Signal-to-noise Ratio Mismatch Research Articles

Pilot Design of the 1-Bit Massive MIMO in Rayleigh-Fading Channel

In the wireless communication system, the pilot is essential for channel estimation. This paper study the pilot design of the 1-bit massive multi-input multi-output system with the flat Rayleigh fading channel. This paper aims to design the pilot matrix minimizing the estimation error of the Bussgang linear minimum mean squared error (BLMMSE) channel estimator, of which the estimation error is given by a closed-form formula. An approximate BLMMSE channel estimation error is derived in the low signal-to-noise ratio (SNR) region. The lower bound of the approximate channel estimation error for all possible pilot matrices is derived. The analysis shows that the pilot matrix with pairwise orthogonal and equal-norm row vectors and equal-norm column vectors is optimal in terms of approximate channel estimation error. The hypersphere-based steepest descent (HSD) algorithm is proposed to design the pilot matrix by optimizing the performance of the BLMMSE estimator. The numerical results show that the proposed HSD algorithm has a noticeable improvement in channel estimation compared with the DFT pilot and the random pilot. The HSD algorithm is also valid for the near maximum likelihood estimator and SNR mismatch.

Signal‐to‐noise ratio mismatch in polar codes

Theoretically, the accurate signal-to-noise ratio (SNR) is necessary when using a successive cancelation (SC) or belief propagation (BP) decoder for polar codes. However, the effect of an SNR mismatch on the bit error rate performance of polar codes has not been addressed yet. The sensitivity of polar decoding with SC and BP decoders to the mismatch of SNR is studied. Theoretical and simulation results show that an estimation of SNR is not necessary for polar codes from a practical point of view.

Online log‐likelihood ratio scaling for robust turbo decoding

Optimal iterative log-MAP decoding of turbo codes requires accurate knowledge of the operating signal-to-noise ratio (SNR). However, the SNR information, available at practical decoders for bit-interleaved coded modulation systems, such as the third generation partnership project high-speed packet access and long-term evolution wireless cellular systems, may be inaccurate. In this study, two decoder architectures for improved turbo decoding in the presence of SNR mismatch are proposed. The SNR-mismatch aware turbo decoder selects the decoder which is estimated to have the best performance at the current mismatch, according to the test criterion. The SNR-mismatch compensated turbo decoder provides a more accurate estimation of the noise variance and concurrently scales the channel and the decoder log-likelihood ratios (LLRs) to continue decoding. Two different methods are proposed to find the optimal scaling factors online, one on the symbol level and the other on the bit level. This study shows that online LLR scaling, without prior knowledge about the noise mismatch statistics, can result in near-optimal turbo decoding regardless of the initial SNR mismatch.

Compensation of SNR and noise type mismatch using an environmental sniffing based speech recognition solution

Multiple-model based speech recognition (MMSR) has been shown to be quite successful in noisy speech recognition. Since it employs multiple hidden Markov model (HMM) sets that correspond to various noise types and signal-to-noise ratio (SNR) values, the selected acoustic model can be closely matched with the test noisy speech, which leads to improved performance when compared with other state-of-the-art speech recognition systems that employ a single HMM set. However, as the number of HMM sets is usually limited due to practical considerations as well as effective model selection, acoustic mismatch can still be a problem in MMSR. In this study, we proposed methods to improve recognition performance by mitigating the mismatch in SNR and noise type for an MMSR solution. For the SNR mismatch, an optimal SNR mapping between the test noisy speech and the HMM was determined by experimental investigation. Improved performance was demonstrated by employing the SNR mapping instead of using the estimated SNR of the test noisy speech directly. We also proposed a novel method to reduce the effect of noise type mismatch by compensating the test noisy speech in the log-spectrum domain. We first derive the relation between the log-spectrum vectors in the test and training noisy speech. Since the relation is a non-linear function of the speech and noise parameters, the statistical information regarding the testing log-spectrum vectors was obtained by approximation using vector Taylor series (VTS) algorithm. Finally, the minimum mean square error estimation of the training log-spectrum vectors was used to reduce the mismatch between the training and test noisy speech. By employing the proposed methods in the MMSR framework, relative word error rate reduction of 18.7% and 21.3% was achieved on the Aurora 2 task when compared to a conventional MMSR and multi-condition training (MTR) method, respectively.

Secure joint source–channel coding with interference known at the transmitter

In this study, the problem of transmitting an independent and identically distributed (i.i.d.) Gaussian source over an i.i.d. Gaussian wire-tap channel, with an i.i.d. Gaussian known interference available at the transmitter is considered. The intended receiver is assumed to have a certain minimum signal-to-noise ratio (SNR) and the eavesdropper is assumed to have a strictly lower SNR compared to the intended receiver. The objective is to minimise the distortion of source reconstruction at the intended receiver. In this study, an achievable distortion is derived when Shannon's source'channel separation coding scheme is used. Three hybrid digital'analogue secure joint source'channel coding schemes are then proposed, which achieve the same distortion. The first coding scheme is based on Costa's dirty-paper-coding scheme and wire-tap channel coding scheme, when the analogue source is not explicitly quantised. The second coding scheme is based on the superposition of the secure digital signal and the hybrid digital'analogue signal. It is shown that for the problem of communicating a Gaussian source over a Gaussian wire-tap channel with side information, there exists an infinite family of secure joint source'channel coding schemes. In the third coding scheme, the quantised signal and the analogue error signal are explicitly superimposed. It is shown that this scheme provides an infinite family of secure joint source'channel coding schemes with a variable number of binning. Finally, the proposed secure hybrid digital'analogue schemes are analysed under the main channel SNR mismatch. It is proven that the proposed schemes can give a graceful degradation of distortion with SNR under SNR mismatch, that is, when the actual SNR is larger than the designed SNR.

