PT106755B - ENCODER AND ELECTRONIC DECODER OF ORTHOGONAL AND PERFECT SIGNS - Google Patents

Abstract

IN THIS INVENTION, AN ELECTRONIC CODE AND DECODER OF ORTHOGONAL SIGNS ARE PRESENTED, WHICH ARE PERFECTLY IMMUNE TO DIAPHONY INTERFERENCES, BASED ON N ELECTRONIC MODULES OF L = 2 ^ N LENGTH THAT CAN BE PERFORMED LINEARLY OR RESURCUALLY. BY DEFINITION, A DISCRETE SEQUENCE "A" IS PERFECT (OR PERFECTLY IMMUNE TO THE DIAPHONY) WHEN ITS PERIODIC SELF-RECORDING FUNCTION CAA (T) IS IDENTICAL TO A UNITARY IMPULSE Δ (T) (DIRAC DELTA FUNCTION). ADDITIONALLY THE REAL PART AND IMAGINARY PART OF THOSE NEW SEQUENCES ARE ORTOGONAL FOR ANY CYCLICAL DISPLACEMENTS BETWEEN THEM. EITHER THE GENERATED ELECTRONIC SIGNS ARE PERFECTLY INHIBITED TO THE DIAPHONY (OF MULTIPLE PATH) INTERFERENCES FOR ANY DELAYS BETWEEN EACH PAIR OF DIFFERENT AND LENGTH SIGNALS. THESE PERFECT ORTOGONAL SEQUENCES CAN BE IMPLEMENTED BY COMPLETING COMPLEX CIRCUITS COMPARED BY VARIOUS TYPES OF ELECTRONIC LOGIC DOORS, OR BE HARDWARE. More specifically, integrated circuits for specific applications (ASIC), programmable electronic devices such as FPGA (FIELD-PROGRAMMABLE GATE ARRAY) or CPLD (COMPLEX PROGRAMMABLE LOGIC DEVICE) CAN BE USED. GENERATORS FROM NEW ORTOGONAL AND PERFECTLY IMMUNE SIGNS TO DIAPHONY INTERFERENCES CAN BE USED IN SYSTEMS OF DETECTION OR ANALYSIS OF SIGNS APPLIED TO ROBOTICS, MULTIPLE COMMUNICATIONS SYSTEMS AND RADAR APPLICATIONS.

Description

Perfect orthogonal electronic signal encoder and decoder

Technical field and state of the art of the invention

The present invention is primarily intended for spectral spread code encoding data transmission systems using an Orthogonal Perfect Discrete Fourier Transform Golay (OPDG) Orthogonal Perfect Discrete Fourier Transform (OPDG) , which are perfectly immune to interfering signals of crosstalk (undesirable signals resulting from multiple path reflections). The invention is not limited solely to that field of application, others such as sonar or radar systems may utilize the present invention.

By definition, a sequence of discrete and finite length values is said to be perfect if the lagged periodic autocorrelation values are all null, as with a Dirac function. In practical terms, a CodeDivision Multiple Access (CDMA) communication system that receives a perfect sequence should be immune to crosstalk interference caused by multiple similar signals that are received simultaneously and have variable time delays. For example, these multiple interfering signals may be generated by multiple reflections on surrounding obstacles or mountains between a transmitter and a radio frequency (RF) CDMA receiver. The delay of each signal is proportional to the distance traveled between the multiple reflections. For example, the signal received without delay may correspond to a straight-line RF transmission.

Two sequences of a given set are called orthogonal if the cross-correlation function is zero for a zero offset. Any codes or sequences that have a perfect or approximately perfect autocorrelation function and are orthogonal or near orthogonal are ideal candidates for use in DS-CDMA (Direct-Sequence Code-Division Multiple Access) asynchronous communication systems.

Alternatively, they can also be used in initial equalization systems, transmission channel estimation systems, communications synchronization systems, radar systems, sonar systems, and many other systems where there are problems with signal reception that are being contaminated by multipath signals. This contamination is considered to be a crosstalk interference. A CDMA receiver should be able to discern several distinct signals received simultaneously if all signals are orthogonal (for any offsets or these codes are bipolar {-1, +1}, then they can be used and transmitted with modulation).

BPSK (Binary

Phase

Shift Keying). Generally bipolar or approximately bipolar codes have desirable low PAPR (Peak-to-their implementations with electronic circuits) values. Another DS-CDMA system is the amount of orthogonal available and which may be important property in orthogonal codes or almost simultaneously used in asynchronous systems Gold orthogonal codes are a good example of this and have excellent correlation properties.For example, it is possible to generate 32 length 32 Gold orthogonal codes that can be great candidates for DSCDMA systems.

Alternative CDMA bipolar codes may be derived from the

Sequences

Perfect Orthogonal DFT

Perfect Orthogonal

DFT

Sequences.

These codes are great candidates in communications systems where it is desirable to minimize the effects

MPI (Multipath

Interference

Interference

Multipath),

MCI (Multicarrier

Interference

Interference

Multiport),

ISI (Inter Symbol)

Interference

Interference

Intersymbolic)

MAI (Multiple

Access Interference).

MAI and ISI interference may be reduced if the selected codes are orthogonal for any offsets or if they have very low cross correlation values. However, codes or sequences should also have very low average values of lagged aperiodic autocorrelation (in absolute values). This last property ensures a low error rate of code detection used in a DS-CDMA system with BPSK modulation. Null or very low cross-correlation values (for phase and lagged values) will allow more codes to be used simultaneously in CDMA communication. In other words, crosstalk interference on a CDMA receiver will be zero or very low.

Low cost, low power Zigbee wireless communication system is defined in IEEE 802.15.4-2003. The performance of this Zigbee communication system can be improved by using alternative PN (pseudo-random noise) sequences, with better correlation properties that are immune to crosstalk interference (or multipath interference). One solution was evidenced in the article by the two inventors: Pereira, J. (member of the Telecommunications Institute and the Polytechnic Institute of Leiria); Silva, Η. A. (member of the Institute of Telecommunications and the University of Coimbra), Alternative Zigbee Codes Derived From Orthogonal Perfect DFT

Sequences, Proc Sixth IEEE Conf.

on Wireless Communication and

Sensor Networks

WCSN, Allahabad, India, Vol. 1, pp. 211

216,

December, 2010. Another solution was presented by the same inventors in the article:

THE. ; Orthogonal perfect discrete Fourier sequences,

IET Signal Processing, Vol.

