A promising approach to avoid the bottleneck of the analog-to-digital converter’s (ADCs) high power consumption at high sampling frequencies is to use only 1-bit quantization resolution. By using temporal oversampling at the receiver, a high resolution in the time-domain can be achieved, which can partly recover the losses in terms of rate caused by a reduced amplitude resolution. However, channel estimation and synchronization has to be performed on 1-bit quantized receive samples, which poses a new challenge.This work is concerned with the phase estimation of a 1-bit quantized system with phase noise in the low signal-to-noise ratio (SNR) range. A block-based least squares (LS) estimator, whose output is interpolated by a Kalman filter is presented to track the phase noise. To enhance the performance, especially for the case of a large spacing between pilot blocks, we study the Rauch-Tung-Striebel (RTS) algorithm. Both algorithms are adjusted to the system characteristics and bounds for the steady state performance are derived. These bounds, as well as numerical results show that the RTS algorithm achieves a lower error variance than the Kalman filter at the price of increased latency, as it is non-causal.

Digital receivers based on 1-bit quantization and oversampling w.r.t. the transmit signal bandwidth promise lower energy consumption. However, since 1-bit quantization is a highly non-linear operation, standard off the shelf receiver algorithms cannot be applied. In this paper we consider an unknown phase rotation and timing offset and a fully digital receiver. To reduce the non-linear behavior introduced by 1-bit quantization, we assume that the receiver applies uniform phase and sample dithering, which can be implemented by sampling at an irrational normalized intermediate frequency and with an irrational oversampling factor, respectively. Based on the least squares objective function we derive a typical digital matched filter receiver with a data- and timing-aided phase estimator and square time recovery based timing estimation. Our main contribution is to show that both estimators are consistent under very general assumptions, e.g., arbitrary colored noise and stationary ergodic transmit symbols. Performance evaluations are done via simulations and are compared against a numerically computable upper bound of the Cramér–Rao lower bound. For low signal-to-noise ratio the estimators perform well but for high signal-to-noise ratio they run into an error floor. The performance loss of the phase estimator due to decision-directed operation or estimated timing information is marginal.

Wireless communications systems beyond 5G are expected to utilize large available bandwidths at frequencies above 100 GHz in order to achieve data rates above 100 Gbit/s. However, the power consumption of the analog-to-digital converters (ADCs) for such systems is becoming a major challenge. Trading a reduced amplitude resolution for an increased temporal resolution by employing temporal oversampling w.r.t. the Nyquist rate is a possible solution to this problem. In this work, we consider a wireless communications system employing zero-crossing modulation (ZXM) and 1-bit quantization in combination with temporal oversampling at the receiver, where ZXM is implemented by combining runlength-limited (RLL) transmit sequences with faster-than-Nyquist (FTN) signaling. We compare the performance and complexity of four different soft-output equalization algorithms, namely, two approximations of the linear minimum mean squared error (LMMSE) equalizer, a BCJR equalizer and a deep-learning based equalizer, for such systems. We consider the mutual information (MI) between the input bits of the RLL encoder and the output log-likelihood ratios (LLRs) of the RLL decoder as a performance measure and evaluate it numerically. Our results demonstrate that one of the proposed LMMSE equalizers outperforms the competing algorithms in the low and mid signal-to-noise ratio (SNR) range, despite having the lowest implementational complexity.

As communication systems require ever higher bandwidths, designing digital receivers based on 1-bit quantization and oversampling w.r.t. the transmit signal bandwidth can reduce circuit complexity and lower the energy consumption. This is due to the fact that high resolution in time domain is less difficult to achieve than high resolution in amplitude domain. However, as 1-bit quantization is a highly non-linear operation, standard channel parameter estimation algorithms for digital receivers cannot be applied. In this paper we consider an unknown phase rotation and an unknown timing offset at the receiver. Furthermore, we assume that the receiver applies uniform phase and sample dithering, which can be implemented by sampling at an irrational normalized intermediate frequency and with an irrational oversampling factor, respectively. Starting from the least squares objective function, we derive a phase independent, non-data aided (NDA) timing estimator. Considering sample dithering, we prove that the estimator is consistent, even if the noise is colored due to oversampling w.r.t. the signal bandwidth. Moreover, we numerically evaluate the variance of the estimator and compare it to the Cramér-Rao lower bound. We find that the qualitative behavior is similar to the Oerder&Meyr estimator that is often used in the unquantized case and that oversampling can significantly improve the performance.

