbols." When used with an interleaved FDMA (IFDMA) subcarrier mapping, the resulting waveform retains the constant envelope property of CPM. Simulations in AWGN and frequency selective channels indicate that by careful selection of the CPM- SC-FDMA parameters, that the bit error rate performance can improve upon that of conventional SC-FDMA.

A detector architecture capable of detecting both shaped offset quadrature phase shift keying (SOQPSK-TG) and Feher's quadrature phase shift keying (FQPSK-JR) is developed and analyzed. Both modulations are embodied as fully interoperable modulations in the Interrange Instrumentation Group (IRIG) standard IRIG-106. It is shown that the common detector achieves near optimal bit error rate performance without knowledge of which modulation is used by the transmitter. The detection techniques are based on a common trellis-coded modulation representation and a common continuous phase modulation (CPM) representation for these two modulations. In addition the common pulse amplitude modulation (PAM) decomposition of the common CPM representation is developed. The common PAM-based detector offers the best performance- complexity trade-off among the detectors considered.

This letter considers the pulse amplitude modulation (PAM) representation of continuous phase modulation (CPM) with a ternary data alphabet. This technique is applied to the problem of constructing reduced-complexity detectors with near-optimum performance. The usefulness of this approach is demonstrated using the ternary CPM variant known as shaped-offset quadrature phase-shift keying (SOQPSK).

The Laurent decomposition expresses any binary single-h CPM waveform as the summation of a finite number of pulse amplitude modulated components, and this result has been useful in the development of a class of reduced complexity CPM detection schemes. In a recent generalization, it has been shown that a similar finite-term amplitude modulation expansion exists for all variants of CPM, regardless of signal complexity, with the important distinction that the amplitude modulated pulses are, generally, data-dependent. Furthermore, it has been shown that most of the signal power is typically concentrated in the first 1-2 principle components of the expansion, which suggests a possible reduction in receiver complexity viz. the optimal maximum likelihood sequence detector. In this paper, we investigate the bit error rate (BER) performance of a maximum likelihood sequence detector when the incoming signal is matched to the data-dependent pulse modulation components found in this new signal representation. Numerical results suggest that there is a negligible decrease in performance between the optimal conventional matched filter receiver and a reduced complexity, sub-optimal scheme that only uses the first 1-2 (principle) signal components in the construction of the matched filter bank.

We develop a reduced-complexity approach for the detection of coded shaped-offset quadrature phase-shift keying (SOQPSK), a highly bandwidth-efficient and popular constant-envelope modulation. The complexity savings result from viewing the signal as a continuous-phase modulation (CPM). We give a simple and convenient closed-form expression for a recursive binary-to-ternary precoder for SOQPSK. The recursive nature of this formulation is necessary in serially concatenated systems where SOQPSK serves as the inner code. We show that the proposed detectors are optimal in the full-response case, and are near-optimal in the partial-response case due to some additional complexity reducing approximations. In all cases, the proposed detectors achieve large coding gains for serially concatenated coded SOQPSK. These gains are similar to those reported recently by Li and Simon, which were obtained using a more complicated cross-correlated trellis-coded quadrature modulation (XTCQM) interpretation.

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.

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 (CPM) interpretation of SOQPSK. We show that the performance of these MBDD schemes approaches that of coherent detection as the multiple-bit observation window N increases. The first scheme uses a detection window that spans the full N-bit observation window (F-MBDD) and is shown to require very large values of N to approach the performance of coherent detection. 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 and requires more modest values of N for high performance. These performance characteristics are identified via a detailed performance analysis, which provides asymptotic formulas for the probability of bit error that are confirmed with computer simulations.

Symbol-by-symbol detection of SOQPSK and FQPSK using detectors designed for offset QPSK represents a simple common detector architecture for these two interoperable waveforms. Unfortunately, this detection method results in a 2 dB loss in bit error rate performance. This paper describes detection methods for recovering this loss without the need for knowing which modulation is used by the transmitter. An equivalent cross-correlated trellis-coded quadrature modulation (XTCQM) representation for SOQPSK is developed which forms the basis of a common TCM detector. An equivalent CPM representation for FQPSK is developed which forms the basis for a common CPM detector. The common XTCQM detector performs slightly better than the common CPM detector, but achieves this gain at the expense of higher complexity

In this paper we develop a reduced-complexity detection scheme for shaped-offset quadrature phase-shift keying (SOQPSK), a highly bandwidth-efficient constant-envelope modulation. The detector is based on the well-known pulse amplitude modulation (PAM) representation of continuous phase modulation (CPM). Since SOQPSK is a ternary CPM, we show how the binary-based PAM technique is extended to accommodate the ternary case. We demonstrate that a detector based on the first two PAM components requires a simple trellis of only 4 states. We show that near-optimum performance is achieved using this reduced-complexity detector. The potential complexity reduction can be quite large, since one version of SOQPSK requires a trellis of 512 states.

