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In this proof-of-principle paper, the application of 2-D optical code-division multiple-access (OCDMA) modulation to long-range automotive time-of-flight (ToF) light detection and ranging (LiDAR) is studied. The regulations and physical constraints that govern the design parameters are reviewed. Using 2-D carrier-hopping prime codes (CHPCs), the modulation model and a novel 2-D hard-limiting decoder are designed and validated with OptiSystem$^{\rm {TM}}$ simulations. Based on the design parameters, the 2-D CHPCs have six times as many distinct sequences (for sensor identification) as 1-D code sequences. Analytical and simulation studies show that the proposed 2-D OCDMA modulation model can eliminate the near-far (power) problem and support more LiDAR sensors with distinctive ToF tags, greater interference robustness for more simultaneous ToF measurements, and better performance than the 1-D counterparts. The simulation results show that the 2-D model can support four times as many simultaneous emitting sensors without false detections as the 1-D model. In summary, the 2-D OCDMA modulation has more benefits and is more cost efficient overall, even though it is more complex.

In this paper, an algebraic construction of channel-hopping (CH) sequences for "small-cell" cognitive-radio wireless networks (CRWNs) is introduced. By applying linear- and quadratic-congruence operators in the finite field, multiple sets of CH sequences can be created quickly without complex algorithms or exhaustive computer searches. Every set carries desired properties, such as enlarged cardinality, full degree-of-rendezvous, and short maximum-time-to-rendezvous, that can enhance spectral efficiency and spectrum utilization. Thus, they can be used to support many Internet-of-thing (IoT) devices with good media-access latency and fairness in small-cell CRWNs. The studies of rendezvous-success rate and throughput show that this algebraic construction carries the best balance between the desired properties and performance than other constructions.

The impact of a differential group delay (DGD) and polarization mode dispersion (PMD) on multi-wavelength picosecond code carriers used by two-dimensional wavelength-hopping time-spreading coding schemes in optical code division multiple access (2D-WH/TS OCDMA systems is investigated. Based on experimental data collected over ten days on a 111 km long commercially used fiber link PMD and DGD parameters are determined and used to find the code carriers temporal broadening. This information is then used to calculate the 2D-WH/TS OCDMA system performance degradation as a function of varying number of simultaneous users for different DGD.

The use of semiconductor-optical-amplifier-based tunable dispersion compensator (SOA-TDC) in ultrafast incoherent fiber-optic code-division multiple-access (FO-CDMA) systems with picosecond multiwavelength codes has recently been demonstrated. In this paper, results on the SOA-TOC’s capability of compensating for fiber chromatic dispersion and distorted autocorrelation function caused by fiber temperature variation (FTV) in such a FO-CDMA system with a long fiber link are reported. The deleterious effects of FTV to the system performance are quantified in terms of “chip granularity” and studied by applying a recent multiple-QoS performance-analytical model.

A family of synchronous-symmetric channel-hopping (CH) sequences for cognitive radio networks is constructed. The CH sequences satisfies the design criteria of channel overlap, even channel use, and full channel utilization. They also carry desirable properties of enlarged cardinality, optimal maximum-time-to-rendezvous (MTTR), full degree-of-rendezvous (DoR), and minimum channel competition. They achieve the unique full-channel-utilization-per-time-slot property and can support the largest number of users without creating channel collisions. Studies of performance metrics, such as rendezvous-success (RS) rate, show that the new CH sequences provide better balance and flexible choices between cardinality, DoR, MTTR, and RS rate than previous works.

In this paper, a family of synchronous-asymmetric channel-hopping (CH) sequences for cognitive radio (CR) networks is constructed and their maximum-time-to-rendezvous (MTTR) lower bound is derived. The new sequences achieve full degree-of-rendezvous and optimal MTTR. They also have the unique property of enlarging cardinality without scarifying the MTTR. Their rendezvous-success (RS) rate and MTTR are compared with prior works. This family provides a flexible choice of CH sequences that have adjustable cardinality and RS rate for the CR networks with variable QoS.

To provide differential quality-of-services (QoS) in multimedia networks, an optical code-division multiple-access (O-CDMA) technique with power control in variable-weight codes has been studied. In this paper, a simplified bit-error-probability model and a new analytical model of the system capacity of such a multimedia O-CDMA network are formulated. Using the new models, the relationship of code weight and chip power is established and they can quickly be adjusted accordingly to achieve differential QoS in real time. Our findings show that such a multimedia O-CDMA network with power-controlled double-weight codes is able to achieve larger system capacity than its conventional single-weight counterpart under certain conditions.

