This paper addresses the well-known local maximum problem of the expectation-maximization (EM) algorithm in blind inter-symbol interference (ISI) channel estimation. This problem primarily results from phase and shift ambiguity due to poor initialization, which a blind EM estimation is inherently unable to distinguish. We propose an effective initialization refinement algorithm that utilizes the decoder output as a metric for model selection. Finite candidate models are generated based on the physical properties of the channel and modulation format, incorporating a joint detection of phase and shift ambiguities. Our results show that the proposed algorithm significantly reduces the number of local maximum cases to nearly onethird for a 3-tap ISI channel under highly uncertain initial conditions. The improvement becomes more pronounced as initial errors increase and the channel memory grows. When used in a turbo equalizer, the proposed algorithm is required only in the first turbo iteration, which limits any complexity increase with subsequent iterations.

Impulsive noise (IN) commonly generated by power devices can severely degrade the performance of highsensitivity wireless receivers. Accurate channel state information (CSI) knowledge is essential for designing optimal maximum a posteriori detectors. This paper examines blind channel estimation methods based on the expectation-maximization (EM) algorithm tailored for scenarios impacted by bursty IN, which can be described by the Markov-Middleton model. We propose a constrained EM algorithm that exploits the trellis structure of the IN model and the transmitted binary phase-shift keying (BPSK) symbols. By enforcing shared variance among specific trellis states and symmetry in the transition matrix, the proposed constrained EM algorithm adapted for the bursty IN channel has an almost two times faster convergence rate and better estimation performance than the standard EM approach. We comprehensively evaluate the robustness of both standard and constrained EM estimators under different types of CSI uncertainties. The results indicate that the final estimations of both EM estimators are robust enough to mismatch MarkovMiddleton model parameters. However, as the level of CSI uncertainty increases, the convergence rate decreases.

Recently, a data-driven Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm tailored to channels with intersymbol interference has been introduced. This so-called BCJRNet algorithm utilizes neural networks to calculate channel likelihoods. BCJRNet has demonstrated resilience against inaccurate channel tap estimations when applied to a time-invariant channel with ideal exponential decay profiles. However, its generalization capabilities for practically-relevant time-varying channels, where the receiver can only access incorrect channel parameters, remain largely unexplored. The primary contribution of this paper is to expand upon the results from existing literature to encompass a variety of imperfect channel knowledge cases that appear in real-world transmissions. Our findings demonstrate that BCJRNet significantly outperforms the conventional BCJR algorithm for stationary transmission scenarios when learning from noisy channel data and with imperfect channel decay profiles. However, this advantage is shown to diminish when the operating channel is also rapidly time-varying. Our results also show the importance of memory assumptions for conventional BCJR and BCJRNet. An underestimation of the memory largely degrades the performance of both BCJR and BCJRNet, especially in a slow-decaying channel. To mimic a situation closer to a practical scenario, we also combined channel tap uncertainty with imperfect channel memory knowledge. Somewhat surprisingly, our results revealed improved performance when employing the conventional BCJR with an underestimated memory assumption. BCJRNet, on the other hand, showed a consistent performance improvement as the level of accurate memory knowledge increased.

In this paper, we concentrate on the per-class accuracy of neural network-based classification in the context of identifying acoustic environments. Even a fully supervised learning framework with an equal amount of data for each class can lead to significant differences in class accuracies. This is then amplified by semi-supervised learning using naturally imbalanced data. To address this problem, we propose an adaptive method for pseudo-label selection via a straightforward optimization of the validation accuracy per class, aimed specifically at reducing the variance between different classes. The proposed method is general and can be applied for both maximum probability and entropy-based confidence criteria. Compared to fully supervised learning as well as state-of-the-art methods for pseudo-labeling, it achieves the lowest variances of per-class accuracy and the highest accuracies of the minority classes when tested on common publicly available environment sound databases.

