Simple Maximum Likelihood Research Articles

Full-rate full-diversity space–time block codes for any odd number of transmit antennas

The authors propose a new class of space-time block codes (STBCs) achieving full-rate and full spatial diversity for general quadrature amplitude modulation (QAM) when using any odd number of transmit antennas under quasi-static Rayleigh fading channels. These codes are the extended works of the conventional Alamouti-ST constellation-rotating (CR) codes which are designed by serially concatenating CR precoders with the Alamouti scheme for an even number of transmit antennas. From the computer simulation results, it is observed that the best code in this class outperforms the existing ST-CR code and also exhibits error performance within only about 1-dB of the maximal ratio combining receiver. The codes possessing quasi-orthogonal (QO) characteristic are also included in this class, allowing simple maximum likelihood (ML) decoding with almost the same error performance as the best code in this class and the conventional QO-STBCs with full diveristy. These codes have identical or much lowered ML decoding complexity compared with the conventional QO-STBCs.

Two-Dimensional Half-Rate Codes Using Two-Dimensional Finite-Field Filter Banks

This correspondence introduces two-dimensional (2-D) filter bank codes (TDFBCs). The synthesis bank of a two-channel two-dimensional filter bank over a finite field is used to design the 2-D code, and the corresponding analysis bank is used to generate the syndrome of the code. First, we study the encoder of half-rate TDFBCs and show that these linear codes are lattice-cyclic. It is proven that any 2-D lattice-cyclic code can also be generated by a 2-D filter bank. Second, we introduce a methodology to design TDFBCs over binary erasure channels. These codes have a simple and efficient maximum-likelihood (ML) decoding algorithm for burst erasures. We show that half-rate TDFBCs of dimensions N1 X N2/ can recover burst erasures of size up to N1 X N2 /2 and N1 /2 X N2 using the proposed decoding technique. Finally, we present examples of TDFBCs that satisfy the Reiger bound with equality, i.e., they are capable of correcting any burst of size N1 X N2 /2 .

Maximum Likelihood Estimation of Integer Frequency Offset in OFDM Systems

This letter presents a simple maximum likelihood (ML) estimation method with one training symbol for the integer frequency offset (IFO) in orthogonal frequency division multiplexing (OFDM) systems. We show that the proposed method performs better than the conventional one through Monte Carlo simulations.

Space-Time Trellis Codes Over Rapid Rayleigh Fading Channels With Channel Estimation---Part I: Receiver Design and Performance Analysis

The performance analysis of space-time trellis codes over rapid nonselective Rayleigh fading channels with imperfect channel state information is considered. A pilot-symbol-assisted-modulation scheme is used for channel estimation. The parameters used in this scheme, i.e., pilot spacing and Wiener filter length are chosen in a tradeoff between estimation accuracy, transmission rate/pilot overhead, and receiver complexity. A simple maximum likelihood receiver for M-ary phase shift keying modulation is derived. An exact closed-form pairwise error probability (PEP) expression and explicit PEP bounds are presented. It is shown that the performance loss caused by channel estimation errors increases mainly with the channel fade rate.

SMLD: Enhanced MIMO-Signal Detection for Wireless MIMO Communication Receivers

This letter proposes a simplified maximum likelihood detection (SMLD) scheme to improve the detection performance of multiple-input multiple-output receivers. The SMLD detects V streams according to the first detected V sub-streams. Through an ML test, the most probable stream is selected. Moreover, to detect the layer with the worst post-detection SNR accurately, reverse ordering is applied to the SMLD. Simulation results show that the performance of the Vertical Bell Laboratories layered space-time (V-BLAST) system can be improved by adopting the SMLD technique. In the case of reverse ordering, the SMLD can achieve a similar ML performance with significant reduction in computational complexity.

Adaptive modeling, adaptive data assimilation and adaptive sampling

For efficient progress, model properties and measurement needs can adapt to oceanic events and interactions as they occur. The combination of models and data via data assimilation can also be adaptive. These adaptive concepts are discussed and exemplified within the context of comprehensive real-time ocean observing and prediction systems. Novel adaptive modeling approaches based on simplified maximum likelihood principles are developed and applied to physical and physical–biogeochemical dynamics. In the regional examples shown, they allow the joint calibration of parameter values and model structures. Adaptable components of the Error Subspace Statistical Estimation (ESSE) system are reviewed and illustrated. Results indicate that error estimates, ensemble sizes, error subspace ranks, covariance tapering parameters and stochastic error models can be calibrated by such quantitative adaptation. New adaptive sampling approaches and schemes are outlined. Illustrations suggest that these adaptive schemes can be used in real time with the potential for most efficient sampling.

