Orthogonal perfect discrete Fourier transform sequences

Pereira, João; Silva, Henrique

doi:10.1049/iet-spr.2010.0195

Cited by 7 publications

(7 citation statements)

References 7 publications

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“…For the estimation of error probability, an asynchronous TS-OCDMA communication system is similar to an asynchronous DS-CDMA (direct-sequence code division multiple access) wireless communication system with a BPSK (binary phase shift keying) modulation. For both communication systems, the average error probability P e is approximately equal to [26][27][28]…”

Section: Ocdma Error Probabilitymentioning

confidence: 99%

“…For example, the power contrast ratio P/C must be investigated to ensure that the condition (B/2) < Δλ < B will not compromise the correlation properties of the codes written in the SSFBG. Using one of the properties of [27]o r [ 28], the power contrast ratio P/C of Gold codes (excluding one of the two m-sequences of the Gold set) is found to be approximately equal to…”

Section: Ssfbg Can Implement Perfect Sequencesmentioning

confidence: 99%

“…For the estimation of error probability, an asynchronous TS‐OCDMA communication system is similar to an asynchronous DS‐CDMA (direct‐sequence code division multiple access) wireless communication system with a BPSK (binary phase shift keying) modulation. For both communication systems, the average error probability P e is approximately equal to [26–28]

P_{normale} ≃ 1 - ϕ (][, {(\frac{N_{0}}{2 E_{b}} + \frac{1}{6 N^{3}} {false\sum}_{\binom{1 k = 1}{1 k \neq i}}^{K} r_{k, i})}^{- 1 / 2})

where E b is the bit energy, N 0 /2 is the two‐sided spectral density of an AWGN (additive white Gaussian noise) channel noise process, ϕ is the normalised (i.e. zero mean, unit variance) Gaussian cumulative distribution function, K is the number of simultaneous users and r k , i is a function of the aperiodic autocorrelation functions C k , k ( l ) = C k ( l ) and C i , i ( l ) = C i ( l ) of the codes k and i [29]

r_{k, i} = 2 N^{2} + 4 \sum_{l = 1}^{N - 1} C_{k} (l) C_{i} false(l false) + \sum_{l = 1 - N}^{N - 1} C_{k} (l) C_{i} ()(, l + 1)

An alternative expression for r k , i is a function of the aperiodic cross‐correlation function C k , i ( l ) [26]

r_{k, i} = 2 \sum_{l = 1 - N}^{N - 1} C_{k, i}^{2} (l) + \sum_{l = 1 - N}^{N - 1} C_{k, i} (l) C_{k,}

…”

Section: Ocdma Error Probabilitymentioning

confidence: 99%

“…Some steps of the proof of this property can be found in [27] or [28]. For example, the sequences

y = \sqrt{N} \times IDFT (][, m_{r} T^{1} ()(, m_{r}))

and

z = \sqrt{N} \times IDFT (][, m_{q} T^{1} ()(, m_{q}))

are perfect sequences because | χ ( u ⊕ T r v ) χ ( T 1 u ⊕ T r +1 v )| = 1 and | χ ( u ⊕ T q v ) χ ( T 1 u ⊕ T q +1 v )| = 1.…”

Section: Ssfbg Can Implement Perfect Sequencesmentioning

confidence: 99%

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Error probability upper bound for perfect sequences implemented with super‐structured fibre Bragg gratings

Pereira

Silva

2014

IET signal process.

