Double Turbo Equalization of Continuous Phase Modulation with Frequency Domain Processing

There are several ways to use iterative decoding techniques with coded continuous phase modulation (CPM). This paper presents a method using parallel concatenation of convolutionally-coded CPM. All CPM schemes can be decomposed into a ring convolutional code and a memoryless signal mapper. This allows a properly designed convolutional code trellis to be combined with the CPM trellis, producing the joint trellis of a constituent code. Parallel concatenation of such constituent codes combined with iterative decoding yields very good performance. We present the results of code searches for two binary CPM schemes, each using bit interleaving and symbol interleaving. Simulation results using various length interleavers are also provided. Low complexity encoders are shown to perform better using bit interleaving, whereas encoders with higher complexity perform better with symbol interleaving.

This paper addresses a novel frequency-domain (FD) derivation of the Minimum Mean Square Error (MMSE) Turbo Equalizer for ST-BICM systems. The receiver consists of a FD MMSE Equalizer and a Time Domain (TD) decoder with iterative information exchange between the two functions. In particular, we propose a FD MMSE equalizer derivation improved from previous approaches, in that feedback and feedforward filters are directly derived in the frequency-domain. The accuracy of the proposed approach is confirmed by comparing the lower bound of the iterative equalizing process with the corresponding analytical results proposed in previous paper. Simulations over multi-path Rayleigh block fading channels show that the resulting algorithm exhibits similar performance with that of the corresponding TD MMSE equalization. The problem of finding the TD filter achieving the best compromise between minimum impulse response length and performance is considered.

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.

In this paper, we investigate the effects of shaping on the bandwidth efficiency and performance of continuous phase modulated (CPM) signals. We show that, theoretically, by properly shaping the unmodulated signal, better bandwidth efficiency and performance can be obtained. We then develop the soft-input soft-output (SISO) de-shaper for trellis shaping and block shaping schemes. For a coded, shaped CPM system, the SISO de-shaper enables joint decoding and de-shaping via iterative detection. We demonstrate that using the SISO deshaper, together with iterative decoding and de-shaping, the theoretical advantage of shaping can be realized with practical complexity

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.

In the paper, a class of LDPC coded continuous phase modulation (CPM) systems is proposed for reliable communication over burst-error channels. A series of binary LDPC codes with code rates 1/4, 1/2 and 2/3 are chosen for binary and quaternary CPM schemes. A non-recursive decomposition of CPM is incorporated to eliminate the error propagation caused by burst errors. To reduce the complexity, an improved demodulation algorithm for noncoherent soft in soft out (N-SISO) is considered. Simulation results show that the proposed LDPC coded CPM offers a better error performance and is abler to recover the transmitted information under severe burst errors than current systems.

The time reversal (TR) technique combined with the ultra-wideband (UWB) system offers a new potential for decreasing the cost and complexity of the UWB receivers. In spite of TR–UWB's good performance in perfect channel state information (CSI), it is very sensitive to the channel estimation error. The effect of channel imperfection on the TR–UWB system is considered in this paper. At first, based on a minimum mean square error (MMSE) equalizer receiver, a prefilter is calculated in closed form to improve the performance of the TR–UWB system in an imperfect CSI scenario. Furthermore, for comparison purposes, a similar calculation for prefilter is carried out based on a simple matched filter (MF) receiver. Then, in order to improve the MF receiver performance, a two-stage iteration-based algorithm is developed. The initial value for this iteration-based improved algorithm is considered to be a prefilter which is calculated in the TR–UWB system with MMSE equalizer. This optimized algorithm causes the channel estimation error in the TR–UWB system to become zero in some steps. Finally, exhaustive simulations are done to demonstrate the performance advantage attained by the improved algorithm.