6, No.

2, pp. 107

113, April, 2012. The above articles attempt to explain why the importance of autocorrelation and cross-correlation properties is important when designing a data communication system using the Code-Division Multiple Access (CDMA) transmission technique.

Golay complementary code pairs are great candidates for use in communication or radar systems. Publication Example: P. Donato, M. Funes, M. Hadad, D. Carrica, Optimized Golay Correlator, Electronics Letters 45 (7) (2009) pp. 380-381.

There are alternative codes to Golay codes that have a slight DS-CDMA performance improvement. These codes are M-ary Mutually Orthogonal Complementary codes

Gold Codes Whose publication is: Pereira, J.; Silva, Η. THE.;

M-ary Mutually

Orthogonal

Complementary Gold Codes, Proc

European Signal

Processing

Conf.

EUSIPCO,

Glasgow, United

Kingdom, pp. 1636

1640, August, 2009.

Unfortunately, favorable autocorrelation characteristics are generally achieved to the detriment of cross-correlation characteristics and vice versa. In other words, codes that have low cross-correlations generally have high-offset autocorrelations. And conversely, when codes are scaled to have low (or null) lagged autocorrelations, they often cross-correlate with higher values. For this reason, there must be a compromise between the two autocorrelation and cross-correlation properties when sizing a specific code set for a CDMA communication system. At the same time, it is also desirable to achieve these optimal correlation properties in the periodic and aperiodic case. Based on these objectives, a patent was proposed in 2007: GOLAY-CODE GENEATION, Pub. No .: US2007 / 0113159 Al, which discloses a Golay code generator circuit. This circuit generates several codes that will be used to identify a piconet of a CDMA Ultra-Wideband (UWB) communication system. That patent claims a code generator derived from Golay codes which has a periodic cross-correlation value of less than 16 and a periodic autocorrelation function with a high correlation peak and null values around that peak. Although US2007 / 0113159 A1 discloses a code generator with optimal correlation properties, it is always possible to find one that can overcome these periodic autocorrelation and cross-correlation properties.

The present invention allows the construction of a new electronic circuit that generates signals with better periodic and aperiodic autocorrelation and cross-correlation properties. For example, the new electronic circuitry generates signals that have a periodic cross-correlation value much lower than 16 (up to zero for a code pair) and a periodic autocorrelation function with a high correlation peak and null values for all offsets. (or delays) of the code (periodic autocorrelation function equal to Dirac pulse). Figures and tables with various correlation properties are shown throughout this document which show the advantages over Golay codes disclosed in US2007 / 0113159 A1 and US2011 / 0209035 A1.

In addition, compared to patent documents US2007 / 0113159 AI and US2011 / 0209035 A1, the present invention differs from them in that it allows codes to be generated more efficiently if a recursive electronic module is used. When codes generated by the new CODEC are long, recursion will result in a reduction in electronic components and a reduction in signal generation times of the new CODEC.

For interpretation purposes it is meant that long code is understood to be longer than 42 bits (in an LFSR current definition of the state of the art see http://www.gaussianwaves.com/2011/02/codes -used-in-cdma-2 /.

In fact at a power of 2.64 is the first higher value

42, with the previous value of 32 bits still being short, as the new OPDG codes of the present invention have lengths equal to a power of 2, we must consider that a long code will be at least 64 bits long (64, 128, 256, 512,

The present invention generates many more codes than those disclosed in US2007 / 0113159 A1 and US2011 / 0209035 A1. In addition, the signals or codes of the present invention are more immune to crosstalk interference than Golay codes. This best performance was confirmed by simulation and the results were presented in figure and table forms throughout this document.

To prove the usefulness of Golay codes, simply verify that they are often used in communication systems. For example, PCT / ES2001 / 000160 METHOD FOR SPREAD SPECTRUM DIGITAL COMMUNICATION BY GOLAY COMPLEMENTARY SEQUENCE MODULATION discloses a modulator that uses these codes. It is added that with the present invention it will be possible to find alternative codes with better crosstalk immunity than Golay codes.

Description of the invention

In this invention, a Golay electronic code generator is drastically transformed to construct a new electronic generator of a pair of perfect orthogonal sequences of length L = 2 ^N , based on N electronic modules (or N floors). These modules can be used recursively to increase the efficiency of the electronic circuit (shorter signal generation time and less hardware).

By definition, a discrete sequence a is said to be perfect when its periodic autocorrelation function Caa (t) is identical to a unit impulse ó (t) (Dirac delta function). In other words, these sequences are immune to crosstalk interference (undesirable multiple pathways).

Remember that Golay code pairs are not perfect sequences. With a pair of Golay codes {a, b}, the impulse only obtained after summing its two autocorrelation functions (Caa

Cbb). Another disadvantage of

Golay is that they are not orthogonal for any cyclic offsets or offsets between codes a and b of a pair (this last disadvantage is eliminated with the present invention, as this latter property will be true with the invention). Despite the disadvantages of Golay codes, you can find them in numerous applications. For example, signal detection or analysis systems applied to robotics, multiple communications systems and radar applications.

The present invention provides a solution for radically transforming the Golay code electronic circuit into a novel electronic circuit generator (101) (601) of perfect orthogonal sequences whose real part and imaginary part are real orthogonal sequences for any cyclic displacements t between them ( ORe [a] im [a] (t) = 0 and C _Re [b] im [b] (t) = 0 with 0 t <L when L> 1). That is, in other words, the electronically generated signals are perfectly unmindful of crosstalk interference (null cross correlations) for any delays between each distinct signal pair (Re [a] and Im [a] or Re [b] and Im [ b], of length L). These specific crosstalk interferences appear when at least two signals are received simultaneously, and one of them can even arrive with any delay (asynchronous reception). Although the electronic circuit receives two signals simultaneously, the electronic decoder 105 can extract the main signal as if the second (interfering) signal was nonexistent. In mathematical terms, both signals are considered orthogonal sequences for any delays (or cyclic offsets).

These perfect orthogonal sequences can be implemented using firmware or hardware. For hardware, application specific integrated circuits (ASIC), programmable electronic devices such as FieldProgrammable Gate Array (FPGA) or Complex Programmable Logic Device (CPLD) may be used.