Optical communication systems are expected to support multimedia services that have different bit rates and quality-of-services. Our recent proposed hybrid, multirate, multimedia optical code-division multiple access (O-CDMA) system meets these requirements with reasonable (hardware and synchronization) complexity and high user/code flexibility. Beside creating strong multiuser interference, a large number of active users increases the optical power in transmission, potentially causing power saturation in optical devices and fiber nonlinearities. To ensure normal operation, a new power model of the hybrid multirate O-CDMA system is formulated. Block probability and average throughput models are presented for quantifying the system performance. Finally, the hybrid system is shown to have higher throughput than conventional O-CDMA systems.

Two multirate techniques, so-called the multiple-code (MC) and multicode-keying (MK) schemes, were recently proposed to support multimedia services with different bit rates in asynchronous optical code-division multiple-access (O-CDMA) systems. In the MC scheme, a user maps multiple data bit 1s to multiple code matrices and transmits them at the same time. In the MK scheme, a user only transmits one of its assigned codewords at a time, and each codeword represents a symbol of multiple data bits. In terms of error probability, the performances of these multirate schemes were also analyzed. Spectral efficiency (SE) is another figure-of-merit useful for comparing O-CDMA schemes. In this paper, the performances and SEs of the multirate MC and MK schemes are formulated and the conditions of which scheme offers a better SE are investigated with formal proofs. Numerical examples are given to validate the analyses.

A class of algebraic codes for incoherent optical code-division multiple access, so-called extended multilevel prime codes, was recently studied. They have asymptotic optimal cardinality and possess a unique tree structure of multiple levels of subsets of codewords; codewords in different subsets have different cross-correlation values for adjustable code performance. In this paper, the performance of the codes under an optimized method of assigning codewords to simultaneous users is formulated. In addition, how the tree structure, large cardinality, and the codes' algebraic properties potentially support rapid codeword switching and physical-layer network security are investigated.

A diversity incoherent optical-wireless code-division multiple-access (OW-CDMA) scheme was recently proposed, in which each simultaneous user transmits multiple (time-shifted) copies of its optical code per data bit of one in order to achieve good performance. The analysis was performed under the ideal “copy-independent” assumption for ease of mathematical treatment. However, complete copy-independency is hard to achieve, especially when short-length optical codes are used, because there are not enough time-slots for the copies to be positioned. In this paper, we combine the effects of copy-dependency and “timeslot granularity” in the analysis of our diversity OW-CDMA scheme and formulate a new, generalized, and more accurate performance model with validation by computer simulation.

In this paper, a “diversity” on-off-keying (OOK) optical code-division multiple-access (O-CDMA) scheme is proposed and analyzed. The scheme transmits multiple copies of an optical code per data bit of one in order to improve code performance. Our results show that the diversity OOK O-CDMA scheme reduces error probability with little degradation on spectral efficiency, under the assumptions of similar code power and bandwidth expansion as the conventional OOK O-CDMA scheme. An important application of our diversity scheme, which solves the low code-cardinality problem of heavy-weight optical codes, is finally discussed.

Coded modulation with Reed-Solomon (RS) codes has recently been proposed to use atop of frequency-hopping code-division multiple access (FH-CDMA) in order to increase data transfer rate. In this paper, a new method on implementing the modulation and demodulation processes of the RS codes in RS/FH-CDMA is proposed. With the use of our specially "pruned" trellis and the Viterbi algorithm, both processes are simplified and so are their computational complexities. The performance and computational complexities of this RS/FH-CDMA system are analyzed and verified with computer simulation.

Frequency-hopping code-division multiple access (FH-CDMA) along with coded modulation using Reed-Solomon (RS) codes has recently been proposed for wireless communications to increase data transfer rate. In this paper, an improved method of implementing the modulation and demodulation of the RS codes in RS/FH-CDMA by means of a trellis and the Viterbi algorithm is proposed and analyzed. We study an efficient algorithm for “pruning” the trellis to decrease demodulation errors. Our pruned-trellis method reduces modulation complexity and substantially simplifies the demodulation process. Finally, the performance of this trellis-based RS/FH-CDMA system is analyzed and compared with the old system without trellis.