This paper proposes a new Frequency-Domain (FD) receiver based on Expectation Propagation (EP) for Faster-Than-Nyquist (FTN) signaling. Our system model is based on a circular convolution of the shaping filter leading to a Circular FTN (CFTN) waveform allowing a FD process at reception without cyclic prefix. We solve a Maximum A Posteriori criterion using EP combined with an original Gaussian family yielding a low-complexity FD Minimum Mean-Square Error (MMSE) equalizer combined with a Constellation Matcher in charge of realigning the symbol estimates with respect to the constellation. This new FD-EP receiver for FTN signaling is compared to RS-BCJR and M*-BCJR receivers as well as the MMSE equalizer. The proposed FD-EP receiver is shown to perform slightly better than MMSE at 1.5 bits/s/Hz, and represents a low complexity alternative compared to RS-BCJR or M*-BCJR. Furthermore, while existing receivers are not able to handle higher spectral efficiencies, our FD-EP allows FTN signaling to almost achieve its matched-filter bound at 3 bits/s/Hz with channel coding.

Application of the EM (Expectation-Maximization) algorithm to sequence estimation in an unknown channel can in principle produce MLSE (maximum likelihood sequence estimates) that are not dependent on a particular channel estimate. The Expectation step of this algorithm cannot be directly performed for continuous phase modulated (CPM) signals transmitted in a time varying multipath channel. We therefore derive a simplification of the EM algorithm for CPM signals in this channel. Simulations applied to the Global System for Mobile Communications (GSM) show that the simplified EM algorithm significantly decreases the amount of training data needed for the channel model considered, and removes the majority of the bit errors that are due to imperfect knowledge of the channel.

The minimum mean-square error (MMSE) criterion is often used for channel estimation in wireless OFDM systems. The MMSE channel estimators perform better than the least-square (LS) criterion-based techniques but their computational complexity is one of the main drawbacks for practical implementation, especially when the number of subcarriers is large. To address this issue while maintaining the performance advantage, we present a new simplified MMSE channel estimator for OFDM systems in multipath fading channels. The proposed method is primarily based on the rank-reduction of the channel correlation matrix in the frequency domain. Simulation results show that the proposed method achieves almost the same performance as the full-rank MMSE method, while significantly reducing the computational complexity.

In minimum mean squared error (MMSE) based turbo equalization, the decoder's extrinsic information is used as the MMSE equalizer's prior information. In order to improve the performance, the combined prior information which consists of the whole decoder's extrinsic information and the partial decoder's full information in the last iteration, is used by the MMSE equalizer. Meanwhile, the MMSE equalizer is lead by matched filter as a preprocessor to reduce the complexity. The extrinsic information transfer (EXIT) chart analysis and simulation results show that the performance of the proposed scheme is much better than that of the conventional turbo equalizer.

In this paper, transmission of continuous phase modulated (CPM) signals over time- and frequency-selective (i.e., doubly-selective) channels is considered. Leveraging on the well-known Laurent representation for a CPM signal, we design a two-stage receiver, composed of a linear time-varying (LTV) equalizer, followed by a detector: the former one aims at mitigating the channel dispersion and it is synthesized under the zero-forcing (ZF) or minimum mean-square error (MMSE) criterion; the latter one recovers the transmitted symbols from the pseudo-symbols of the Laurent representation in a simple recursive manner. Relying on a Basis Expansion Model (BEM) of the doubly-selective channel, we derive frequency-shift (FRESH) versions of the proposed LTV equalizers, discussing also their complexity issues and proposing simplified implementations. Monte Carlo simulation results, carried out in two typical aeronautical scenarios (arrival/takeoff and en-route), show that the proposed approach is able to work satisfactorily also over rapidly time-varying channels.

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.

In this paper, we analysis the receiver of orthogonal frequency division multiplexing (OFDM) systems over frequency selective fading channels where the multipath delay exceeds the guard interval duration and propose a novel receiver scheme. The proposed receiver consists of the Inter Symbol Interference (ISI) canceller and the turbo equalizer. At each iteration, the proposed turbo equalization algorithm performs soft Inter Carrier Interference (ICI) cancellation and frequency domain minimum mean-square error (MMSE) filtering to minimize the performance degradation caused by ICI distortion and frequency-selective channels. Simulation results of the system performance show that the proposed receiver effectively recovers the contaminated OFDM signals.