Optimal Signal Sets Research Articles

Reinforcement learning for traffic signal control: Incorporating a virtual mesoscopic model for depicting oversaturated traffic conditions

Recently, with increasing urban traffic congestion, there has been an upsurge in studies on reinforcement learning for traffic signal control (RL-TSC), which enables efficient traffic management. However, most existing RL-TSC research relies on simulation, and instances of real-world application are relatively scarce. Furthermore, existing RL-TSC methods employ a step-based approach, controlling traffic signals every short step. This approach can be inefficient in oversaturated traffic conditions, where large deviations in traffic demand between movements prevent traffic signals from being effectively managed based on the overall traffic situation. In this study, we aim to transform simulation-based RL-TSC into a more practical and applicable model. We have developed a RL-TSC method capable of responding to oversaturated traffic conditions, designing an action space that enables the agent to derive an optimal signal set for every cycle length, thereby understanding the traffic situation across all movements. During each cycle length, our proposed model conducts traffic signal optimization and identifies the optimal signal through an iterative exploration. To facilitate a fast and accurate strategy search process, we developed a kinematic wave-based mesoscopic model. This model estimates the density across the entire link, based on collected traffic data and derives the state and reward values. We have validated the field applicability of the proposed RL-TSC method through a real-world demonstration at a congested intersection in Seoul, Korea. The results indicated a significant improvement in traffic congestion, with the average queue length at the intersection reduced by up to 11.4%.

Optimization of Signal Design for Poly-Polarization Multiplexing in Satellite Communications

A poly-polarization multiplexing (PPM) scheme, that simultaneously utilizes two orthogonal polarization signals to create virtual additional planes, has been studied to enhance the spectrum efficiency for fixed satellite communication in the Ku band (12, 14 GHz). In this paper, to further increase the spectrum efficiency, we propose an enhanced PPM (E-PPM) scheme. By formulating the generalized linear mapping for two orthogonal polarization planes, the proposed scheme derives the optimal E-PPM signal set that has the largest minimum Euclidean distance. As a fundamental study, this paper focuses on an AWGN channel, and we show the achievable performance of the proposed scheme. In the computer simulations assuming no depolarization effects, we show that the E-PPM scheme reduces the required E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> /N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> by 1.80 dB and 0.70 dB at BER =10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-7</sup> compared with the conventional orthogonal polarization multiplexing (OPM) and PPM scheme, respectively.

Orthogonal Binary Waveform Optimization for Mimo Radar Systems

Waveform optimization for multiple-input multiple-output (MIMO) radar systems for good autocorrelation and crosscorrelation properties based on the direct design of the set of orthogonal transmitted time series is considered. Exploiting the orthogonality of non identical walsh functions, which have been used successfully in spread spectrum communication, the Walsh-Hadamard matrix is used as the orthogonal binary signal set followed by the simulated annealing statistical optimization tool to provide an optimal orthogonal binary signal set with the desired correlation properties

Multilectin Assay for Detecting Fibrosis-Specific Glyco-Alteration by Means of Lectin Microarray

Despite the progress made in understanding glyco-alterations of specific glycoproteins such as α1-acid glycoprotein (AGP) associated with liver fibrosis, there has been no useful diagnostic assay with a lectin recognizing the fibrosis-specific alteration and an antibody against the core protein. We therefore developed a compatible multiple lectin-antibody sandwich immunoassay on the basis of the results obtained by the lectin microarray analysis for monitoring fibrosis. AGP-enriched fractions derived from 0.5-μL sera of 125 patients with staging-determined fibrosis (26.4% F0-F1, 25.6% F2, 24% F3, and 23.2% F4) were subjected to systematic analysis by antibody-overlay lectin microarray. Data were analyzed to statistically relate to the degree of fibrosis progression. Additionally, we applied an optimal lectin signal set on the microarray to distinguish 45 patients with cirrhosis from 43 patients with chronic hepatitis. Signal patterns of the 12 selected lectins reflected fibrosis-associated glyco-alteration of AGP. Among the 12 lectins, we found a specific lectin at each stage of fibrosis (i.e., significant fibrosis, severe fibrosis, and cirrhosis) (P < 0.0001). The test for the detection of cirrhosis showed that combinational use of 3 lectins (AOL, MAL, and DSA) on the array enhanced the diagnostic value for liver cirrhosis to 95% diagnostic sensitivity and 91% diagnostic specificity. The multiple lectin-antibody sandwich immunoassay targeting AGP enables monitoring of disease progression in chronic hepatitis patients at risk of developing hepatocellular carcinoma.

