Frequency-domain equalization for continuous phase modulation

Continuous phase modulation (CPM) consists of a large family of signals that are especially suitable for wireless communication. CPM signals have not been represented by discrete points in signal space because the phase of the carrier is time-variant. However, in this paper we present a new method to represent the binary CPM signals by discrete points in signal space by utilizing the amplitude modulated pulse (AMP) representation of the CPM signals. We use this new signal space representation to compute the Euclidean distance for any CPM signal and we compare the performance of CPM signals with each other and with other modulation schemes.

The underwater acoustic (UWA) communication system is characterized by limited bandwidth, while continuous phase modulation (CPM) offers a constant envelope, improving power and spectrum utilization efficiency. However, severe inter-symbol interference (ISI) poses a significant challenge in CPM-based UWA communication. Traditional CPM frequency domain equalization (FDE) combined with simple phase detection neglects the inherent coding gain from CPM, leading to performance degradation. Although Viterbi detection provides high performance, its complexity makes it unsuitable for computationally constrained UWA systems. This paper proposes a symbol detection algorithm based on posterior probabilities combined with FDE (PS-FDE). PS-FDE improves CPM signal detection performance by effectively separating information, applying delay, and performing multiple rounds of information merging. Simulations using minimum shift keying (MSK) and Gaussian MSK signals demonstrate significant performance improvement in just a few iterations over UWA channels. A sea trial further validates the algorithm, showing a 15.83% reduction in bit error rate after three information mergings.

In this letter, an orthogonal space-time (ST) block coding (STBC) technique for continuous phase modulation (CPM) is proposed and combined with a frequency domain equalizer (FDE) to obtain high performance gains over frequency-selective channels. The new method maintains the constant envelope and phase continuity of the CPM waveforms perfectly by using appropriate tail symbols during the addition of cyclic prefix and interblock transitions and, therefore, has no negative impact on the spectral efficiency. Because the STcoded CPM blocks remain orthogonal, FDE is applied as in the case of single antenna transmissions without any increase in the computational load. Simulations corroborate the performance improvement offered by STBC while also preserving the desired bandwidth efficiency of CPM.

Continuous phase modulation (CPM) and trellis-coded modulation are well-understood schemes that layer trellis codes with multilevel modulation to produce efficient bandwidth waveforms. This paper describes a novel modulation scheme which takes advantage of existing trellis codes and adds parallel branches to create a new modulation with greater spectral efficiency and reduced receiver complexity. The first part of the paper discusses the trade-off between Euclidean distance and modulation bandwidth for the standard 1-REC CPM waveform. A set of orthogonal signals can be added to the CPM constellation which provides a series of parallel branches in the natural trellis structure of the CPM modulation. The corresponding bandwidth expansion and throughput improvement is analyzed and the advantages of this modulation technique are discussed. This new, non-constant envelope CPM waveform is compared to the multi-level, multi-amplitude CPM waveform (described in Proakis). In similar fashion, a trellis-coded, shaped PSK modulation is expanded to include orthogonal signal shaping and the power and spectral efficiencies are discussed.

The complexity of the multiple-symbol detection structures for partial response continuous phase modulation (CPM) signals goes exponentially with the length of the pulse shaping filter and the observation length as well. Simple no coherent trellis receivers for partial response CPM signals are proposed in this paper. Parallel to the simple coherent detectors, where CPM signals are approximately represented by a sum of Phase Amplitude Modulation waveforms, Laurent decomposition is applied to reduce the complexity. The proposed no coherent receiver is structured with only fixed K matched filters in the front-end and a processor which uses Viterbi algorithm with a 2N-1 states trellis to perform the sequence estimation. It is attractive because the structure does not involve any matrix calculations. The good error performance is confirmed by simulation results.

In 1986, Laurent showed that binary continuous phase modulated (CPM) signals can be decomposed into pulse amplitude modulated (PAM) waveforms. This result, later extended to multilevel CPM signals by Mengali and Morelli, has attracted much attention, especially for the design of simplified receivers. The paper proceeds from the premise that the decomposition into PAM waveforms is not unique, and follows a systemtheory approach that leads to a natural formulation. First, the CPM modulator is represented by a nonlinear part (encoder) followed by a linear part (bank of PAM modulators).The two parts are then rearranged with the aim of obtaining real-valued continuous PAM waveforms and to reduce their number. Several classes of decompositions arise with this approach, each of which admits an infinite number of different decompositions of the same CPM signal, among which the Laurent and MengaliMorelli results appear as special cases. Throughout the paper, a systematic use is made of the Kronecker product, which appears to be the natural tool for dealing with CPM decompositions and for expressing results in a very simple form.