Copula as a Measure of Affiliation in First Price Auctions

Estimating distribution of bidders' ex-ante valuation is an important structural parameter in corporate auctions design and setting the optimal reserve price. This parameter is unobserved to researcher as the observed bids are strategic response and at best is a monotonic function of bidders ex ante valuation. This paper presents a simple, based, two step semiparametric estimator for structural estimation of distributions of bidders' unobserved in first price auctions. In the first step, the marginal distributions of valuations are non-parametrically estimated using the equilibrium distribution of bids. The second stage involves a simple maximum likelihood procedure to estimate the copula parameter which measures the association (affiliation) between the valuations. We apply our methodology to data from wildcat oil tract auctions. Wildcat auctions resembles a corporate auction where the target's value is highly uncertain and the market or industry provides a signal about the value of the target. The estimation and testing procedure rejects the hypothesis of independence of signals and opts for non-linear dependence structure in the tails of the distributions. This has important implications for auction choice and mechanism design. The methodology is well suited for corporate nance and market microstructure applications with general informational assumptions. The estimated optimal reserve price found to be much higher than the actual reserve price.

Performance Analysis of Two-Branch Space-Time Block-Coded DS-CDMA Systems in Time-Varying Multipath Rayleigh Fading Channels

For the two-branch space-time (ST) block-coded direct-sequence code-division multiple-access (DS-CDMA) systems, the impacts of a time-varying multipath channel on the downlink transmission are analyzed. By considering the systems using the random binary spreading code (RBSC) and deterministic binary spreading code (DBSC), the effects of the multipath interference and multiuser interference are included in the analyses of the bit-error rate and bit-error outage. Also, for the performance analysis of the system employing the decision-feedback (DF) detector, the effect of error propagation is taken into account. It is known that enlarging the spreading factor can enhance the interference-rejection ability of a DS-CDMA system and, hence, can improve the performance. However, it also lengthens the symbol duration and, thus, stiffens the diversity penalty resulting from the channel variation within an ST-code-word duration. Thus, a moderate spreading factor should be chosen. In this paper, for the RBSC system using the simple-maximum-likelihood (SML) detector, we derive an optimum spreading factor that is optimum in the minimum-error-probability sense. Numerical results have revealed that the derived optimum spreading factor is a good estimate of the ones for the DBSC systems using the SML, zero-forcing, and DF detectors. Therefore, it is very useful for system designers in determining the system parameters

Hyperspectral imagery for mapping intertidal vegetation at Roberts Bank tidal flats, British Columbia, Canada

This study assesses the effectiveness of hyperspectral airborne imagery to map the intertidal vegetation at Roberts Bank, a large salt marsh and tidal flat complex in the Fraser River delta, British Columbia, Canada. This ecosystem is an important habitat for migratory and resident birds and fish and is part of the largest single salmon-producing stream in the world, the Fraser River. Imagery acquired by the compact airborne spectrographic imager (CASI) was radiometrically and geometrically corrected and mosaicked. A simple maximum likelihood classifier was used to classify intertidal vegetation cover. Training and test sites were collected using field observations and oblique aerial photographs. Seven vegetation-substrate classes were accurately (92.3%) classified, ranging from muddy sediments in the regularly inundated tidal flat and low marsh areas, to higher marsh communities of cattails, grasses, sedges, and rushes. This study showed that both the hyperspectral and hyperspatial characteristics of the CASI imagery were important for achieving high separability among the classes due to reduced spectral mixing of different substrates at the subpixel scale when compared with simulated Landsat and Ikonos imagery.

A Simplified Maximum Likelihood Detection for MIMO Systems

SUMMARY In this paper, we propose a simplified Maximum Likelihood (ML) detection scheme for Multiple-Input Multiple-Output (MIMO) system that has much less computational complexity than the conventional ML detection scheme. Simulation results verify that the bit error rate (BER) performance of the proposed scheme is close to that of the ML detection

A new non-orthogonal space-time code with low decoding complexity

A full diversity block space-time code over two transmit antennas and two symbol periods is introduced. In this method, each code is equal to the addition of two matrices; A/sup m/ and DA/sup n/, where A and D are the two constant matrices and m and n are the two data symbols. A is selected such that the set A/sup m/, 0 /spl les/ m /spl les/ 2/sup b/ - 1 is closed under the matrix multiplication. This structure allows a simple maximum likelihood (ML) decoding method, and at the same time, simplifies the optimization of the coding advantage. Simulations show that the performance of the new code is very close to that of the Damen code (M. O. Damen et al., 2002) which is the best known block space-time code in terms of the coding advantage. Moreover, the decoding complexity of the proposed method is significantly lower than that of the Damen code.