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The success of coherent optical code-division multiple-access (OCDMA) systems is strongly dependent on the optical encoder/decoder technology and on the selection of the correct OCDMA codes/sequences. For this reason, in this study, the authors present a method to implement perfect sequences with Super-Structured Fibre Bragg Gratings (SSFBGs). A new SSFBG power reflection model has been found. They have also derived a property that explains why the SSFBGs should use codes derived from m-sequences. Usually, OCDMA researchers try many different codes into SSFBGs in order to select the SSFBG encoders that result in lower error probability. In the authors work, they show that a SSFBG can be considered to be a perfect sequence encoder. For this reason, the codes written into the SSFBGs should be selected based on their new property. This property permits to design and select quickly the correct codes with low power contrast ratios. In addition, a new error probability upper bound, which is a function of the code family and of its power contrast ratio is also presented. With this new bound, it is not necessary to use an optical simulator to estimate the maximum bit error rate of an OCDMA system, if some power contrast ratios of the selected SSFBG code set are known.

show abstract

Section: Ocdma Error Probabilitymentioning

confidence: 99%

Section: Ssfbg Can Implement Perfect Sequencesmentioning

confidence: 99%

P_{normale} ≃ 1 - ϕ (][, {(\frac{N_{0}}{2 E_{b}} + \frac{1}{6 N^{3}} {false\sum}_{\binom{1 k = 1}{1 k \neq i}}^{K} r_{k, i})}^{- 1 / 2})

r_{k, i} = 2 N^{2} + 4 \sum_{l = 1}^{N - 1} C_{k} (l) C_{i} false(l false) + \sum_{l = 1 - N}^{N - 1} C_{k} (l) C_{i} ()(, l + 1)

An alternative expression for r k , i is a function of the aperiodic cross‐correlation function C k , i ( l ) [26]

r_{k, i} = 2 \sum_{l = 1 - N}^{N - 1} C_{k, i}^{2} (l) + \sum_{l = 1 - N}^{N - 1} C_{k, i} (l) C_{k,}

…”

Section: Ocdma Error Probabilitymentioning

confidence: 99%

“…Some steps of the proof of this property can be found in [27] or [28]. For example, the sequences

y = \sqrt{N} \times IDFT (][, m_{r} T^{1} ()(, m_{r}))

and

z = \sqrt{N} \times IDFT (][, m_{q} T^{1} ()(, m_{q}))

are perfect sequences because | χ ( u ⊕ T r v ) χ ( T 1 u ⊕ T r +1 v )| = 1 and | χ ( u ⊕ T q v ) χ ( T 1 u ⊕ T q +1 v )| = 1.…”

Section: Ssfbg Can Implement Perfect Sequencesmentioning

confidence: 99%

See 2 more Smart Citations

Error probability upper bound for perfect sequences implemented with super‐structured fibre Bragg gratings

Pereira

Silva

2014

IET signal process.

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“…Efficient identification algorithms for linear filters, which require just a multiplication, an addition and a subtraction per sample, have been developed for perfect sequences [8] and have been then extended to imperfect periodic sequences [9]. PPSs have been also considered in areas related to signal processing, such as information theory [10], [11], communications [12], [13], [14], [15], and acoustics [4], [16].…”

Section: Introductionmentioning

confidence: 99%

Perfect periodic sequences for identification of even mirror fourier nonlinear filters

Carini

Sicuranza

2014

2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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In this paper we consider the identification of a class of linear-in-the parameters nonlinear filters that has been recently introduced, the socalled even mirror Fourier nonlinear filters. We show that perfect periodic sequences can be derived for these filters. A periodic sequence is perfect for a nonlinear filter if all cross-correlations between two different basis functions, estimated over a period, are zero. By applying perfect periodic sequences as input signals to even mirror Fourier nonlinear filters, it is possible to model unknown nonlinear systems exploiting the cross-correlation method. Then, the most relevant basis functions, i.e., those that guarantee the most compact representation of the nonlinear system according to some information criterion, can be easily estimated. Experimental results on the identification of a real nonlinear system illustrate the effectiveness of the proposed approach.

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Optimal design of perfect DFT sequences

Pereira

Silva

2013

Physical Communication

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Orthogonal perfect discrete Fourier transform sequences

Cited by 7 publications

References 7 publications

Error probability upper bound for perfect sequences implemented with super‐structured fibre Bragg gratings

Error probability upper bound for perfect sequences implemented with super‐structured fibre Bragg gratings

Perfect periodic sequences for identification of even mirror fourier nonlinear filters

Optimal design of perfect DFT sequences

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