Algorithms for optimal signal set design

The problem of choosing an optimal signal set for non-Gaussian detection was reduced to a smooth inequality-constrained mini-max nonlinear programming problem by Gockenbach and Kearsley. Here, we consider the application of several optimization algorithms, both global and local, to this problem. The most promising results are obtained when special-purpose sequential quadratic programming algorithms are embedded into stochastic global algorithms.

Quarternary Signal Sets for Digital Communications with Nonuniform Sources

This letter considers the signal design problems for quaternary digital communications with nonuniform sources. The designs are considered for both the average and equal energy constraints and for a two-dimensional signal space. A tight upper bound on the bit error probability (BEP) is employed as the design criterion. The optimal quarternary signal sets are presented and their BEP performance is compared with that of the standard QPSK and the binary signal set previously designed for nonuniform sources. Results shows that a considerable saving in the transmitted power can be achieved by the proposed average-energy signal set for a highly nonuniform source.

Global and Local Optimization Algorithms for Optimal Signal Set Design.

The problem of choosing an optimal signal set for non-Gaussian detection was reduced to a smooth inequality constrained mini-max nonlinear programming problem by Gockenbach and Kearsley. Here we consider the application of several optimization algorithms, both global and local, to this problem. The most promising results are obtained when special-purpose sequential quadratic programming (SQP) algorithms are embedded into stochastic global algorithms.

Optimal Signal Sets for Non-Gaussian Detectors

Identifying a maximally separated setof signals is important in the design of modems. The notion of optimality is dependent on the model chosen to describe noise in the measurements; while some analytic results can be derived under the assumption of Gaussian noise, no such techniques are known for choosing signal sets in the non-Gaussian case. To obtain numerical solutions for non-Gaussian detectors, minimax problems are transformed into nonlinear programs, resulting in a novel formulation yielding problems with relatively few variables and many inequality constraints. Using sequential quadratic programming, optimal signal sets are obtained for a variety of noise distributions.

Stochastic iterative algorithms for signal set design for Gaussian channels and optimality of the L2 signal set

We propose a stochastic iteration approach to signal set design. Four practical stochastic iterative algorithms are proposed with respect to equal and average energy constraints and sequential and batch modes. By simulation, a new optimal signal set, the L2 signal set (consisting of a regular simplex set of three signals and some zero signals), is found under the strong simplex conjecture (SSC) condition (equal a priori probability and average energy constraint) at low signal-to-noise ratios (SNR). The optimality of the L1 signal set, the confirmation of the weak simplex conjecture, and two of Dunbridge's (1967) theorems are some of the results obtained by simulations. The influence of SNR and a priori probabilities on the signal sets is also investigated via simulation. As an application to practical communication system design, the signal sets of eight two-dimensional (2-D) signals are studied by simulation under the SSC condition. Two signal sets better than 8-PSK are found. Optimal properties of the L2 signal set are analyzed under the SSC condition at low SNRs. The L2 signal set is proved to be uniquely optimal in 2-D space. The class of signal sets S(M, K) (consisting of a regular simplex set of K signals and M-K zero signals) is analyzed. It is shown that any of the signal sets S(M, K) for 3/spl les/K/spl les/M-1 disproves the strong simplex conjecture for M/spl ges/4, and if M/spl ges/7, S(M, 2) (the L1 signal set) also disproves the strong simplex conjecture. It is proved that the L2 signal set is the unique optimal signal set in the class of signal sets S(M, K) for all M/spl ges/4. Several results obtained by Steiner (see ibid., vol.40, no.5, p.721-31, 1994) for all M/spl ges/7 are extended to all M/spl ges/4. Finally, we show that for M/spl ges/7, there exists an integer K'<M such that any of the signal sets consisting of K signals equally spaced on a circle and M-K zero signals, for 4/spl les/K/spl les/K', also disprove the strong simplex conjecture.