A new ML detection algorithm for Orthogonal Multicode system in Nakagami fading channel

Based on the Maximum-Likelihood (ML) criterion, this paper proposes a novel noncoherent detection algorithm for Orthogonal Multicode (OM) system in Nakagami fading channel. Some theoretical analysis and simulation results are presented. It is shown that the proposed ML algorithm is at least 0.7 dB better than the conventional Matched-Filter (MF) algorithm for uncoded systems, in both non-fading and fading channels. For the consideration of practical application, it is further simplified in complexity. Compared with the original ML algorithm, the simplified ML algorithm can provide significant reduction in complexity with small degradation in performance.

The Canada‐France Deep Fields Survey. III. Photometric Redshift Distribution to I AB = 24

We compute accurate redshift distributions to IAB=24 and RAB=24.5 using photometric redshifts estimated from six-band UBVRIZ photometry in the Canada-France Deep Fields Photometric Redshift Survey (CFDF-PRS). Our photometric redshift algorithm is calibrated using hundreds of CFRS spectroscopic redshifts in the same fields. The dispersion in redshift is sigma/(1+z)<~0.04 to the CFRS depth of IAB=22.5, rising to sigma/(1+z)<~0.06 at our nominal magnitude and redshift limits of IAB=24 and z<=1.3, respectively. We describe a new method to compute N(z) that incorporates the full redshift likelihood functions in a Bayesian iterative analysis, and we demonstrate in extensive Monte Carlo simulations that it is superior to distributions calculated using simple maximum likelihood redshifts. The field-to-field differences in the redshift distributions, while not unexpected theoretically, are substantial even on 30' scales. We provide IAB and RAB redshift distributions, median redshifts, and parameterized fits of our results in various magnitude ranges, accounting for both random and systematic errors in the analysis.

SLM and PTS peak-power reduction of OFDM signals without side information

Selected mapping (SLM) and partial transmit sequence (PTS) are well-known techniques for peak-power reduction in orthogonal frequency-division multiplexing (OFDM). We derive a simplified maximum likelihood (ML) decoder for SLM and PTS that operates without side information. This decoder exploits the fact that the modulation symbols belong to a given constellation and that the multiple signals generated by the PTS or SLM processes are widely different in a Hamming distance sense. Pairwise error probability (PEP) analysis suggests how SLM and PTS vectors should be chosen. The decoder performs well over additive white Gaussian noise (AWGN) channels, fading channels, and amplifier nonlinearities.

Simple maximum likelihood estimates of efficacy in randomized trials and before-and-after studies, with implications for meta-analysis

Efficacy, which we define as the effect of receiving intervention on health outcomes among a group of subjects, is the quantity of interest for many investigators. In contrast, intent-to-treat analyses in randomized trials and their analogue for observational before-and-after studies compare outcomes between randomization groups or before-and-after time periods. When there is switching of interventions, estimates based on intent-to-treat are biased for estimating efficacy. By constructing a model based on potential outcomes, one can make reasonable assumptions to estimate efficacy under 'all-or-none' switching of interventions in which switching occurs immediately after randomization or at the start of the time period. This paper reviews the basic methodology, with emphasis on simple maximum likelihood estimates that arise with completely observed outcomes, partially missing binary outcomes, and discrete-time survival outcomes. Particular attention is paid to estimating efficacy in meta-analysis, where the interpretation is much more straightforward than with intent-to-treat analyses.

