Low Signal-to-noise Ratio Values Research Articles

Iterative Detection of Unity-Rate Precoded FFH-MFSK and Irregular Variable-Length Coding

Iterative decoding of an irregular variable-length coding (IrVLC) scheme concatenated with precoded fast frequency-hopping (FFH) M-ary frequency-shift keying (MFSK) is considered. We employ extrinsic information transfer (EXIT) charts to investigate the three-stage concatenation of the FFH-MFSK demodulator, the rate-1 decoder, and the outer IrVLC decoder. The proposed joint source and channel coding scheme is capable of operating at low signal-to-noise ratios (SNRs) in Rayleigh fading channels contaminated by partial-band noise jamming (PBNJ). The IrVLC scheme is composed of a number of component variable-length coding (VLC) codebooks employing different coding rates that encode particular fractions of the input source symbol stream. These fractions may be chosen with the aid of EXIT charts to shape the inverted EXIT curve of the IrVLC codec so that it can be matched with the EXIT curve of the inner decoder. We demonstrate that using the proposed scheme, an infinitesimally low bit error ratio (BER) may be achieved at low SNR values.

Error vector magnitude to SNR conversion for nondata-aided receivers

Error vector magnitude (EVM) is one of the widely accepted figure of merits used to evaluate the quality of communication systems. In the literature, EVM has been related to signal-to-noise ratio (SNR) for data-aided receivers, where preamble sequences or pilots are used to measure the EVM, or under the assumption of high SNR values. In this paper, this relation is examined for nondata-aided receivers and is shown to perform poorly, especially for low SNR values or high modulation orders. The EVM for nondata-aided receivers is then evaluated and its value is related to the SNR for quadrature amplitude modulation (QAM) and pulse amplitude modulation (PAM) signals over additive white Gaussian noise (AWGN) channels and Rayleigh fading channels, and for systems with IQ imbalances. The results show that derived equations can be used to reliably estimate SNR values using EVM measurements that are made based on detected data symbols. Thus, presented work can be quite useful for measurement devices such as vector signal analyzers (VSA), where EVM measurements are readily available.

Comparison of SNR and CNR for in vivo mouse brain imaging at 3 and using well matched scanner configurations

Signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) for magnetic resonance microimaging were measured using two nearly identical magnetic resonance imaging (MRI) scanners operating at field strengths of 3 and 7 T. Six mice were scanned using two imaging protocols commonly applied for in vivo imaging of small animal brain: RARE and FLASH. An accounting was made of the field dependence of relaxation times as well as a small number of hardware disparities between scanner systems. Standard methods for relaxometry were utilized to measure T1 and T2 for two white matter (WM) and two gray matter (GM) regions in the mouse brain. An average increase in T1 between 3 and 7 T of 28% was observed in the brain. T2 was found to decrease by 27% at 7 T in agreement with theoretical models. The SNR was found to be uniform throughout the mouse brain, increasing at higher field by a factor statistically indistinguishable from the ratio of Larmor frequencies when imaging with either method. The CNR between GM and WM structures was found to adhere to the expected field dependence for the RARE imaging sequence. Improvement in the CNR for the FLASH imaging sequence between 3 and 7 T was observed to be greater than the Larmor ratio, reflecting a greater susceptibility to partial volume effects at the lower SNR values at 3 T. Imaging at 7 T versus 3 T in small animals clearly provides advantages with respect to the CNR, even beyond the Larmor ratio, especially in lower SNR regimes. This careful multifaceted assessment of the benefits of higher static field is instructive for those newly embarking on small animal imaging. Currently the number of 7 T MRI scanners in use for research in human subjects is increasing at a rapid pace with approximately 30 systems deployed worldwide in 2008. The data presented in this article verify that if system performance and radio frequency uniformity is optimized at 7 T, it should be possible to realize the expected improvements in the CNR and SNR compared with MRI at 3 T.

Study of bifurcation behavior of two-dimensional turbo product code decoders

Turbo codes, low-density parity-check (LDPC) codes and turbo product codes (TPCs) are high performance error-correction codes which employ iterative algorithms for decoding. Under different conditions, the behaviors of the decoders are different. While the nonlinear dynamical behaviors of turbo code decoders and LDPC decoders have been reported in the literature, the dynamical behavior of TPC decoders is relatively unexplored. In this paper, we investigate the behavior of the iterative algorithm of a two-dimensional TPC decoder when the input signal-to-noise ratio (SNR) varies. The quantity to be measured is the mean square value of the posterior probabilities of the information bits. Unlike turbo decoders or LDPC decoders, TPC decoders do not produce a clear “waterfall region”. This is mainly because the TPC decoding algorithm does not converge to “indecisive” fixed points even at very low SNR values.