The present invention is a circuit for implementing an electronic CODEC (101) (601) of a complementary pair of orthogonal and perfect sequences (OPDG). Pairs (OPDG1 and OPDG2) are discrete sequences of finite length L that can be transformed into actual codes or bipolar codes {-1, +1} in an equal amount to length L. All of these generated code types have great properties of auto and periodic and aperiodic cross correlation.

Tables I, II, III and IV are presented to highlight the viability of the new codes compared to the Golay codes and tables V, VI, VII and VIII to highlight the applicability of the new OPDG codes compared to another set. well-known code set and called the Gold orthogonal code set. These gold orthogonal codes exist in the same amount as the new OPDG codes. That is, the amount is equal to the length L.

The first column of all these tables presents the different code sets that are under analysis. The parameters analyzed are in the following columns and are: the maximum phase autocorrelation; the maximum lagged autocorrelation; the average lagged autocorrelation; the in-phase cross correlation; the lagged cross correlation; and the average lagged cross correlation. The tables also indicate whether the mathematical correlation functions (autocorrelation and cross correlation) were calculated to be of the type, periodic (there is no time interval between transmission of the same code) or aperiodic (there is a time interval L between transmission of the same code). All the different types and parameters of correlation functions, shown in the tables, were calculated based on standard mathematical definitions.

Tables I, II, III and IV show different correlation properties for different sequence sets and allow to verify that some of the properties of OPDG sequences and OPDG derived sequences are better than Golay sequences.

Tables V, VI, VII and VIII show different correlation properties for different sequence sets and show that some of the properties of OPDG-derived bipolar sequences are better than those of Gold orthogonal sequences and exist in the same amount L (equal to at length).

Codes {tone no-iwalkadas periodic correlations .. L = 32, q = -l) Max-phase autocorrelation Offset autocorrelation max Offset Aoto-Correlation In-phase crossword correlation Offset cross correlation {Golay 1 £ Li 32 12 1.55 0 12 IC-PDG 1) U {QPDG 2) 32 B 0 0 SgnER (OPDG 1}] U SgnlRefOPDG 2j] 32 12 3.01 0 s Ref OPDG 1} U 1) 13 5.3 2.11 0 yes Sgn [Re (OFOG 1)] ϋ 32 12 3.Ú4 2 6th Re {OPDG 2) U 2J Ifi $., £ 2.17 0 0 32 s 4.13 0 3 32 0 0 6th 16 Sgn {Re (OPDG U Sgr ^ RefOPDG2j-Hm (OPDG2}} 32 3 2 _r S4 0 12

Table I - Autocorrelation property and periodic cross-correlation of various length codes L = 32.

Table I reveals some of the autocorrelation and periodic cross-correlation properties of various codes derived from OPDG codes when the encoder of Figure 7 is used. These codes are compared to Golay codes of the same length (L = 32). Perfect autocorrelation property is evidenced with the (OPDG 1) U codes (OPDG 2) and the [Re (OPDG 1) codes.

Im (OPDG 1)] U [Re (OPDG 2) + Im (OPDG highlight that bipolar codes Sgn [Re (OPDG 1) + Im (OPDG 1)] U

Sgn [Re (OPDG + Im (OPDG 2)] have a lower autocorrelation offset value than the Golay codes.

In terms of periodic cross-correlation and periodic autocorrelation lagged maximum value, the Re (OPDG 1) U codes

Im (OPDG 1)

Re (OPDG 2) U Im (OPDG 2) reveal better characteristics than Golay codes.

The same tests from the previous table were performed using autocorrelation and aperiodic cross correlation functions.

Codes {with standardized aperiodic corrections, 1 = 32, q = -lj Maximum in-phase autocorrelation Maximum Offset Self-Interaction * Average lagged autocorrelation In-phase cross correlation Offset cross offset {GoíaylJUÍGoiayí} 32 7th 1Λ Q 13 (OPOG 1; U | C <PS> G 2} 32 7.5 2.47 0 2Q4 SgnjRe (OPIZ> G 1) 1 U.Sgn {Re (OPDG 2) 1 32 15 3.24 0 7th 8e (OP&G 1} U! Rn {OPDG 1! 13 7.4 1.33 0 2.65 SgniReJOPDG 1) 1 VSgnitoJOPDG 10 32 15 3.05 2 7th ReJOPOS 2) U (mjOPDG 2.J 16 7.4 1.79 0 2.92 Sgn {Re (OPDG 2)) U Sgn [lm (OPDG 2)} 32 11 3.59 Q 9th {RegOPDG i) -Hm {OPDG 0: fte {OPDG 2) -Hm {OPDG 2) 1 32 5.9 '2.01 0 16.1 Sgn: Re (OP »G 1) + im (OPOG 1) 1 U .Sgn [Re (OPDG 2} <- magnet (OP» G 2} 1 32 3 2.35 0 12

Table II - Autocorrelation property and aperiodic cross-correlation of several length codes L = 32.

Once again the bipolar codes Sgn [Re (OPDG 1) + Im (OPDG 1)] U

Sgn [Re (OPDG 2) + Im (OPDG 2)] have excellent autocorrelation and cross correlation properties. Similarly, the other codes derived from the OPDG codes also show excellent results compared to the Golay codes.

Codes (with normalized periodic correlations, 1 = 64 cj = -l} Maximum in-phase autocorrelation Maximum offset autocorrelation Autolorrelsçac average lagged In-phase cross correlation Maximum offset cross correlation (Golay 1 | 6 (Gclsy 2) 64 12 2.03 Q 24 {OPDG 1 {«{OPDG 2) 64 ΰ 6th 0 40.8 SgnJReJOPDGlH U $ gn {Ke (OPDG;} 64 20 7 _X 11 0 16 RejOPDG W imjpPDG 1} 34 12 2.88 0 0 Sgn (Re ('OPDG 1; 1 U Sgri [magnet? OG 1}) 64 23 7.78 2 14th SeJOPDG 2) D! M (OPDG 2) 32 12 2.91 0 0 Sgn {Re {OPDG 2) 1 D Follow! SmiOP & G 2) 1 64 16 7.62 0 16 {RejOPDG 1} + im ('OPDG 1}) U {RejOPDG 2; + in5 (OPDG 2;) 64 9th 9th 0 32 Sgn (Re {O? 8G 1 Hm (OPDG J1 ϋ Sgn [Re {OPDG 2) -Hm {OPDS 2) { 64 12 5.21 0 24

Table III - Autocorrelation property and periodic cross-correlation of several L-length codes.

