Optical orthogonal codes with unequal auto- and cross-correlation constraints

An optical orthogonal code (OOC) is a collection of binary sequences with good auto- and cross-correlation properties; they were defined by Salehi and others as a means of obtaining code-division multiple access on optical networks. Up to now, all work on OOCs have assumed that the constraint placed on the autocorrelation and that placed on the cross-correlation are the same. We consider-codes for which the two constraints are not equal. Specifically we develop bounds on the size of such OOCs and demonstrate constriction techniques for building them. The results demonstrate that a significant increase in the code size is possible by letting the autocorrelation constraint exceed the cross-correlation constraint. These results suggest that for a given performance requirement the optimal OOC may be one with unequal constraints. This paper also views OOCs with unequal auto- and cross-correlation constraints as constant-weight unequal error protection (UEP) codes with two levels of protection. The bounds derived are interpreted from this viewpoint.<>     

Optical orthogonal pulse compression codes by hopping

The letter describes a simple digital processing technique for using standard M sequences or quadratic residue codes in such a way that their optical correlation is truly orthogonal. This finds important application in optical radar applications where near stationary targets are involved.     

Optical orthogonal codes: design, analysis and applications

An optical orthogonal code (OOC) is a family of (0,1) sequences with good auto- and cross-correlation properties, i.e the autocorrelation of each sequence exhibits the `thumbtack' shape and the cross correlation between any two sequences remains low throughout. The use of optical orthogonal codes enables a large number of asynchronous users to transmit information efficiently and reliably. The thumbtack-shaped autocorrelation facilitates the detection of the desired signal, and low-profile cross correlation reduces interference from unwanted signals. Theoretical upper and lower bounds on the maximum possible size of OOCs are derived. Methods for the design and analysis of OOCs, using tools from projective geometry, the greedy algorithm, iterative constructions, algebraic coding theory, block design, and various other combinational disciplines, are discussed     

Optical orthogonal codes with large crosscorrelation and their performance bound for asynchronous optical CDMA systems

Optical orthogonal codes (OOCs) are commonly used as signature codes for optical code-division multiple-access (OCDMA) communication systems. Many OOCs have been proposed and investigated. Asynchronous OCDMA systems using conventional OOCs have a very limited number of subscribers and few simultaneous users. Recently, we reported a new code family with large code size by relaxing the crosscorrelation constraint to 2. In this paper, by further loosening the crosscorrelation constraint, we adopt the random greedy algorithm to construct a code family which has larger code size and more simultaneous users. We also derive an upper bound of the number of simultaneous users for a given code length, code weight, and bit error rate. The study shows that it is possible to have codes approaching this bound.     

Impact of spatial correlation on the performance of orthogonal space-time block codes

We analyze the impact of transmitter and receiver spatial correlation on the performance of a multiple-input multiple-output (MIMO) system which applies an orthogonal space-time block code with no channel state information at the transmitter and perfect channel state information at the receiver. We derive a general formula for the bit error rate of a MIMO system with arbitrary number of transmit and receive antennas as a function of the correlation at the transmitter and the receiver. We prove that the diversity advantage is given by M/spl middot/N if M is the rank of the transmit correlation matrix and N the rank of the receive correlation matrix, respectively.     

Extending orthogonal block codes with partial feedback

During the last few years a number of space-time block codes have been proposed for use in multiple transmit antennas systems. We propose a method to extend any space-time code constructed for m transmit antennas to m p transmit antennas through group-coherent codes (GCCs). GCCs make use of very limited feedback from the receiver (as low as 1 bit). In particular the scheme can be used to extend any orthogonal code (e.g., Alamouti code) to more than two antennas while preserving low decoding complexity, full diversity benefits, and full data rate.     

Geometrical properties of orthogonal space-time codes

We discuss the geometrical properties of a transmission scheme with orthogonal space-time codes. In particular, we show that the transmission channel can be interpreted as the rotation of a vector of transmit symbols in an Euclidean space, together with an attenuation and additive noise. We show that the receiver - as intuitively obvious - essentially has to perform a back-rotation. This geometrical interpretation applies to real vector spaces of signals, i.e., the complex transmit and receive symbols have to be split up into their real and imaginary parts.     

Performance of concatenated channel codes and orthogonal space-time block codes

In this paper we analyze the performance of an important class of MIMO systems that of orthogonal space-time block codes concatenated with channel coding. This system configuration has an attractive combination of simplicity and performance. We study this system under spatially independent fading as well as correlated fading that may arise from the proximity of transmit or receive antennas or unfavorable scattering conditions. We consider the effects of time correlation and present a general analysis for the case where both spatial and temporal correlations exist in the system. We present simulation results for a variety of channel codes, including convolutional codes, turbo codes, trellis coded modulation (TCM), and multiple trellis coded modulation (MTCM), under quasi-static and block-fading Rayleigh as well as Rician fading. Simulations verify the validity of our analysis.     