Maximum-mean-square soft-output (M2S2O): a method for carrier synchronisation of short burst turbo coded signals

The use of short bursts transmissions in modern communication systems is increasing as the use of packet data communication replaces traditional, continuous bit stream data communication. Turbo codes, which revolutionised communication coding, enable the operation of receivers in low signal-to-noise ratio (SNR) conditions, thus increasing the range of operation of the communication system. However, carrier frequency and phase synchronisation, needed for optimal coherent performance of the receiver, still remains an open problem at low SNR conditions for short bursts. A new efficient carrier synchronisation method for turbo coded short packet communication operating at low SNR values is presented. This method is based on maximising a newly invented objective function, the MSSO(Δf, φ) function, which uses the turbo decoder's soft decision outputs to iteratively improve the carrier synchronisation. This method is suitable for non-data-aided acquisition and tracking of the carrier frequency and phase offsets. It is shown, via simulations, that this algorithm achieves the lower bound on bit-error-rate performance of the turbo decoder at very low SNR values.

On the Design of MIMO Block-Fading Channels With Feedback-Link Capacity Constraint

In this paper, we propose a combined adaptive power control and beamforming framework for optimizing multiple-input/multiple-output (MIMO) link capacity in the presence of feedback-link capacity constraint. The feedback channel is used to carry channel state information only. It is assumed to be noiseless and causal with a feedback capacity constraint in terms of maximum number of feedback bits per fading block. We show that the hybrid design could achieve the optimal MIMO link capacity, and we derive a computationally efficient algorithm to search for the optimal design under a specific average power constraint. Finally, we shall illustrate that a minimum mean-square error spatial processor with a successive interference canceller at the receiver could be used to realize the optimal capacity. We found that feedback effectively enhances the forward channel capacity for all signal-to-noise ratio (SNR) values when the number of transmit antennas (n/sub T/) is larger than the number of receive antennas (n/sub R/). The SNR gain with feedback is contributed by focusing transmission power on active eigenchannel and temporal power waterfilling . The former factor contributed, at most, 10log/sub 10/(n/sub T//n/sub R/) dB SNR gain when n/sub T/>n/sub R/, while the latter factor's SNR gain is significant only for low SNR values.

The turbo decoding algorithm and its phase trajectories

This paper analyzes phase trajectories and fixed points of the turbo decoding algorithm as a function of the signal-to-noise ratio (SNR). By exploiting the large length of turbo codes, the turbo decoding algorithm is treated as a single-parameter dynamical system, parameterized (approximately) by the SNR. This parameterization, along "with" extensive simulations at practical SNRs and asymptotic analysis as SNR goes to zero and infinity, is used to subdivide the entire SNR range into three regions with the "waterfall region" in the middle. The turbo decoding algorithm has distinctive phase trajectories and convergence properties in these three SNR regions. This paper also investigates existence and properties of fixed points in these SNR regions. The main fixed points of the turbo decoding algorithm are classified into two categories. In a wide range of SNRs (corresponding to bit-error rates less than 10/sup -1/), the decoding algorithm has "unequivocal" fixed points which correspond to mostly correct decisions on the information bits. Within this range, toward the lower values of SNR, there is another fixed point which corresponds to many erroneous decision on the information bits. Fixed points of this type are referred to as "indecisive" fixed points. It turns out that the indecisive fixed points bifurcate and disappear for SNRs in the waterfall region. This paper associates the qualitative transition of phase trajectories in the waterfall region to the bifurcation of indecisive fixed points. These bifurcations also explain empirically observed quasi-periodic and periodic phase trajectories of the turbo decoding algorithm.

Realizable lower bounds for time delay estimation. 2. Threshold phenomena

In time delay estimation of narrowband signals the mean square error (MSE) plotted as a function of the signal to noise ratio (SNR) exhibits threshold phenomena. The thresholds divide the domain of SNR values into several disjoint segments. For very low SNR values the observations are dominated by noise and are essentially useless for delay estimation. Here the MSE is determined largely by the available a priori information. For intermediate SNR values, time delay estimates are possible, but are subject to ambiguities resulting from the oscillatory nature of the signal sample correlation. For very high SNR values, these ambiguities are resolvable and the Cramer-Rao bound (CRB) yields a realistic bound for the attainable performance. A previous paper by Zeira and Schultheiss (see IEEE Trans. Signal Processing, vol.41, p.3102-3113, Nov. 1993) used the Barankin (1949) bound to obtain a realizable lower bound for the intermediate SNR region but left open the question where the transitions from low to medium and medium to high SNR operation occur. Since the attainable MSE in the three regions can be very different, the location of the SNR thresholds is of considerable practical interest. The present paper addresses this issue. It obtains threshold values for the single and two echo problems, with emphasis on the effect of echo separation in the two echo case. It concludes that the location of the thresholds is only weakly dependent on echo separation, even though the attainable MSE in both the intermediate and high SNR regions varies drastically as the echo separation changes. >

A procedure for the choice of prior estimates of pair correlation functions for maximum entropy inversion of neutron diffraction structure factors in disordered systems

A procedure to obtain estimates of the pair-correlation functions g( r) from structure factors measured in neutron diffraction experiments on disordered materials is presented. The g( r) functions reconstructed from the structure factors in high signal-to-noise ratio (SNR) measurements are of similar quality to those obtained from full Maximum Entropy (ME) calculations. In cases of moderate or low SNR values, the estimated g( r) can be used safely as a prior distribution for subsequent ME computations. Finally a way to obtain realistic estimates of the noise present in the measured data is discussed.