The same tests in Table I were performed using similar 64 length codes (derived from OPDG codes). The new results obtained are presented in table III. Again, some of the codes derived from OPDG have better autocorrelation and periodic cross-correlation characteristics than Golay codes.

Normalized aperiodic correlation codes, 1 = 64, <F ~ 1) Airtocorrection The maximum lagged correlation The average lagged biochemistry In-Phase Cross Correction Maximum offset cross correlation {Golay 1'i C (Golay 2} 64 13 1.83 0 19 (OPDG 1} B (OPDG 2} 64 15 3.19 G 40.3 Sgn [Re (OPDG U 2} 1 64 15 5.12 9th 17 8e (OPDG 1) li Sm {OPDG I; 34 1.4 2.52 0 5.16 Sgn ^ OPDG 1} I B Sgn {hn (OPDG 1}} 64 25 5.53 2 14th SefOPDQ 2} U 32 M 2.55 0 5.52 Sgn [Re (OPDG 2) J ϋ Sgn [! M (OPDG 2} | 64 19 5.18 0 12 (Re (OPDG l} + lm (O?> DG U {Re (OPDG 2} * im (OPDG 2}] 64 11 2.46 O 36 Sgn [Re (QPDG 1) + magnet | OPDG 1}] · Sgn [Re (OPDG 2) + 5m (OPDG 2} 1 64 14th 3.53 Q 24

Table IV - Property of autocorrelation and aperiodic cross correlation of various length codes L = 64.

The same tests as in the previous table (table III) were performed using autocorrelation and aperiodic cross correlation functions with the same length codes 64.

For example, codes

Sgn [Re (OPDG 2)]

U Sgn [Im (OPDG 2)] show better cross-correlation characteristics than Golay codes.

Codes (with normalized periodic corrections, 1-32, <$ = -!] Maximum in-phase autocorrelation Maximum lagged autocorrection Correctness: ·. ' average lag Creation in-phase crusade Run! maximum lagged cross action Run: Take the medium-offset crusade Orího & ofis! Goid Cedes, Q = 32 32 20 4.43 ΰ 20 12.25 }} + D ^ JnXOI> DG 1}], Q = 52 32 β β 23.8 23.8 18.24 Sgn {Re (OPGG ·>)] - φ4! Ίϊΐί 3PBS 1)}}. 0 = 32 32 12 3.17 24 24 14.7 ReiOPOG 2} -f-Di [opiOPDG 2}], Q = 32 32 0 and 21Λ 21.8 18.17 Sgn (Re (OPDG 2; '+ 3; II mt, OPDG 2} p, Q = 32 32 1d 3.29 24 24 14.37

Table V - Autocorrelation property and periodic cross correlation of various length codes L = 32.

In the table

V are presented autocorrelation and periodic cross-correlation properties of various length codes L

32. The reference codes chosen are orthogonal Gold codes that exist in an amount equal to the length and have excellent correlation properties.

The other codes, derived from the OPDG codes, selected in this comparative test are Re (OPDG 1) + Di [Im (OPDG 1)], Sgn {Re (OPDG 1) +

Di [Im (OPDG 1)]}, Re (OPDG 2) + Di [Im (OPDG 2)] and Sgn {Re (OPDG 2) +

Di [Im (OPDG 2)]}. All selected codes exist in quantity Q = 32. Re (OPDG 1) + Di [Im (OPDG 1)] and Re (OPDG 2) + Di [Im (OPDG 2)] codes stand out from the others because they are codes. with perfect autocorrelation. Bipolar codes Sgn {Re (OPDG 1) +

Di [Im (OPDG 1)]} and Sgn {Re (OPDG 2) + Di [Im (OPDG 2)]} reveal maximum and average lagged autocorrelation values lower than Gold's orthogonal codes.

Codes {with standard ape-rior corrections, 1 = 32, q = -l) Maximum in-phase autocorrelation Max Offset Self-Correction Autocorrection average lag Correction in-phase crusade Maximum Offset Cross Correction Medis offset cross correlation Qrthog onai Gcid Codes. Q-32 32 12 2.98 8th 13 10.34 MOFOG Ιί-Φ ^ ηΐϊ OPEK3 Ijj, 0 = 32 32 8.4 1.92 23.8 23.8 18.11 Sgo; Re (OPDG 0 = 32 32 14th 2.71 24 24 14.29 FefOPDG 2> + D; (MOPE> G 2J] _; 0 = 32 32 7.5 1.76 21.5 21.5 16.38 2}}}, Q = 32 32 12 2.65 24 24 13.03

Table VI - Property of autocorrelation and aperiodic cross correlation of various length codes L = 32.

Table VI presents the properties of autocorrelation and aperiodic cross-correlation of several length codes L = 32. The reference codes chosen are the same as in table V. The codes Re (OPDG 1) + Di [Im (OPDG 1)], Sgn {Re (OPDG 1) + Di [Im (OPDG 1)]}, Re (OPDG 2) + Di [Im (OPDG 2)] and Sgn {Re (OPDG 2) + Di [Im (OPDG 2)]} show maximum and average lagged autocorrelation values lower than Gold's orthogonal codes. These latter properties will influence the optimal error detection probability values of figures 14 and 15.

Codes (with normalized periodic correlations, 1 = 64, q = -1) Maximum in-phase autocofrelsção Maximum lagged auto-erosion Average lagged autocorrelation In-phase crosscretion Correlation maximum lagged crusade Offset cross correlation 0-rthogctn.si Goid Cedes, Q = 3‘2 64 28 5.93 0 36 20.9 RejOPDG 1} + & j [im (OPDG 1}], 0 = 32 64 0 D 42.7 42.7 34.95 Sgn (Re (OPDG t! M (OPD-G 1)]}, 0 = 32 64 24 4.64 44 44 25.94 Re (OPOG 2j + Du? Rn (OPCG 2 & 0 = 32 64 0 0 43.7 43.7 34> 91 Sgn {Re {OPDG 2jj + DIMCOPDG 2} Γ ·. 0 = 3'2 64 20 4.65 46 46 26.28

Table VII - Autocorrelation property and periodic cross-correlation of several length codes L = 64.