On the Construction of High-Rate Quasi-Orthogonal STBC for MIMO QR Demodulation

Orthogonal space-time block codes (STBCs) [1],[2] appear to be a very fascinating means of enhancing reception quality in quasi-static MIMO channels due to their full diversity, and especially their simple maximum-likelihood (ML) decoders. However, full-rate full-diversity orthogonal STBCs do not exist for more than two transmit antennas. Vertical layered space-time architecture (so-called the V-BLAST) [3] with a nulling- and cancelling-based detection algorithm, in contrast, has an ability of achieving high transmission rates at the cost of having very low diversity gain, an undesirable consequence caused by the interference and cancelling processes. The uncoded V-BLAST system is able to reach its ML performance with the aid of the sphere decoder algorithm [4] at the expense of higher detection complexity. Undoubtedly, the tradeoff between transmission rates, diversity, and complexity is inherent in designing space-time codes. This paper investigates a method to increase the nulling diversity gains for a general high-rate space-time code and introduces a new design strategy for high-rate space-time codes detected based on interference and cancelling processes, thanks to which high-rate quasi-orthogonal space-time codes for MIMO applications are proposed. We show that when nT transmit and nR = nT receive antennas are deployed, the first code offers a transmission rate of (nT - 1) with a minimum diversity order of 3, whereas the second one offers a transmission rate of (nT - 2) with a minimum diversity order of 5. Therefore, the proposed codes significantly outperform the V-BLAST as nR = nT. Simulation results and discussions on the performance of the proposed codes are provided.

A Simplified Maximum Likelihood Detector for OFDM-SDM Systems in Wireless LAN

This paper presents a reduced-complexity maximum likelihood detection (MLD) scheme for orthogonal frequency division multiplexing with space division multiplexing (OFDM-SDM) systems. Original MLD is known to be an optimal scheme for detecting the spatially multiplexed signals. However, MLD suffers from an exponentially computational complexity because it involves an exhaustive search for the optimal result. In this paper, we propose a novel detection scheme, which drastically reduce the complexity of MLD while keeping performance losses small. The proposed scheme decouples the spatially multiplexed signals in two stages. In stage one, the estimated symbols obtained from zero-forcing (ZF) are used to limit the candidate symbol vectors. In stage two, to form a final estimate of the transmitted symbol vector, the Euclidean or original defined likelihood metric is examined over all symbol vectors obtained from stage 1. Both the bit error rate (BER) and packet error rate (PER) performances are evaluated over a temporally and spatially uncorrelated frequency selective channel through the computer simulations. For a four-transmit and four-receive OFDM-SDM system transmitting data at 144 Mbit/s and 216 Mbit/ss i.e., employing 16 Quadrature Amplitude Modulation (16QAM) and 64QAM subcarrier modulation over 16.6 MHz bandwidth channel, the degradation in required SNR from MLD for PER = 1% are about 0.6 dB and 1.5 dB, respectively. However, the complexity of MLD is reduced to 0.51000% and 0.01562%.

Noncoherent sequential code acquisition based on simplified maximum likelihood ratios

In this paper, we consider the noncoherent code acquisition problem using sequential schemes. To alleviate the computational complexity of the maximum likelihood method, simplified schemes are proposed and analyzed for the truncated sequential probability ratio test. The performance of the simplified and original schemes are compared in additive white Gaussian noise and slowly varying fading channels. Numerical results show that the proposed schemes have essentially the same performance as the original schemes while allowing simpler structures.

A simplified noise-predictive partial response maximum likelihood detection using M-algorithm for perpendicular magnetic recording channels

We propose a simplified noise-predictive partial response maximum likelihood (NPML) system in conjunction with M-algorithm for dual-layered perpendicular magnetic recording channels. The complexity, which is increased by the construction of noise prediction filter, can be reduced through the M-algorithm. Despite the complexity of the proposed scheme (M=4) is decreased to 1/4 than one of the full NP(12321)ML system, two systems maintain almost the same bit-error rate and the detection performance of the noise-predictive maximum likelihood is better than that of the conventional PRML.

Performance Analysis of Two-Branch Transmit Diversity Block-Coded OFDM Systems in Time-Varying Multipath Rayleigh-Fading Channels

Based on Alamouti code, Lee and Williams proposed two-branch transmit diversity block-coded orthogonal frequency-division multiplexing (TDBC-OFDM) systems, namely, space-time block-coded OFDM (STBC-OFDM) and space-frequency block-coded OFDM (SFBC-OFDM). However, they employed the simple maximum-likelihood (SML) detector, which was designed under the assumption that the channel is static over the duration of a space-time/frequency codeword. Therefore, STBC-OFDM/SFBC-OFDM suffers from the high time/frequency selectivity of the wireless mobile fading channel. In this paper, besides the original SML detector, three detectors proposed by Vielmon et al. are applied to improve the two-branch TDBC-OFDM systems. Additionally, assuming sufficient cyclic prefix, the performances of all systems in spatially uncorrelated time-varying multipath Rayleigh-fading channels are evaluated by theoretical derivation and computer simulation, as well. According to the derived bit-error rate (BER), we further derive the bit-error outage (BEO) to provide a more object judgment on the transmission quality within a fading environment. Numerical results have revealed that significant performance improvement can be achieved even when the systems are operated in highly selective channels.