Probabilistic amplitude shaping (PAS) combines an outer shaping layer with an inner, systematic forward error correction (FEC) layer to close the shaping gap. Proposed for PAS, constant composition distribution matching (CCDM) produces amplitude sequences with a fixed empirical distribution. We show that CCDM suffers from high rate losses for small block lengths, and we propose to use Enumerative Sphere Shaping (ESS) instead. ESS minimizes the rate loss at any block length. Furthermore, we discuss the computational complexity of ESS and demonstrate that it is significantly smaller than shell mapping (SM), which is another method to perform sphere shaping. We then study the choice of design parameters for PAS. Following Wachsmann et al., we show that for a given constellation and target rate, there is an optimum balance between the FEC code rate and the entropy of the Maxwell-Boltzmann distribution that minimizes the gap-to-capacity. Moreover, we demonstrate how to utilize the non-systematic convolutional code from IEEE 802.11 in PAS. Simulations over the additive white Gaussian noise (AWGN) and frequency-selective channels exhibit that ESS is up to 1.6 and 0.7 dB more energy-efficient than uniform signaling at block lengths as small as 96 symbols, respectively, with convolutional and low-density parity-check (LDPC) codes.

The dependency between the Gaussianity of the input distribution for the additive white Gaussian noise (AWGN) channel and the gap-to-capacity is discussed. We show that a set of particular approximations to the Maxwell- Boltzmann (MB) distribution virtually closes most of the shaping gap. We relate these symbol-level distributions to bit-level distributions, and demonstrate that they correspond to keeping some of the amplitude bit-levels uniform and independent of the others. Then we propose partial enumerative sphere shaping (P-ESS) to realize such distributions in the probabilistic amplitude shaping (PAS) framework. Simulations over the AWGN channel exhibit that shaping 2 amplitude bits of 16-ASK have almost the same performance as shaping 3 bits, which is 1.3 dB more power- efficient than uniform signaling at a rate of 3 bit/symbol. In this way, required storage and computational complexity of shaping are reduced by factors of 6 and 3, respectively.

Enumerative sphere shaping of N-dimensional constellations is discussed. It is proven that a finite-precision number representation is suitable for use in two enumerative indexing algorithms: Enumerative sphere shaping and Divide & Conquer (D&C) shaping. This representation decreases the storage complexities of these methods significantly. D&C is the basis of the well-known shell mapping algorithm and thus our approximations also apply there.

A constellation shaping scheme is proposed. The motivation is to decrease the required transmit power for a specified spectral efficiency. Instead of imposing a non-uniform distribution on the constellation or using nonuniformly spaced symbols, a sphere constraint is employed on the n-dimensional signal space. An efficient algorithm called enumerative amplitude shaping is given to find and index all signal points in the sphere. A comparison with a prominent probabilistic shaping algorithm is provided. The enumerative approach achieves the target rate more efficiently for small block lengths. To introduce error correction, the convolutional encoder used in IEEE Std 802.11 is combined with the shaper in a novel way. Instead of utilizing a larger constellation in combination with shaping, a higher code rate is used by puncturing. Gains up to 1.61 dB are observed for the rates 3 to 6 bits/2-D with 64- and 256-QAM schemes in AWGN channels. The contribution of puncturing in these gains is discussed.

Code-division multiple access (CDMA) is a multiplexing technique where a number of users simultaneously access a transmission channel by modulating and spreading their signals with preassigned codewords. This paper studies the performance of CDMA signals with orthogonal (Walsh-Hadamard) codewords and synchronization errors smaller than the chip time. Two high-order modulation techniques, M-level quadrature amplitude modulation (M-QAM) and M-level phase-shift keying (M-PSK) are compared with respect to bit-error rate (BER). The results are especially important for the return channel of cable TV networks and summarized as follows: 1) Synchronization errors between transmitters lead to interference noise, whereas synchronization errors between the transmitter and the receiver lead to a decreased amplitude of the received user signal. Both effects have significant impact on the system performance. 2) Closed expressions are obtained for the BER of a CDMA signal with M-PSK and M-QAM with a given maximum synchronization error. 3) The higher the modulation order, the more sensitive the system gets for synchronization errors. 4) The BER is highly dependent on the assigned codewords out of the Walsh-Hadamard code set. 5) The BER performance of M-QAM outperforms that of M-PSK.