The same tests in Table V were performed with the same codes when the length is incremented to the value 64. Again the codes Re (OPDG 1) + Di [Im (OPDG 1)], Sgn {Re (OPDG 1) + Di [Im (OPDG)

1)]}, Re (OPDG 2) + Di [Im (OPDG 2)] and Sgn {Re (OPDG 2) + Di [Im (OPDG

2)]} reveal maximum and average values of lagged autocorrelation lower than Gold orthogonal codes.

Codes {with aperiodic cones normalsza-das, L = 64, q = -ii Maximum in-phase traction Maximum lagged autocorrection AulocoireAverage Offset In-phase cross action Maximum lagged crossover Medium Offset Cross Belt Orihcgor-a: Gcíd Codes, G = 32 64 21 1.46 W 21 13.35 lj}, 0 = 32 64 16 2.67 42.7 42.7 14.34 SgntRetOPEfo 0 = 32 64 21 3.73 44 44 25.92 Re (DPDG2 DjMOPDG2}} + l _f Q = 32 64 17 2.65 43.7 43.7 32.11 Sgr-Rf OPOG 2. 0 = 32 64 20 3.7? 46 46 23.24

Table VIII - Autocorrelation property and aperiodic cross-correlation of several length codes L = 64.

The same tests in Table VI were performed with the same codes when the length is incremented to 64. Again the codes Re (OPDG 1) + Di [Im (OPDG 1)], Sgn {Re (OPDG 1) + D; [Im (OPDG 1)]}, Re (OPDG 2) + Di [Im (OPDG 2)] and Sgn {Re (OPDG 2) + Di [Im (OPDG 2)]} show maximum and average autocorrelation values. less than Gold's orthogonal codes. These latter properties will influence the optimal error detection probability values of figures 14 and 15.

Detailed Description of the Invention

Although the invention may be represented by various forms and modifications, the detailed explanation thereof, as well as some examples of its preferred embodiments, are given below, in addition to the detailed explanation of the presented figures. It should be understood that the presentation of these examples is not intended to limit the invention to a particular disclosure form, but rather to contemplate all possible modifications, equivalents, and alternative representations which are in the same spirit as the invention.

It should be noted that the set of an encoder (101) (601) and decoder (105) is called CODEC, so when referring to the present invention we also refer to the terms of: new CODEC; new CODEC OPDG electronic; electronic code generator OPDG; or simply by electronic code generator circuit. You will also find alternative terms that designate only one of the features of the new CODEC. For example: electronic OPDG encoder; electronic OPDG decoder; generator circuit (encoder) of a pair of perfect orthogonal sequences (OPDG 1 and OPDG 2); or decoder circuit of a pair of perfect orthogonal sequences.

The first block (Fig. 1) - Electronic OPDG Encoder (101) represents the present invention, namely an electronic OPDG code generator (101). The pair of OPDG codes are represented by ^a NM and ^b N [t]. The second block schematics the last floor of the DAC encoder (102). The third block (Transmission Medium) (103) symbolizes the means of transmitting the codes signals ^to N, x [t], ^to N, Y [t], b _NX [t] _and b _NY [t]. includes the first floor block of the ADC decoder (104) whose inputs are the previous noise contaminated signals. The fifth block 105 implements an OPDG code correlation function and serves to decode the OPDG codes of the present invention. Confirmation of correct detection will be made by a Threshold Detector block (106), whose function is to determine whether or not the correlation level performed by the previous block (Electronic OPDG Decoder (105)) is above a certain predefined level. Above this level the OPDG code is detected. Below this level the OPDG code is not detected.

The present invention includes a code generating electronic circuit (Figure 2 a)) which has a perfect periodic autocorrelation function equal to the unit pulse (or Dirac delta function). The OPDG 1 and OPDG 2 code pairs are orthogonal and perfect finite length L codes. This electronic coder consists of N basic modules which are composed of at least one adder (201) (202) (209), at least one differentiator (221) (222) (229) and at least one multiplier (211) (212) (219) for a Twiddle Factor PA = exp (-J2n / A).

All elements of a basic module can be implemented by hardware (electronics). The q value can take the value -1 or +1. The value t represents the index of the sequences (or the temporal displacement). The generated orthogonal and perfect sequences have lengths L ₂ n

The value A represents a constant input signal (or constant sequence of L = 2 ^N discrete values) that can take values all equal to -1 or +1.

The value A may take different actual values if, for example, an autocorrel normalization is implemented.

The specific links of the three operators (from the basic module in figure 2 a)) will allow the generation of OPDG codes of a certain length. This generation is a recursive process. That is, the generation of an OPDG code of length 2 ^N is obtained based on a code of length 2 ^W_I . The first module will be generated using a constant unit input (eg A = ± 1). The value A is a constant vector that can be equal to 1 when the OPDG code user wants to transmit binary information 0 and can be A = -1 when the user wants to transmit binary information 1. Each basic module will use the outputs of the previous basic module. The outputs of the last basic module will be used to generate an OPDG code pair. The output ^at N [t] is designated by code OPDG 1 and the output [t] is designated by code

OPDG 2. This OPDG code pair represents the result of the recursive coding process of the present invention.

The unique properties of these codes are achieved based on the specific links of each basic electronics module. The specific links within each electronic basic module and the recursive chaining of each module are fundamental in the present invention and allow to generate very specific code pairs that have perfect autocorrelation (same as null cross correlation. Unlike OPDG codes have perfect autocorrelation without adding the two autocorrelation of each OPDG impulse code

) in Dirac) and in Golay, the to be required 1 and OPDG 2. THE

A disadvantage of Golay codes is that only the two individual autocorrelation functions of each complementary Golay code are summed between them.

The present invention may use electronic basic modules in a recursive process (Figure 2b)). The two outputs of a basic module (figure 2 a)) are stored in a memory component. This memory component will have two outputs that will be used as base module inputs when the module index n (equal to the recursive process iteration) is greater than or equal to 2. In the first iteration, when n = 1, the module inputs will be equal to a constant vector equal to A and of length L = 2 ^W.