We develop a reduced-complexity approach to the detection of military-standard (MIL-STD) shaped-offset quadrature phase-shift keying (SOQPSK), a highly bandwidth-efficient constant-envelope waveform. The complexity savings result from viewing the signal as a continuous phase modulation (CPM). The proposed detector has a matched filter bank which is one-fourth as complex as previously reported designs. We establish that this reduced-complexity detector achieves optimal performance for uncoded MIL-STD SOQPSK. We also show a simple and convenient closed-form expression for a recursive precoder for SOQPSK, which is necessary in serially concatenated systems. Finally, we show that the proposed reduced-complexity detector achieves the large coding gains that have recently been reported for serially concatenated coded MIL-STD SOQPSK.

It is well understood that the pulse amplitude modulation (PAM) representation of continuous phase modulation (CPM) can lead to reduced-complexity detectors with near optimum performance. It has recently been shown that the PAM representation also extends to CPM schemes with multiple modulation indexes (multi-h CPM). In this paper, we present a detector for multi-h CPM which is based on the PAM representation. We also give an exact expression for the pairwise error probability for the entire class of PAM-based CPM detectors (single- and multi-h, optimal, and reduced-complexity) over the additive white Gaussian noise (AWGN) channel and show that this bound is tighter than the previously published bound for approximate PAM-based detectors. In arriving at this expression, we show that PAM-based detectors for CPM are a special case of the broad class of mismatched CPM detectors. We also show that the metrics for PAM-based detectors accumulate distance in a different manner than metrics for other CPM detectors. These distance properties are especially useful in applications with greatly reduced trellis sizes. We give thorough examples of the analysis for different single- and multi-h signaling schemes. We also apply the new bound in comparing the performance of PAM-based detectors with other reduced-complexity detectors for CPM.

It is known that any multilevel continuous phase-modulated (CPM) signal with a single modulation index can be exactly represented by a sum of pulse-amplitude modulated (PAM) waveforms. In this paper, we show how multi-h CPM signals can also be represented in this manner. The decomposition is presented in general terms as a function of the alphabet size, modulation indexes, and phase pulse of the CPM scheme. The number of pulses required to exactly construct the signal is shown to increase over that previously given for single-h schemes; this increase is in proportion to the number of modulation indexes. We propose an approximation which significantly reduces the number of signal pulses and which minimizes the mean-squared error for an arbitrary set of modulation indexes. We show that this approximation can have two objectives: 1) to reduce the number of pulses in the same manner as has been proposed for single-h schemes; and/or 2) to reduce the number of multi-h pulses; we also show the conditions where this latter objective is most practical. We compare this minimum mean-squared error approximation with another method which was recently proposed for CPM. We also give numerical results on detection performance which demonstrate the practicality of the proposed approximation.

We present an optimal maximum likelihood sequence estimating (MLSE) receiver which is based on the pulse amplitude modulation (PAM) representation of multilevel multi-h continuous phase modulation (CPM). We also give four different approaches to constructing suboptimal receivers which use a significantly reduced number of signal terms. We apply these techniques to two multi-h schemes in current use and evaluate receiver performance with computer simulations. In one instance we reduce the number of trellis states from 512 to 32, and the number of matched filters from 96 to 3, with a degradation of 0.7 dB. The simulations also show that the complexity reductions preserve the performance advantage multi-h CPM schemes have over single-index schemes.

The selection of interleaver depth for the land-mobile satellite channel is investigated by analyzing the performance of convolutionally encoded BPSK and DPSK over a frequency-nonselective correlated Ricean fading channel. By extending previous analyses of partially interleaved convolutional codes over such channels, a new figure of merit-which is a function of the channel correlation function-is identified. Simulation results for the first-order Butterworth, Jakes (1974), and Divsalar (1991) fading spectra are presented which demonstrate the applicability of the figure of merit as an aid in interleaver design. The figure of merit also tracks the nonmonotonic, or quasi-oscillatory, behavior of the decoded bit error rate with increasing interleaver depths in those situations where this occurs.