Existing space-time codes have focused on multiple- antenna systems with linear modulation schemes such as phase- shift keying and quadrature amplitude modulation. Continuous phase modulation (CPM) is an attractive scheme for digital transmission because of its constant envelope which is needed for power efficient transmitters. Recent research has shown that space-time coded CPM can achieve transmit diversity to improve performance while maintaining the compact spectrum of CPM signals. However, these efforts mainly combine space- time coding (STC) with CPM to achieve spatial diversity at the cost of a high decoding complexity. In this paper, we design space-time block codes (STBC) for binary CPM with modulation index h = 1/2 and derive low-complexity receivers for these systems. The proposed scheme has a much lower decoding complexity than STC CPM with the Viterbi decoder and still achieves near-optimum error performances.

CPM waveforms which are utilized in both MIL-STD-188-181B (181B) and high performance waveform SATCOM operation undergo appreciable distortion due to the effects of the bandlimiting and hard-limiting satellite transponder. In this application, the traditional LMS equalizer can remove some of the intersymbol interference, but at the higher symbol rates, the modem performance is still far off from the same bit error rate achieved in an environment which only contains additive white Gaussian noise. Observation of the SATCOM channel has shown that the CPM waveform is predictable, distorted in phase during symbol transitions. Large phase transitions incur a larger, proportional amount of distortion when compared to smaller phase transitions. A characterization of the phase error as a function of all the possible clockwise and counterclockwise adjacent phase transitions for the CPM phase constellation illuminates this proportion property of the distortion caused by the intersymbol interference. Once this error is characterized for all the symbols, it can be removed via complex multiplication. This method has been shown to outperform the traditional LMS equalizer in this application especially when considering the noise enhancement inherent in the LMS equalizer implementation. This paper documents the simulation comparison of the LMS equalizer and the new non-linear equalizer approach along with actual radio bit error rate curves.

In this paper a general soft-based synchronization technique for continuous phase modulations (CPM) is presented. In particular two soft carrier phase estimation algorithms are derived, being the phase the parameter that shows the lower implementation complexity. These algorithms exploit the trellis structure inherent in the modulator of CPM signals and make use of a symbol-based BCJR, developed in an ad-hoc way for an uncoded CPM signal. The algorithms are blind and are designed to work with all CPM family. Simulation results for the soft carrier phase estimation are presented in terms of Root Mean Square Estimation Error (RMSEE). The modified Cramer-Rao bound (MCRB) is also shown for reference. RMSEE of soft recovery approach is very close to MCRB for all the examined formats.

Continuous Phase Modulation (CPM) schemes are advantageous for low-power radios. The constant envelope transmit signal is more efficient for both linear and non-linear amplifier architectures. A standard, coherent CPM receiver can take advantage of modulation memory and is more complex than a coherent Phase Shift Keyed receiver. But the CPM signal can be demodulated non-coherently and still take advantage of the trellis structure inherent in the modulation. With this complexity reduction, the CPM receiver is comparable in performance to a Phase Shift Keyed radio with the power utilization of a Frequency Shift-Keyed design. In this paper, we discuss two methods for increasing the modulation memory of the CPM signal. In the first method, the distribution of the transmitted symbol across multiple phase pulses is investigated and the bit error rate analyzed. In the next method we address the addition of convolutioncodes. In both cases the effects of the CPM memory to quasi-coherent demodulation is analyzed and discussed. The differences in complexity will be analyzed and the overall performance enhancements of several different modulation schemes will be illustrated. 1

The huge bandwidth available at 60 GHz will allow short range wireless communication to deliver bit rates over 1 Gbps. However the design of millimeter wave analog blocks is more critical than at lower frequencies, leading to a possible high non ideality of the radio front-end (FE). A suitable air interface for low cost, low power 60 GHz transceivers should thus use a modulation technique that has a high level of immunity to FE non-idealities. In this paper, we compare the sensitivity to FE non-idealities of two promising air interfaces namely offset quadrature phase shift keying (OQPSK) with frequency domain equalization (FDE) and continuous phase modulation (CPM) with time domain equalization (TDE). Our study focus on three main analog imperfections that are likely to have the biggest impact on the overall system performance: phase noise generated by the voltage control oscillator (VCO), clipping and quantization errors caused by the analog-to-digital converter (ADC) and non-linearity in the power amplifier (PA). Results show that CPM based air interface is more robust than OQPSK-based regarding the FE non-idealities. However the latter is less complex to design and offers much higher data rate than the former in the same bandwidth.