The decomposition of perfect orthogonal complex sequences into their real and imaginary parts (eg using hardware) takes into account the following aspects:

• the outputs N, x [t], N, Y [t], b _NX [t] b _NY [t] g _to Figures 3 a), 3 b) and 1, are discrete analog value sequences resulting from DAC (Digital-to-Analog Converter) converters (308) (309) (318) (319);

• sequence selection is based on two multiplexers (MUX) (307) and (317);

• D values; 302 and 312 are memory components and delay to implement the effect of a

time shift the sequences ^to N [t] = cyclic; OPDG 1 and ^b _N [t] = OPDG 2 are sequences complex that can be decomposed and transformed electronically in codes real or in real codes

bipolar;

and presents the following steps of the transforming electronic circuit of these sequences ^at N and B _N: decomposing these complex sequences into two real sequences using a Re {} and Im {} (301) and imaginary electronic circuit respectively;

2.

creation of time delayed sequences of a value equal to the index i of a sequence Im {} with respect to sequence Re {} by two electronic circuits D;

3

generation of bipolar sequences {-1, +1}, by another electronic circuit identified by Sgn ± 1 (signal function), the electronic circuits MUX (307) and (317) will allow selecting the sequence to be used;

5. the last part of the electronic circuit of the transformer sequences N _N b is to use simple digital / analog converters (DAC) (308) (309) ( 318) (319) ;

6. The four resulting output sequences will be designated by the sequence N, x [t], ^& Ν, υ [5, _X [t] _{θ β Ν,} γ [ί] and depend essentially multiplexers MUX (307) and ( 317).

The electronic decoder (figure 4 a)) implements an autocorrelation function of the input when the correct sequences are sequences ^{(η νΝ} = b ^{η νΝ} _C [t] = B _n [t]), in the _case of a correct detection is obtained if two optional types of output signals: an autocorrelation function proportional to the unitary impulse δ (t) and a constant function proportional to the amplitude A of the encoder of Figure 2 (a). In case of incorrect detection a null cross correlation (t = 0) is obtained.

The invention also includes an electronic decoder of an OPDG 1 and OPDG 2 sequence pair. This circuit is comprised of N basic electronic modules which are composed of an adder (401), a differentiator (421) and a multiplier (411) by one. Twiddle Factor signal Pi / 1 = exp (-J2n / A). Once again, the value q can take the value -1 or +1 and the value t represents the index of the sequences (or the time shift). The last module (432) of this circuit electronically implements the real part of a Fast Fourier Transform (FFT) identified by Re {FFT}. The output of this electronic transform will be equal to a Dirac unit pulse with amplitude equal to A [q] ^w 2 ^{2w + 1} . This pulse will appear to be shifted temporally from a value of 2 ^W -1. Re {FFT} block input is a complex value that can be used to extract a constant sequence equal to the value A ² 2 ^{2w + 2} . This operation requires the use of an electronic circuit that can implement the squared value of the absolute value (equal to the multiplication operation of a complex sequence with its conjugate). Depending on the type of application, blocks 432 and / or 433 may be omitted.

OPDG electronic code decoder (105) can use the basic modules in a recursive process (Figure 4 b)). The two outputs of a basic module of figure 4 a) are stored in a memory component. This memory component will have two outputs that will be used as base module inputs when the module's index n (equal to the recursive process iteration) is less than or equal to N. In the first iteration, when η = N, the module inputs will be equal to the codes to be decoded (vector pair: OPDG 1 and OPDG 2 of length L = 2 ^W ). In the last iteration, when n = 1, the two outputs can be summed as with the OPDG decoder (105) of figure 4 a), when using the summing component (431).

In short, the electronic and perfect encoder contains:

a code generator with

N basic modules each consisting of two inputs, two outputs, one adder one differentiator one multiplier one generator of a twiddle factor signal interconnected as follows, in each basic module:

i. the second input and the twiddle factor generator element are connected to the multiplier inputs;

ii. the multiplier output and the first input are linked to the adder inputs;

iii. the first input and the output of the multiplier are linked to the differentiator inputs;

iv. the first exit is directly connected to the first entrance of the next floor and the second exit is directly connected to the second entrance of the next floor;

v. Inputs and outputs are adapted for input and output signals of 2 ^N length;

B. top floor of the DAC encoder consisting of a complex signal extractor (301) (311), memory components (302) (312), adder (303) (313), converter of a signal into a bipolar signal (304) (305 ) (306) (314) (315) (316), multiplexers (307) (317) and analog digital converters (308) (309) (318) 319), interconnected as follows:

i. one output is coupled to a complex signal extractor and its output is coupled to a memory component that implements temporally delayed sequences of a value equal to the index i of a sequence Im {} with respect to the sequence Re {};

i. the memory component output and one of the complex signal extractor outputs are connected to the inputs of a adder, the output of that adder being connected to the input of a multiplexer;

iii. The multiplexer inputs are connected to all of the above outputs and their output is connected to one or more digital analog converters.

Description of the figures

Figures 1, 2 a), 2 b), 3 a), 3 b), 4 a) and 4 b) show how to implement the invention (electronic CODEC) for an OPDG code pair.

Figures 5, 6, 7, 8 were used to exemplify the applicability of OPDG codes when the length is 32.

Figures 9, 10, 11, 12, 13, 14 and 15 show the superiority of OPDG codes over Golay codes or Gold orthogonal codes.

Figure 1 - Simplified diagram of applying the actual OPDG codes in a noise communication data system according to the embodiment of the invention shows how to integrate all electronic circuits of the invention into an OPDG sequence coding and decoding communication system . 0 encoder

Electronic OPDG (101) is identified by the block

OPDG encoder and represents the circuits of the

B) . The electronic sequence transformation circuit ^at N designated by the block

Top floor of encoder with

DAC represents the circuitry of the figures

The four transmission means are designated by the block. Transmission means may be received with an additive noise signal called

Noise.

sequence receiving circuit, contaminated with noise, is designated by the

First floor decoder with ADC and basically represents an electronic circuit converter (ADC) and filters to minimize the effect of noise. The second to last block in Figure 1 represents the OPDG decoder designated by

Decoder

OPDG (105) may be equivalent to the electronic circuit of

b) or the simplified circuit of the figure

6

In addition, the figure is a diagram of an example of using OPDG codes when the electronic circuits of the

b) are incorporated into the present invention.

OPDG Encoder Block (101) is the electronic codes generator

OPDG of Figure 2 Electronic OPDG Codes Detector Transmitted on Transmission Medium (103)

CDMA in the presence of noise or electronic interference.