RMS bandwidth constrained signature waveforms that maximize the total capacity of PAM-synchronous CDMA channels

Optimum time-limited signal sets of equal and unequal energies are obtained under root mean square (RMS) bandwidth constraints. The total capacity and the total asymptotic efficiency of the PAM synchronous Gaussian CDMA (PSG-CDMA) channel are considered as the optimality criteria. The latter measure is monotonic with the determinant of the correlation matrix, R, and the former is monotonic with det(I+/spl sigma//sup -2/R), where /spl sigma//sup 2/ represents the noise level. Average as well as maximum RMS bandwidth constraints are considered in the equal-energy case, and the energy-weighted RMS bandwidth constraint is considered for unequal energy signals. For the equal-energy problem, signal sets are found that simultaneously optimize the total asymptotic efficiency under both average and maximum RMS bandwidth constraints. For the total capacity measure, such simultaneously optimal signal sets are also obtained, albeit under the restriction that the number of signals n be a Hadamard matrix dimension. When the Hadamard dimension is in particular a power of two, we obtain optimum signal sets that are shown to yield equal optimum multiuser detector asymptotic efficiencies for all users of an uncoded PSG-CDMA channel. Unequal energy signal sets are also found under an energy-weighted RMS bandwidth constraint for both optimality criteria.

On the relationship between measures of discrimination and the performance of suboptimal detectors

The problem of designing and analyzing suboptimal detectors via statistical measures is considered. As a preliminary result, we show that only the minimum and maximum probability of error are valid measures of discrimination between the input statistics. This result would seem then to imply that the use of measures in this context can be inappropriate. However, to overcome this apparent obstacle, we demonstrate explicit relationships between various f-divergences and the loss in performance of an arbitrary detector relative to the optimal detector. In particular, we establish both upper and lower bounds on the performance loss of a suboptimal detector in terms of the distance between the pertinent statistics of both the optimal and suboptimal detectors. While designing detectors by minimizing these upper bounds can be an elusive task, in many practical cases, the lower bound presented herein holds with equality. In this case, minimizing the separation of the output statistics of the detector with respect to a particular f-divergence equivalently minimizes the resulting probability of error of the detector. To facilitate design, other researchers have established conditions under which one may design arbitrary detection strategies with respect to a specific f-divergence (Kullback-Leibler being a principal example). We extend this approach by deriving necessary and sufficient conditions under which one may design detection strategies with respect to an arbitrarily chosen f-divergence. Thus when these conditions are met, one may optimize a detector with respect to the most analytically tractable measure to obtain the minimum probability of error detector over a selected class of detection strategies. Examples demonstrating the utility of this theory for the problem of designing optimal linear detectors and optimal signal sets are presented. >

The strong simplex conjecture is false

The design of M average-energy-constrained signals in additive white Gaussian noise is addressed. The long-standing strong simplex conjecture, which postulates that the regular simplex signal set maximizes the probability of correct detection under an average-energy constraint, is disproven. A signal set is presented that performs better than the regular simplex signal set at low signal-to-noise ratios for all M/spl ges/7. This leads to the result that, for all M/spl ges/7, there is no signal set of M signals which is optimal at all signal-to-noise ratios. Furthermore, the optimal signal set at low signal-to-noise ratios is not an equal energy set for any M/spl ges/7. The regular simplex is shown to be the unique signal set which maximizes the minimum distance between signals. It follows that a signal set which maximizes the minimum distance is not necessarily optimum. However, the regular simplex is shown to be globally optimum in the sense of uniquely maximizing the union bound on error probability at all signal-to-noise ratios. >

Optimization of signal sets for partial-response channels. II. Asymptotic coding gain

For Pt. I see ibid., vol.37, no.5, p.1327-141 (1991). For a linear, time-invariant, discrete-time channel with a given transfer function H(f), and information rate R bits/T, where T is the symbol interval, an optimal signal set of length K is defined to be a set of 2/sup RK/ inputs of length K that maximizes the minimum l/sub 2/ distance between pairs of outputs. The author studies the minimum distance between outputs, or equivalently, the coding gain of optimal signal sets as K to infinity . He shows how to estimate the coding gain, relative to single-step detection, of an optimal signal set length K when K is large.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On optimal signal sets for digital communications with finite precision and amplitude constraints