Wireless communications systems beyond 5G are foreseen to utilize the large available bandwidths above 100 GHz. However, the power consumption of analog-to-digital converters (ADCs) for such systems is expected to be prohibitively high, because it grows quadratically with the sampling rate for high amplitude resolutions. Shifting the resolution from the amplitude to the time domain, i.e., by reducing the amplitude resolution and by employing temporal oversampling w.r.t. the Nyquist rate, is expected to be more energy efficient. To this end, we propose a novel low-cost sub-terahertz system employing zero crossing modulation (ZXM) transmit signals in combination with 1-bit quantization and temporal oversampling at the receiver. We derive and evaluate new finite-state machines for efficient de-/modulation of ZXM transmit signals, i.e., for efficient bit sequence to symbol sequence de-/mapping. Furthermore, the coded performance of the system is evaluated for a wideband line-of-sight channel.

Digital receivers based on 1-bit quantization and oversampling w.r.t. the transmit signal bandwidth promise lower energy consumption. However, since 1-bit quantization is a highly non-linear operation, standard receiver algorithms cannot be applied. Thus, we derive performance bounds for phase, timing, and frequency estimation in order to gain a deeper insight into the impact of 1-bit quantization and oversampling. We identify uniform phase and sample dithering as crucial to combat the effect of the non-linearity introduced by 1-bit quantization. Since oversampling results in noise correlation, a closed form of the likelihood function is not available. Thus, we study a system model with white noise by adapting the receive filter bandwidth to the sampling rate. Considering the aforementioned dithering, we obtain very tight closed form lower bounds on the Cramér-Rao lower bound (CRLB) in the large sample regime. We show that with uniform phase and sample dithering, all large sample properties of the CRLB of the unquantized receiver are preserved under 1-bit quantization, except for an signal-to-noise ratio (SNR) dependent performance loss that can be decreased by oversampling. Numerical computations show that the properties of the CRLB for white noise still hold for colored noise except that the performance loss due to 1-bit quantization is reduced.

Designing digital receivers based on 1-bit quantization and oversampling w.r.t. the transmit signal bandwidth enables lower power consumption and a reduced circuit complexity compared to conventional amplitude quantization, since high resolution in time domain is less difficult to achieve than high resolution in amplitude domain. However, standard receiver synchronization algorithms cannot be applied, since 1-bit quantization is a highly non-linear function. This paper is a first step to understand the influence of 1-bit quantization on the estimation of the channel parameters (e.g., timing, phase, and frequency offset). We will derive the Fisher Information (FI) matrix of phase and frequency, considering a known timing error and white Gaussian noise. Moreover, we propose to apply a uniformly distributed phase dither at the receiver, prior to 1-bit quantization, in order to reduce the nonlinear effect. The same effect can be achieved in practice by sampling at a low intermediate frequency. We obtain analytical results for the FI matrix with uniform phase dithering at the receiver and derive tight closed form upper bounds for the low and high SNR case.

In this paper we optimize spatially coupled protographs for window decoding (WD) and arbitrary rate. Previous studies found that the belief propagation (BP) threshold of spatially coupled code ensembles achieves the maximum a posteriori (MAP) threshold of their underlying block code ensemble. This property requires a large coupling length L and thus the window decoder is considered to reduce latency and complexity of the decoding. To approach the BP threshold fast in the size of the window W, it is well known that the code requires a special structure to avoid degree-1 variable nodes inside the window. We further require additional structure to construct a systematic code with low encoding complexity, which unfortunately forces degree-1 variable nodes inside the window. Thus, we formulate an optimization problem to maximize the WD threshold and solve it by applying a differential evolution (DE) based algorithm. Compared to the regular protographs obtained by edge spreading, our optimized irregular protographs show a significant improvement in terms of WD threshold and finite length performance for small window sizes, hence leads to small decoding latency and complexity. Furthermore, for high rates our codes can compete with the highly optimized LDPC block codes from the WiMAX standard.

Spatially-coupled low-density parity-check (SC-LDPC) codes have been shown to be superior in performance than LDPC block codes. In order to comply with the practical constraints on latency, SC-LDPC codes are decoded using a window decoder that reduces the decoder latency and complexity compared to traditional block-wise decoding. However, so far the literature only considers the structural decoding latency of window decoder, ignoring the processing latency. Note that the processing latency directly impacts the decoder's throughput and is an important parameter in any modern communication system. The throughput of an iterative decoder is directly influenced by the number of iterations and hence in this paper we propose a fully parallel window decoder architecture for SC-LDPC codes where the decoding iterations are performed in parallel. This guarantees a high throughout while fulfilling the low latency requirements. The overall decoding latency (structural and processing latency) of the proposed window decoder architecture is compared with the classical window decoder.