In this paper, we study the combination of code-weight variation and bit-power control in order to provide differential quality-of-service (QoS) in multimedia optical codedivision multiple access. A simplified performance model is formulated for studying the interaction of the weight-variation and power-control approaches. For sake of illustration, double-weight codes are studied in this paper. Our results show that the QoS of double-wight codes can be fine-tuned by controlling both code weight and bit power.

In this paper, we propose three code-mapping methods, which make use of existing optical codes of one dimension to construct optical codes of a different dimension. A reverse code-mapping method is first introduced, which allows the generation of 1-D prime codes from their 2-D counterparts. Afterwards, the one-to-one correspondence between 1-D and 2-D optical codes is established with the use of the Chinese remainder theorem. This theorem is then used for the first time to generate rare, difficult-to-construct 1-D optical codes of cross-correlation values of at most two. Finally, an improved zero-padding folding method for mapping 1-D to 2-D optical codes with more flexible selection of code parameters than previous methods is detailed.

The use of optical codes with variable weight has been considered as a desirable candidate to provide differential quality-of-service in optical code division multiple access (O-CDMA). It is because code weight plays a dominant role in determining the performance of O-CDMA codes as heavy-weight codes always outperform light-weight codes under the conventional assumption of identical power in every optical pulses (i.e., same chip power). In this paper, we assume the use of optical codes with same power in each bit duration (i.e., same bit power). In other words, heavy-weight codes have less power per chip than light-weight codes. For illustration, we focus our work on double-weight codes and compare the performance between heavy-weight and light-weight codes under both same-chip-power and same-bit-power assumptions. Most importantly, we develop a new and accurate analytical method to evaluate the performance of these double-weight codes. Validating with computer simulation, our results show that heavy-weight codes do not always perform better than light-weight codes under the same-bit-power assumption.

In this paper, a two-level frequency-hopping code-division multiple-access (FH-CDMA) scheme, which is flexible in the selection of modulation codes and FH patterns, is studied. This two-level FH-CDMA scheme can be modified by the partition of the modulation codes in order to support more subscribers without increasing the number of FH patterns. The performance and spectral efficiency (SE) analyses show that our scheme supports higher data rate and SE than Goodman's frequency-shift-keying FH-CDMA scheme, making the former more attractive for wireless communication systems.

“Multi-level” wavelength-time codes with asymptotic-optimal code cardinality and flexible code length are constructed and analyzed. The codes can be partitioned into multiple levels of codes with different cross-correlation functions, thus supporting the trade-off between code cardinality and performance for different system requirements (e.g., capacity and throughput).

In this paper, we study a new class of two-dimensional codes, here called multi-level prime codes, with expanded code cardinality by relaxing the maximum cross-correlation function to any arbitrary positive integer n. Besides having asymptotically optimal cardinality and zero autocorrelation sidelobes, these multi-level prime codes can be partitioned into n levels, such that the cross-correlation function between any two code matrices in level l is at most l, where l ∈ [1, n]. The performance of the new codes in an optical code-division multiple-access system with hard-limiting detection is analyzed. Our results show that the unique partition property of the multi-level prime codes allows the trade-off between code cardinality and performance for meeting different system requirements, such as capacity and throughput.

In this paper, a new family of two-dimensional (2D) wavelength-time codes, which uses one-dimensional (1D) optical orthogonal codes (OOCs) with the maximum cross-correlation value of two as the time-spreading codes is proposed and analyzed. By relaxing the cross-correlation functions to at most two, the new 2D codes can provide larger code cardinality to accommodate more subscribers. They also have better performance than 1D optical codes because they can support heavier code weight, for a given code length. Moreover, our numerical examples show that the heavier code weight supported by our new 2D codes results in better performance than some of our previously proposed 2D codes, which have the maximum cross-correlation value of one.

Genetic alterations, such as chromosomal gains and losses, are key causes of tumorigenesis. Comparative Genomic Hybridization (CGH) is a molecular method for detecting such DNA copy number alterations in tumor cells. Recent observations have reported that in many tumors, the mRNA transcript changes measured by gene expression profiling (GEP) are correlated with corresponding DNA copy number alterations, supporting the possibility of predicting DNA copy number alterations from GEP data. In this paper, contrary to the traditional use of GEP, we present a new analytical approach utilizing GEP data for predicting DNA copy number alterations. The proposed approach is built on a hidden Markov model and trained in the light of paired GEP and CGH data on a sufficient number of tumor cases of the same tumor type. Then it can be applied to new cases of that tumor type to predict the CGH profiles from their GEP profiles.

