Shaped-offset Quadrature Phase-shift Keying Research Articles

Rate-Compatible, Bandwidth-Efficient, Low-Density Parity-Check (LDPC) Codes for Aeronautical Telemetry

Low-density parity-check (LDPC) codes form part of the IRIG-106 standard and have been successfully deployed for the Telemetry Group version of shaped-offset quadrature phase shift keying (SOQPSK-TG) modulation. Recently, LDPC code solutions have been proposed and optimized for continuous phase modulations (CPMs), including pulse code modulation/frequency modulation (PCM/FM) and the multi-h CPM developed by the Advanced-Range TeleMetry program (ARTM CPM), the latter of which was shown to perform around one dB from channel capacity. In this paper, we consider the effect of the random puncturing and shortening of these LDPC codes to further improve spectrum efficiency. We perform asymptotic analyses of the ARTM0 code ensembles and present numerical simulation results that affirm the robust decoding performance promised by LDPC codes designed for ARTM CPM.

Novel radar and communication integration waveform based on shaped octal phase-shift keying modulation

In light of increasing requirement for electromagnetic spectrum, spectrum efficiency improvement of radar and communication integration waveform is gaining interest. In this paper, to improve conventional linear frequency modulation (LFM)–continuous phase modulation (CPM) spectrum efficiency, a modified radar and communication integration waveform is proposed. Considering high spectral efficiency of shaped-offset quadrature phase-shift keying (SOQPSK), we generate a new modulation: shaped octal phase-shift keying (S8PSK) by combining the precoding method and CPM with octal phase-shift keying (8PSK). S8PSK is then used to encode communication data into LFM radar signal to form a novel radar and communication integration waveform: LFM-S8PSK. Numerical results demonstrate that compared with LFM–CPM, LFM-S8PSK can provide better spectrum efficiency in exchange for slightly worse bit error rate (BER). Also, it is shown that LFM-S8PSK almost maintains comparable radar performance with respect to LFM.

Burst-Mode Synchronization for SOQPSK

We consider a comprehensive synchronization strategy for burst-mode transmission of shaped-offset quadrature phase-shift keying (SOQPSK) signals over the additive white Gaussian noise channel. Due to the similarities between SOQPSK and continuous phase modulation (CPM), we make use of recent results for synchronization of burst-mode CPMs. We first derive a training sequence that is optimal in the sense that it jointly minimizes the Cramer–Rao bounds (CRBs) for frequency offset, phase offset, and timing offset estimation. Additionally, we develop a maximum likelihood data-aided algorithm for joint estimation of the synchronization parameters for SOQPSK signals. We show that the proposed algorithm for the optimal training sequence can be adapted to work with the suboptimal training sequence that is being considered for use in burst-mode integrated network enhanced telemetry. This demonstrates an immediate practical application for our approach. We present numerical results on the mean-squared error performance of the proposed algorithm for both training sequences and for different versions of SOQPSK. The numerical results show that our joint estimation algorithm yields performance that is very close to the CRBs for all three synchronization variables. Finally, we compare the overall performance of our proposed training sequence and synchronization algorithm for different sequence lengths by simulating a burst-mode SOQPSK receiver. This allows us to employ the right training sequence length based on the desired complexity and bit error rate performance.

Non‐data‐aided timing recovery algorithm for MIL‐STD SOQPSK

The phase trajectory of military standard (MIL-STD) shaped-offset quadrature phase shift keying (SOQPSK) is analysed and the fourth-power nonlinearity and phase accumulation technology is used to eliminate the self-noise caused by symbol information. After the operation, the MIL-STD SOQPSK signal is converted into a pure tone during a symbol period and the timing offset is estimated from the initial phase of the tone. Computer simulation shows that its estimation performance is remarkably close to the modified Cramer-Rao bound and better than that of the existing non-data-aided method in terms of estimation accuracy.

