In this paper, we introduce a new robust 1-bit compressive sensing reconstruction algorithm in the noisy environment, where a lot of signs are flipped. By calculating the number of inconsistencies, this algorithm can adaptively detect the positions where sign flips occur. Subsequently, the sparse signals can be recovered by using "corrected" measurements without a priori knowledge of the noise level. Numerical experiments show the high performance of signal recovery for the proposed algorithm in the presence of both measurement noise and transmission noise.

It is recognized that, for digital symbols taken from a discrete and finite alphabet, perfect transmultiplexing at a signaling rate larger than the Nyquist rate can be achieved by modulation with overcomplete frame pulses. By invoking the spectral distribution theory of large random matrix, the spectral efficiency of digital transmission scheme via overcomplete frames in band-limited additive white Gaussian noise (AWGN) channel with discrete, finite, and uniform alphabets is investigated in this paper. It is shown that the proposed digital signaling scheme can asymptotically achieve the maximum spectral efficiency dictated by the Shannon capacity theorem for reliable transmission without employing signal shaping techniques. The extension to the case of non-white Gaussian noise/spectrally shaped channels is also considered. It is shown that the employment of Weyl-Heisenberg frames facilitates the optimal “water-filling” power allocation and rate adaptation by adjusting the signal amplitudes and energy-dispersion factors. Some numerical results are provided to support the theoretical finding.

The issue of multicarrier transmission with high spectral efficiency and low interference over time-frequency (TF) dispersive channels is addressed in this paper. Specifically, we propose a digital signal transmission scheme employing overcomplete Weyl-Heisenberg (W-H) frames as modulation pulses. The proposed W-H frame transmission scheme, which relaxes the conventional orthogonality/biorthogonality constraints for perfect transmultiplexing, can be viewed as a generalization of the orthogonal frequency division multiplexing (OFDM) and nonorthogonal (biorthogonal) frequency division multiplexing (NOFDM). With this new transmission scheme, one can not only achieve higher spectral efficiency effectively but also design the pulse shape more flexibly to combat the impact of the propagation channel. In order to optimally mitigate the intersymbol interference (ISI) and interchannel interference (ICI) caused by the wireless channel, the selections of the Gaussian pulse shape and T-F grid parameters are addressed jointly from the viewpoint of minimum energy perturbation for several typical channel scattering functions. Simulation results are presented to study the performance of the proposed system. It is shown that the proposed overcomplete W-H frame transmission system with a lower-order constellation is more robust against the TF dispersive channels than the incomplete Riesz basis system employing a higher-order constellation with the same spectral efficiency.

This paper presents a distributed estimation scheme (DES) along with the bit allocation algorithm, which minimizes the total required bandwidth while ensuing a given average estimation mean-squared error (MSE). The DES comprises of a probabilistic Lloyd-Max quantization rule, and a best linear unbiased estimation (BLUE). Since the optimum bit allocation problem does not have a closed form, we present a suboptimal solution utilizing the alternating minimization (AM) algorithm. Finally, simulation results are provided to show the effectiveness of the proposed DES along with the bit allocation algorithm.