The detection or not of a code

OPDG assigned to a particular user will be proportional to the information transmitted by the user of the OPDG code. Block 102 represents the invention illustrated by figures 3 a) and 3 b). Block 104 represents a filter and an ADC converter. Block 106 represents a threshold detector.

Figure 2 a) - Generating (encoding) circuit of a pair of perfect orthogonal sequences (OPDG 1 and OPDG 2) of length L = 2 ^N , according to the embodiment of the invention (Pi / i = exp (-j2n / L) is shows the electronic encoder (or generator) 101 (601) of a pair of discrete, orthogonal and perfect sequences ^at N [t] (referred to as OPDG code (referred to as OPDG code 2). OPDG codes incorporate a set of adder, a set of a set of multipliers a complex electronic vector (specific twiddle factor) .The value of the vector for twiddle factor in each electronics module is fundamental to the generation of a pair of perfectly autocorrelated and correlated OPDG codes null crusade.

Figure 2b) - OPDG electronic code encoder when electronic basic modules are used in a recursive process. Instead of having N chained electronic modules, only one that is recursively called N times is used. This method is advantageous when the N value is high. The recursive process is defined with two complex electronic input vectors ^at _n -i [* ·] and

Ki [t] and two complex electronic output vectors ^at n [t] and K [t], where n is an integer l <n <N, where the output ^at n [t] is equal to the expression:

a, | / output K [t] is equal to the expression:

The initial condition is [t] = A _and tb [t] = ^A , where A is a real constant vector or signal, and each electronics module uses a complex electronics vector equal to:

in length L = 2 ^W , where Pi / 1 = exp (-j2n / A).

The two outputs ^a n M and b _n [t] are stored in a memory component before being injected into the two inputs of the electronic basic module (with index n) in the next iteration. The initial condition is at [t] = ^A and tb [t] = ^A is only executed the first time, at the first iteration η = 1.

electronic code generator (encoder) alternative to that of Figure 2 (a) incorporates an adder (208), a differentiator (228) and a multiplier (218).

Figures 3 - a) Complex sequence transformation ^to N, according to the embodiment of the invention, shows how to apply a set of electronic transformations to the codes ^at N [ ¹ ]; and b) Complex sequence transformation b _{N r} according to the embodiment of the invention illustrates how applying the same set of electronic transformations to the codes b _N [t] _# p _{s in} figures 3 a) and 3 b) are complementary to figure 2 a ). The OPDG codes 1 in figure 2 a) will be the input codes in figure 3 a). The OPDG codes 2 give the input codes of figure 3 b). The (317) will allow the user to use the desired exit codes which may be: ^a N, x [ ^b ], ^a N, Y [t], ^b N, X [t] and ^b N, Y [^ ]. The blocks of complex signal vector which and (311) separate the real electronic complex part. The outputs are memory components, and part of the blocks illustrate the imaginary implementation of a translation of the elements of an input electronic vector of a value i proportional to the index of the input electronic vector. The electronic summing circuits blocks.

Blocks are electronic circuits that implement the conversion of an analog signal into a digital signal with two amplitude levels equivalent to the +1 and -1 amplitude. This conversion is similar to the sign function Sgn (r) of a real number r that returns + 1 if r is positive and returns -1 if the number r is negative. Multiplexers 307 (317) manipulate binary vectors that represent certain types of complex, real or bipolar codes. All vectors have length L = 2 ^N.

The code ^a N, 6 L ^b J is a bipolar code obtained based on the real part of the vector ^a N [t]. The code ^b N, 6 ^] is a bipolar code obtained based on the actual part of the vector ^b N [t]. The code ^at N, 5 [t] is a real type code obtained from the real part of the vector ^at N [* ·]. The code ^b N, 5 [* ·] is a real type code obtained based on the real part of the vector ^b N [t]. The code ^at N, 4 [^] is a bipolar code obtained based on the real part of the vector ^at N [t] plus the imaginary part of the code ^at xM when this vector is offset by Dx. The code is a bipolar code obtained from the actual part of the ^b NN vector plus the imaginary part of the b _N [t] code when this vector shifts.

Di. The code ^a Ns [t] is a real code obtained based on the imaginary real part of the code ^a N [ ^b ] when that of the vector ^a N [ ^b ] plus

vector suffers a displacement Di. 0 code ^b N, 3 [t] is obtained based on real part of the vector ^b N [ ^b ] imaginary code ^b N [t] When that vector suffers D; 0 code ^to N, 2 [t] it is a code real obtained with imaginary code ^to N [t] When that vector suffers Di. 0 code ^b N, 2 [t] it is a code real obtained with imaginary code Mt] When that vector suffers

one code one offset one offset one offset

Di. 0 code based on the base part in the part added to N, i [t] is the real one bipolar code obtained based on the imaginary part of ^the code C [t] when this undergoes a displacement vector

Di. 0 code ^b N, l M is a bipolar code obtained from the imaginary part of the code ^a N [t] when this vector shifts

Di. The code ^a N, the [t] is the code ^a N [t]. 0 code ^b N, the [t] is code ^b N [ ^b ].

(DAC) and may be required to generate the analog signals that will be injected into the transmission media.

electronic encoder of Figure 2 (a), of a pair of codes

OPDG requires an electronic decoder capable of reversing the operation of the specific encoding.

Figure 4 a)

Decoder circuit of a pair of perfect orthogonal sequences according to the embodiment of the invention illustrates the electronic decoder of the perfect orthogonal sequences which consists of