On orthogonal designs and space-time codes

Orthogonal-design-based space-time (ODST) codes of size (n/spl times/n) offer maximum diversity gain advantage and a simple yet optimal decoding algorithm under an arbitrary signal alphabet or constellation A. However, these designs only exist for n=2, 4, 8 when A is real and for n=2 when A is complex. In this letter, we address the question of the existence of ODST codes of other sizes when A is restricted to be a proper subset of either real or complex numbers. We refer to these as restricted-alphabet ODST (RA-ODST) codes. We show that real RA-ODST codes of size greater than 8 that also guarantee maximum diversity advantage do not exist. Without the diversity requirement, RA-ODST codes exist only when A={a,-a}, 0   

Polyphase codes with good nonperiodic correlation properties

N-phase Codes are described which have an autocorrelation function with one main peak and very small side peaks. WithNphases anN^{2}long pulse sequence is generated. Properties have been verified forNup to8and a rule for main peak-to-side-peak ratio is conjectured for largerN. ForNgreater than5. the ratio is substantially better than the best ratios which have been shown for binary bipolar codes. Doppler shift effects appear to be similar to those of linear FM radar pulse compression.     

Bit-error probability for orthogonal space-time block codes with differential detection

Explicit closed-form expressions of the bit-error probabilities are obtained for space-time block codes based on generalized orthogonal designs with differential encoding and differential detection using 2/sup b/-ary phase-shift keying mapping. The frequency-nonselective, block-wise constant Rayleigh fading channel is considered here. The results are applicable to any number of transmit and receive antennas, where the number of transmit antennas is dictated by the available coding schemes.     

OCDMA系统SAC编解码实现方案及性能研究

讨论了基于FBG的谱幅编解码spectral-amplitude-coding(SAC)系统的原理；提出了(N，w,λ)=(q^2 q l,q l，1)光正交码的SAC编解码器实现方案：给出了该系统在码分功率不均匀时，以多址干扰为主的系统信噪比和误码率。分析了谱幅编解码OCDMA系统的应用前景。     

Counterexample of truncated Costas optical orthogonal codes

The following results are proven in this paper: 1) neither periodic autonor cross-correlation of the truncated Costas optical orthogonal code (TC OOC) is upper bounded by 1; 2) TC OOC is a class of (ω(2p-3), ω,2,2) optical orthogonal codes     

New construction of multiwavelength optical orthogonal codes

We investigate multiwavelength optical orthogonal codes (MWOOCs) for optical code-division multiple access. Particularly, we present a new construction method for (mn,/spl lambda/+2,/spl lambda/) MWOOCs with the number of available wavelengths m, codeword length n, and constant Hamming weight /spl lambda/+2 that have autocorrelation and cross-correlation values not exceeding /spl lambda/. In the proposed scheme, there is no constraint on the relationship between the number of available wavelengths and the codeword length, and it is also possible to use an arbitrary /spl lambda/. We show that the constructed code is optimal, especially for /spl lambda/=1. Finally, we analyze the bit error rate of the new code and compare it with that of other optical codes.     

Dynamic assignment of orthogonal variable-spreading-factor codes inW-CDMA

This paper presents an optimal dynamic code assignment (DCA) scheme using orthogonal variable-spreading-factor (OVSF) codes. The objective of dynamic code assignment is to enhance statistical multiplexing and spectral efficiency of W-CDMA systems supporting variable user data rates. Our scheme is optimal in the sense that it minimizes the number of OVSF codes that must be reassigned to support a new call. By admitting calls that would normally be blocked without code reassignments, the spectral efficiency of the system is also maximized. Simulation results are presented to show the performance gain of dynamic code assignment compared to a static assignment scheme in terms of call blocking rate and spectral efficiency. We also discuss various signaling techniques of implementing our proposed DCA scheme in third-generation wideband CDMA systems     

Channel estimation for space-time orthogonal block codes

Channel estimation is one of the key components of space-time systems design. The transmission of pilot symbols, referred to as training, is often used to aid channel acquisition. In this paper, a class of generalized training schemes that allow the superposition of training and data symbols is considered. First, the Cramer-Rao lower bound (CRLB) is derived as a function of the power allocation matrices that characterize different training schemes. Then, equivalent training schemes are obtained, and the behavior of the CRLB is analyzed under different power constraints. It is shown that for certain training schemes, superimposing data with training symbols increases CRLB, and concentrating training power reduces CRLB. On the other hand, once the channel is acquired, uniformly superimposed power allocation maximizes the mutual information and, hence, the capacity.