Joint Source-Channel Coding with Correlated Interference

We study the joint source-channel coding problem of transmitting a discrete-time analog source over an additive white Gaussian noise (AWGN) channel with interference known at transmitter. We consider the case when the source and the interference are correlated. We first derive an outer bound on the achievable distortion and then, we propose two joint source-channel coding schemes. The first scheme is the superposition of the uncoded signal and a digital part which is the concatenation of a Wyner-Ziv encoder and a dirty paper encoder. In the second scheme, the digital part is replaced by the hybrid digital and analog scheme proposed by Wilson et al. When the channel signal-to-noise ratio (SNR) is perfectly known at the transmitter, both proposed schemes are shown to provide identical performance which is substantially better than that of existing schemes. In the presence of an SNR mismatch, both proposed schemes are shown to be capable of graceful enhancement and graceful degradation. Interestingly, unlike the case when the source and interference are independent, neither of the two schemes outperforms the other universally. As an application of the proposed schemes, we provide both inner and outer bounds on the distortion region for the generalized cognitive radio channel.

Design of irregular LDPC codes for BIAWGN channels with SNR mismatch

Belief propagation (BP) algorithm for decoding low-density parity-check (LDPC) codes over a binary input additive white Gaussian noise (BIAWGN) channel requires the knowledge of the signal-to-noise ratio (SNR) at the receiver to achieve its ultimate performance. An erroneous estimation or the absence of a perfect knowledge of the at the decoder is referred to as SNR mismatch can significantly degrade the performance of LDPC codes decoded by the BP algorithm. In this paper, using extrinsic information transfer (EXIT) charts, we design irregular LDPC codes that perform better (have a lower threshold) in the presence of mismatch compared to the conventionally designed irregular LDPC codes that are optimized for zero mismatch. Considering that min-sum (MS) algorithm is the limit of BP with infinite over-estimation, the EXIT functions generated in this work can also be used for the efficient analysis and design of LDPC codes under the MS algorithm.

Performance of Belief Propagation for Decoding LDPC Codes in the Presence of Channel Estimation Error

In this paper, we investigate the performance of the belief propagation (BP) algorithm for decoding low-density parity-check codes over the additive white Gaussian noise channel when there is an incorrect estimate of the channel signal-to-noise ratio (SNR) (referred to as mismatch) at the decoder. At the extremes for over- and underestimation of SNR, the performance of BP tends to that of min-sum algorithm and the channel bit-error rate, respectively. Our results for regular codes indicate that the sensitivity to mismatch increases by increasing the variable-node degree and by decreasing the check-node degree. The effect of variable-node degree, however, appears to be more profound, such that at a given rate, the codes with the smallest variable and check degrees are more robust against SNR mismatch. For irregular codes, by comparing the thresholds of a few ensembles, we demonstrate that the ensemble which performs better in the absence of mismatch can perform worse in the presence of it. To obtain our asymptotic results, we propose a computationally efficient method based on the Gaussian approximation of density evolution in the presence of SNR mismatch. We also show that the asymptotic results are consistent with simulation results for codes with finite block lengths

A Note on “Signal-to-Noise Ratio Mismatch for Low-Density Parity-Check Coded Magnetic Recording Channels” by W. Tan and J. R. Cruz

In this letter, we prove that the minimum signal-to-noise ratio (SNR) threshold of the iterative belief propagation algorithm for a low-density parity-check (LDPC) coded magnetic recording channel is obtained when the SNR mismatch factor is half the ratio of variance to mean for the Gaussian distribution at the channel output. This result was first observed by Tan and Cruz empirically

Signal-to-Noise Ratio Mismatch for Low-Density Parity-Check Coded Magnetic Recording Channels

Signal-to-noise ratio (SNR) mismatch is found in simulations to have great influence on the performance of low-density parity-check coded magnetic recording channels. While an inappropriate SNR mismatch degrades the performance dramatically, a properly selected optimum SNR mismatch can improve it significantly. In this paper we analyze the causes of this phenomenon and find optimum SNR mismatch values for specific magnetic recording systems with physical impairments such as electronic and media noise as well as erasures, using both density evolution analysis and Monte Carlo simulations. We observed that two characteristics of the probability density function (pdf) of the channel message, namely, the Gaussianity and the variance-to-mean ratio (VMR) have a major effect on the SNR mismatch. Generally speaking, if the channel message is approximately Gaussian-distributed and the VMR is larger than two, a negative SNR mismatch substantially improves the system performance. Numerical results show that for a magnetic recording channel with additive white Gaussian noise (AWGN), the optimum SNR mismatch is about -3 to -2 dB, while for a channel with 10% AWGN and 90% media noise, is about -10 to -8 dB, whether erasures are present or not.

SNR mismatch in bit-interleaved turbo-coded modulation

Bit-interleaved turbo-coded modulation is more sensitive to signal-to-noise ratio (SNR) overestimation than turbo code with BPSK. An explanation is given from the effect of SNR mismatch on bit-metric generation, which consequently affects the log-MAP turbo-decoding algorithm.