The maximum data rate that can be reliably communicated given a linear, time-invariant, dispersive channel, a receiver that samples the channel output to within an accuracy of +or-d where d>0, and a transmitter with an output amplitude constraint is evaluated. For any dispersive channel the maximum rate depends on d and is finite. The transmitted waveforms must be designed so that two channel outputs associated with two distinct transmitted signals are separated in amplitude at a particular time by d. It is shown that given any channel impulse response with rational Laplace transform, there exists an optimal sets of inputs that are +or-A everywhere where A is the maximum allowable amplitude. Furthermore, in any finite time interval, each input changes sign a finite number of times. If the channel impulse response is a single decaying exponential, it is shown that simple binary signaling, in which A or -A, depending on the current message bit, is transmitted during each symbol interval, maximizes the data rate.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Vector coding for partial response channels

A linear technique for combining equalization and coset codes on partial response channels with additive white Gaussian noise is developed. The technique, vector coding, uses a set of transmit filters or 'vectors' to partition the channel into an independent set of parallel intersymbol interference (ISI)-free channels for any given finite (or infinite) block length. The optimal transmit vectors for such channel partitioning are shown to be the eigenvectors of the channel covariance matrix for the specified block length, and the gains of the individual channels are the eigenvalues. An optimal bit allocation and energy distribution, are derived for the set of parallel channels, under an accurate extension of the continuous approximation for power in optimal multidimensional signal sets for constellations with unequal signal spacing in different dimensions. Examples are presented that demonstrate performance advantages with respect to zero-forcing decision feedback methods that use the same coset code on the same partial response channel. Only resampling the channel at an optimal rate and assuming no errors in the feedback path will bring the performance of the decision feedback methods up to the level of the vector coded system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Signal Design for Totally Phase-Incoherent Communications

A set of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> equally-likely equal-energy transmittable signals is considered, each of which consists of a linear combination of tones from <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</tex> free running oscillators <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(D \leq M)</tex> . The oscillator tones are assumed sufficiently disjoint to be orthogonal. The design problem consists of finding the optimal receiver and signal set for various <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</tex> . For the additive white Gaussian noise channel, the optimal receiver first forms the sufficient statistic which consists of noncoherently detecting the energy in each of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</tex> tones. Unlike previous designs of digital transmitters based on minimization of the probability of error, when noncoherent oscillations are employed, the optimal receiver and signal set are dependent on the signal-to-noise ratio. The imposed constraints restrict the signal vectors to the all-positive subspace of the surface of a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</tex> -dimen sional sphere. The optimal receiver, signal set, and resulting prob ability of error and channel capacity are determined for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M \geq D = 2</tex> for low and high signal-to-noise ratios. Severe performance constraints imposed by using a suboptimal square-law receiver are discussed. Preliminary results have been obtained for the general case <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M \geq D &gt; 2</tex> .

The Global Optimization of Incoherent Phase Signals

The problem of global optimization of M incoherent phase signals in N complex dimensions is formulated. Then, by using the geometric approach of Landau and Slepian, conditions for optimality are established for $N = 2$, and the optimal signal sets are determined for $M = 2,3,4,6$ and 12.The method is the following: The signals are assumed to be equally probable and to have equal energy, and thus are represented by points ${\bf s}_j $, $j = 1,2, \cdots ,M$, on the unit sphere $S_1 $ in $C^N $. If $W_{jk} $ is the half space determined by ${\bf s}_j $ and ${\bf s}_k $ and containing ${\bf s}_j $, i.e., $W_{jk} = \{ {{\bf r} \in C^N :| {\langle {{\bf r},{\bf s}_j } \rangle } |\geqq | {\langle {{\bf r},{\bf s}_k } \rangle } |} \}$, then $\{ {\mathfrak{R}_j = \cap _{k \ne j} W_{jk} :j = 1,2, \cdots ,M} \}$, the maximum likelihood decision regions, partition $S_1 $. For additive complex Gaussian noise ${\bf n}$ and a received signal ${\bf r} = {\bf s}_j e^{i\theta } + {\bf n}$, where $\theta $ is uniformly dist...

Signal-design considerations for the noncoherent Gaussian channel (Corresp.)

The choice of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> equiprobable equipowered narrow-band waveforms of equal duration for the noncoherent communication system is considered. With the bandwidth constrained, the problem of finding optimal signal sets of given dimension is formulated as a variational one. For dimensionality <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D \leq 2M - K</tex> , <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K \leq 2[M/3]</tex> , where [ ] denotes "integer part of," and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M \geq 6</tex> , signal inner-product matrices consisting of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</tex> regular simplices placed mutually orthogonal to one another, are local extremals of the probability of error, thereby establishing a marked similarity between the coherent and noncoherent signal-design problems.