FEC Systems for Aeronautical Telemetry

We consider the design of capacity-approaching forward error correction (FEC) systems for use in the aeronautical telemetry environment. The modulation format is the bandwidth-efficient telemetry-group version of shaped-offset quadrature phase-shift keying (SOQPSK-TG). The FEC codes are a low-density parity-check (LDPC) code and a serially concatenated convolutional code (SCCC). The block structure of the two types of FEC is designed such that the two code words are formatted as similarly as possible. This unified format allows the flexibility of the FEC-encoded signal to be received by legacy test-range assets that are not equipped with FEC?although no coding gain is realized in such a case. We also show how a wide range of near-optimal SOQPSK demodulators can be paired with the FEC decoders; this includes the most widely deployed SOQPSK demodulator (the so-called symbol-by-symbol (SxS) demodulator), which so far has not been considered for use in FEC applications. In all of our demodulator/decoder designs, we apply techniques that are simple and robust and that fully decouple the demodulator's tasks (e.g., synchronization, filtering) from the decoder's tasks (e.g., path metrics, soft outputs). For both LDPC and SCCC, we show that very attractive system designs can perform within 0.5 dB of optimum, while requiring only a fraction of the complexity of the optimum system.

Shaped offset quadrature phase shift keying (SOQPSK) modulation scheme and its application in optical wavelength-division multiplexed (DWDM) transmission

This paper presents a new quaternary modulation scheme called SOQPSK. The principle on the optical SOQPSK generation is derived and analyzed, which is implemented by traditional Mach–Zehnder modulators. The performance of the optical SOQPSK modulated system is evaluated and compared with those of quadrature phase shift keying (QPSK) and offset QPSK (OQPSK) modulation systems via simulation, in terms of spectral efficiency, receiver sensitivity and density DWDM transmission performance. Simulations show that the novel modulation scheme improves spectral efficiency for DWDM transmission and provides better transmission performance than QPSK.

Decision feedback detectors for SOQPSK

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.

Symbol Timing Recovery for CPM with Correlated Data Symbols

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.

Decision-Directed Symbol Timing Recovery for SOQPSK

Shaped-offset quadrature phase shift keying (SOQPSK) is a highly bandwidth efficient modulation technique used widely in military and aeronautical telemetry standards. It can be classified as a form of continuous phase modulation (CPM), but its major distinction from other CPMs is that it has a constrained (correlated) ternary data alphabet. CPM-based detection models for SOQPSK have been developed only recently. While these detectors offer an appreciable performance gain over current detection schemes, one roadblock standing in the way of their being adopted is the lack of a CPM-based symbol timing recovery scheme that will work with SOQPSK. We show how an existing CPM-based timing error detector (TED) can be adapted to the unique characteristics of SOQPSK. The TED is formulated for a coherent detector but can be extended to the noncoherent case. We apply this timing recovery method to the versions of SOQPSK used in military (MIL-STD SOQPSK) and telemetry group (SOQPSK-TG) standards. We derive the theoretical performance limits on the accuracy of timing recovery for SOQPSK, as given by the modified Cramer-Rao bound (MCRB), and show that the proposed decision-directed TED (DD-TED) performs close to these bounds in computer simulations and is free of false-lock points. We also show that the proposed scheme outperforms a non-data-aided TED (NDA-TED) that was recently developed for SOQPSK. These results show that the proposed scheme has great promise in a wide range of applications due to its low complexity, strong performance, and lack of false-lock points.

PAM representation of ternary CPM

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).

Multiple-Bit Differential Detection of Shaped-Offset QPSK

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

Reduced-Complexity Approach to Iterative Detection of Coded SOQPSK

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.

Performance of Coded OQPSK and MIL-STD SOQPSK With Iterative Decoding

We show that military standard (MIL-STD) shaped-offset quadrature phase-shift keying (SOQPSK), a highly bandwidth-efficient constant-envelope modulation, can be represented in the form of a cross-correlated trellis-coded quadrature modulation. Similarly, we show that offset QPSK (OQPSK) can be decomposed into a "degraded" trellis encoder and a memoryless mapper. Based on the representations of OQPSK and MIL-STD SOQPSK as trellis-coded modulations (TCMs), we investigate the potential coding gains achievable from the application of simple outer codes to form a concatenated coding structure with iterative decoding. For MIL-STD SOQPSK, we describe the optimum receiver corresponding to its TCM form and then propose a simplified receiver. The bit-error rate (BER) performances of both receivers for uncoded and coded MIL-STD SOQPSK are simulated and compared with that of OQPSK and Feher-patented QPSK (FQPSK). The asymptotic BER performance of MIL-STD SOQPSK is also analyzed and compared with that of OQPSK and FQPSK. Simulation results show that, compared with their uncoded systems, there are significant coding gains for both OQPSK and MIL-STD SOQPSK, obtained by applying iterative decoding to either the parallel concatenated coding scheme or the serial one, even when very simple outer codes are used.