We present a coherent detection technique for continuous phase modulation (CPM) operating in the Rayleigh flat fading channel. The technique is based on the idea of inserting periodically data dependent pilot symbols that force the CPM signal to pass through known phase states. This transmission format enables the receiver to extract from the received signal the channel fading gains at regularly spaced instants. When coupled with proper channel estimation filters, very accurate channel state information (CSI) can be estimated at the receiver for fading compensation. Moreover, the accuracy of the CSI can be further refined by adopting a multiple-pass decoding approach. The paper discusses (a) the pilot symbol encoding technique required to force a M-level CPM scheme with a modulation index of p/M, p is an integer, to return periodically to a set of known phase states, (b) the optimal channel estimation filters, (c) a trellis-based precoding technique that can reduce the bit error rate in M-level CPM systems by close to 50%, and (d) a multiple-pass channel estimator/demodulator. Analytical and simulation results are presented for minimum shift keying (MSK), Gaussian MSK, and four-level continuous phase frequency shift keying with a modulation index of 1/4. It is observed that our pilot symbol-assisted CPM schemes exhibit no irreducible error floor even at a channel fade rate of three percent the symbol rate. The implicit phase coding in CPM and the accurate CSI provided by the pilot symbols lead to a diversity effect in the bit error rate curves of these modulation schemes.

Some properties of digitally phase modulated (DPM) signals are presented. Phase modulation with (overlapping) pulses generated by a digital FIR filter belong to this class, which may be considered to be a practical approximation to continuous phase modulated (CPM) signals. The power spectra of DPM signals are derived analytically. The ability of these signals to operate through an additive white Gaussian noise channel is assessed by calculating their minimum Euclidean distance. Their noise and spectral properties are found to be similar to those of CPM signals. Assuming that a Viterbi decoder is used to resolve symbol interference, the out-of-band power tends to decrease as the pulse duration increases, and the noise immunity is enhanced. At the same time the receiver complexity grows exponentially. Hence, noise immunity and spectrum compactness are achieved at the cost of higher received complexity. Modems for DPM signals are believed to be easier to implement than those for CPM signals. This is because filter design is simple and a residual carrier component can be retained to facilitate carrier regeneration. Furthermore, the accumulated carrier phase does not need to be continuously evaluated in order to perform matched filtering. The analytic results derived are supported by measurements and simulations.

In the next generation mobile communication systems, high-speed and high-quality packet data services are demanded. Hybrid ARQ (HARQ) is known as one of the promising error control techniques for wireless packet transmission. However, in a severe frequency-selective fading channel, the single-carrier (SC) HARQ throughput performance degrades due to inter-next generation mobile communication hybrid ARQ intersymbol interference Tomlinson-Harashima precoding frequency-domain equalization frequency-diversity gain Rayleigh fading channelsymbol interference (ISI). In this paper, we consider joint Tomlinson-Harashima precoding (THP) and frequency-domain equalization (FDE) to obtain the frequency-diversity gain while suppressing the residual ISI after FDE. We evaluate, by computer simulation, the SC HARQ throughput performance using joint THP/FDE in a frequency-selective Rayleigh fading channel.

Signals transmitted over a land mobile radio channel are very often subjected to frequency selective fading. A detection technique is proposed for continuous phase modulation (CPM) operating in such an environment. The technique uses embedded pilot symbols for channel impulse response estimation. The estimated channel response is updated from symbol to symbol and is used during the sequence detection of the CPM signal. Unlike pilot symbol assisted linear modulation, the pilot symbols in this CPM system are divided into two groups. The first group of pilot symbols is data-dependent and is used to force the modulator to return periodically to a known system state. The second group is not data-dependent and is used to specify a known waveform emanating from the periodic known state, for the purpose of channel estimation. The proper pilot symbol encoding rules, as well as the structure of the companion channel estimator, are presented. It is shown that CPM schemes employing this detection technique exhibit no irreducible error floor even in the presence of fast fading and large delay spread. The modem actually performs better in a heavily frequency selective fading environment, due to the implicit diversity effect provided by the channel. The difference in energy efficiency between frequency selective and flat fading can be as large as 5 dB at a 10-3 bit error rate and 8 dB at a 10-4 error rate. These results suggest that the proposed technique is very suitable for use in a system which employs diversity.