Various multirate transmission techniques, such as the multiple-code (MC) and multicode-keying (MK) schemes, have been proposed for optical code division multiple access (O-CDMA) systems with multimedia services. In this paper, a metric of comparison, so-called the normalized spectral efficiency (NSE), is derived to compare, as a whole, the performance and system efficiency of these two schemes. The NSE of the conventional single-rate on-off-keying (OOK) O-CDMA scheme is also derived for a baseline comparison. Our numerical results show that the MC scheme always has larger NSE than the single-rate OOK scheme, while the MK scheme has the largest NSE under certain conditions.

In this paper, a new family of wavelength-time codes, which is based on (n, w, 1,2) time-spreading optical orthogonal codes (OOCs), is proposed. By having cross-correlation values of at most two, the new two-dimensional (2D) codes provide larger code cardinality to accommodate more subscribers and support heavier code weight to result in better code performance. Under certain conditions, our results show that the new codes outperform other 2D codes that have the cross-correlation values of at most one, such as our previously studied multiple- wavelength OOCs and 2D codes based on (n, w, 2,1) OOCs.

In this paper, a new family of two-dimensional optical codes with the maximum cross-correlation value of two is constructed and analyzed. The new construction supports larger code cardinality (i.e., more subscribers) and heavier code weight (i.e., better code performance or more simultaneous users) without increasing the code length or number of wavelengths. Our results show that the new code performs better than our multiple-wavelength optical orthogonal code, which had the cross-correlation values of at most one.

In this paper, we propose a "sub-chip-level" receiver for two-dimensional (2D) optical code division multiple access (O-CDMA). In a chip-level receiver, one detects the total received optical intensity in a chip time. In our sub-chip-level receiver, we detect the received optical intensity in multiple sub-chip intervals in order to further reduce decoding errors. Afterwards, the "chip-asynchronous" performance of 2D optical codes with arbitrary cross-correlation values in the sub-chip-level receiver is analyzed as a function of the number of sub-chips. The performance is also compared with that of the chip-level receiver under the chip-asynchronous assumption.

In this paper, we study a new family of carrier-hopping prime codes (CHPCs), so-called quadratic- congruence CHPC (QC-CHPC), with expanded code cardinality by relaxing the maximum cross-correlation function to two (i.e., lambdac = 2). An application of the new code is for multicode keying in wavelength-time optical code-division multiple access (O-CDMA), in which each user is assigned M = 2m code matrices to represent m data bits per symbol. The advantages are that 1) a lower baud multicode-keying O-CDMA system can support a higher bit rate and 2) user's code obscurity is enhanced, as compared to the transmission of one code matrix (per user) for each data bit one in conventional "on-off keying" O-CDMA systems. Our performance analysis shows that there is a trade-off between the code performance and hardware complexity/speed related to the choice of M, for a given bit rate.

We propose a more accurate method to analyze multilevel frequency-shift-keying frequency-hopping code-division multiple-access (MFSK/FH-CDMA) wireless communication systems using ldquoone-hitrdquo FH patterns, instead of random FH patterns. By also removing the over-optimistic symbol-synchronous assumption, the new method provides a more realistic performance analysis as the MFSK modulation may result in two hits even when one-hit FH patterns are used if symbol transmissions are not synchronized.

While two-dimensional (2-D) orthogonal variable spreading factor (OVSF) codes were proposed for multicarrier direct-sequence code-division multiple-access (MC/DS-CDMA) systems in order to eliminate multiple-access interference, the number of orthogonal sequences (or code cardinality) was restricted by the number of carrier frequencies. Non-orthogonal 2-D frequency-time-spreading (FTS) codes were then proposed to increase the code cardinality by sacrificing some code performance. To improve the code performance, we here propose a modified 2-D FTS code. We also evaluate the performance of the new code in the MC/DS-CDMA system over a non-fading additive white Gaussian noise channel and a Rayleigh fading channel, and compare with those of the 2-D OVSF, random and original FTS codes.