N basic electronic modules. Each basic electronic module consists of a adder (401), a differentiator (421) and a multiplier (411) by a complex electronic vector derived from a twiddle factor (Piá = exp (-j2n / A)) specific to each of the electronic modules. The specific connections of the three operators (from the basic module in figure 4 a)) allow the electronic decoding of OPDG codes of a certain length. Such electronic generation is a recursive process, that is, the decoding of a 2 ^W length OPDG code is obtained based on the electronic decoding of a 2 ^W_I length code. The OPDG electronic decoder (105) incorporates an adder assembly (401) (402) (403) (404) (405) (406) (407) (408) (409), a set of differentiators (421) ( 422) (423) (424) (425) (426) (427) (428) (429) and a set of multipliers (411) (412) (413) (414) (415) (416) (417) ( 418) (419) (multiplication by a specific electronic twiddle factor complex vector). The correct value of the twiddle factor vector in each module is critical for the correct electronic decoding of a pair of OPDG codes that have perfect periodic autocorrelation and zero cross correlation. The factor q selected to generate the electronic encoder of figure 2 a) can be the value +1 or -1. The same value q should be selected in the electronic decoder (of the same CODEC) as in figure 4 a). The input codes ^a N [t] and ^b N [t] of the first basic module of figure 4 a) can be the same as codes aN [t] and bN [t] of figure 2 a), respectively. However, input codes C [t] ^b NN may also be codes ^is N, X [t], N, Y [t], ^b n, x [t] and ^B is N, Y [t] of figures 3 a) and 3 b). In addition, aN [t] and ^b N [t] entry codes may also be the codes referred to above when they are contaminated by noise or another source of electronic interference. The outputs of the last electronic basic module of figure 4 a) are connected to each other by means of an adder represented by block 431. Applying an electronic squared modulus operation to the output of this block (431) gives a signal Ν222Ν + 2 generated by the block (433). Block 432 of FIG. 4 a) performs the electronic operation of a real FFT (Fast Fourier Transform) that generates the signal equal to a Dirac unit pulse with amplitude A [q] ^N 2 ^{2N + 1} . This pulse will appear to be temporally offset from a value of 2 ^W -1.

Figure 4b) - OPDG electronic code decoder (105) when the basic modules are used in a recursive process. Instead of having N chained electronic modules, only one that is recursively called N times is used. This method is advantageous when the N value is high. The recursive process is defined by two complex output vectors ^a n [t] and bn [t] z two complex output vectors ^a ni [t] and bna [t], where n is an integer

with

In the last iteration, two output vectors ^a o [t] and b ₀ [t] are summed to generate a uni modular complex vector. Each specific module of an iteration, represented by an index n, uses a complex vector equal to:

in length L = 2 ^W , where W1 = exp (-j2n / i).

The two outputs Ni b M ^ Jt], the electronic module are stored in a memory component before being injected into the two inputs of the electronic basic module (index n) in the next iteration. The initial condition is N [T] and N ^b [t] is only executed the first time at the first iteration η = N. Unlike OPDG encoder, here the iteration index is decremented by one unit starting from η = N and ending in n = 1.

Note: The OPDG Electronic Code CODEC consists of the electronic encoder (101) (601) of Figure 2 a) or Figure 2 b) and the electronic decoder (105) of Figure 4 a) or Figure 4 b). In certain situations the encoder 101 (601) of FIG. 2 a) or FIG. 4 b) may be supplemented by the circuits of FIGS. 3 a) and 3 b). The electronic OPDG code generator (decoder) alternative to that of Figure 4 (a) incorporates an adder (408), a differentiator (428) and a multiplier (418).

Figure 5 - Simplified diagram of applying OPDG bipolar codes {-1, +1} in a noise communication data system according to the embodiment of the invention illustrates the communication system of Figure 1 when a single signal ^to N, i [t] of Figure 3 a) is used and transmitted by the transmission means (603). This signal is a bipolar sequence {-1, +1} that depends on the cyclic displacement Di (302) applied. Because the value i can take L different values (0-i <L), it will be possible to generate L distinct bipolar sequences of length L. These bipolar codes have excellent correlation properties. The detection of the correct sequence can be done with an electronic circuit that allows to estimate the autocorrelation value. This circuit is designated by the Autocorrelation Estimator block of ^a N, i [t] (604) and can be the circuit of figures 4a), 4b) or the circuit of figure 6. It is added that figure 5 represents figure 1 when the OPDG code selected in block 602 (equivalent to the representation of figures 3 a) and 3 b)) is the bipolar code ^at N, 4 p]. Block 604 (Autocorrelation Estimator of ^a Nn [t]) can be the electronic decoder represented by Figure 4 a) or Figure 4 b) or even the classic electronic decoder of Figure 6. Figure 5 is no longer It is a particular case of FIG. 1, where the encoder 601 is equal to 101, and the last stage of encoder 602 is identical to that of the last stage 102.

Figure 6 - Circuit for performing a code correlation function ^at N, 4 [t] - illustrates a circuit that implements a classic correlation function where the input signal is multiplied by the sequence ^at Nn [t] (which has a cyclic shift specific i). The integrator will electronically implement a sum of L discrete elements. This circuit is an alternative to the decoder of figures 4a), 4b), when the sequences have a short length. When the length (L = 2 ^W ) is long, it is preferable to use the circuit of the invention of FIGS. 4a) or 4b). Figure 6 shows a correlation function of the vector received ^at N, 4 [t] with the reference vector ^at N, 4 [t]. This correlation function is multiplied by block 701 and the integration (or summation) function is performed by block 702.

Figure 7 - Generator (encoder) circuit of a pair of 32 length OPDG sequences according to the embodiment of the invention exemplifies the implementation of the encoder electronic circuit of Figure 2 a) when N = 5. 5 basic electronic modules of the figure were used. 2 a). Figure 7 is equivalent to the generator of Figure 2 a) when there are 5 electronic basic modules for generating length 32 OPDG codes. The OPDG electronic code encoder (101) (601) incorporates a set of adders (801) (802) (803) (804) (805), a set of differentiators (821) (822) (823) (824) (825), and a set of multipliers (811) (812) (813) (814) (815) ( multiplication by a complex electronic vector twiddle specific factor).

Figure 8 - Decoder circuit of a pair of length 32 OPDG sequences according to the embodiment of the invention exemplifies the implementation of the decoder electronic circuit of figure 4 a) when N = 5. 5 basic electronic modules of figure 4 a) were used. . Depending on the type of application, blocks 932 and 933 may be missing. Figure 8 represents the present invention of the electronic decoder of the OPDG codes of figure 7, or of figure 2 a) when the electronic encoder consists of 5 basic electronic modules. The OPDG electronic decoder (105) incorporates an adder assembly (901) (902) (903) (904) (905) and (931), a set of differentiators (921) (922) (923) (924) (925) and a set of multipliers (911) (912) (913) (914) (915) (multiplication by a specific electronic twiddle factor complex vector).

Figure 9 - Periodic Autocorrelation Functions for Multiple Codes - represents periodic autocorrelation functions for various codes generated based on the encoder in Figure 7. The superiority of OPDG 1 and OPDG 2 codes is enhanced over Golay codes. The periodic autocorrelations of the sequences OPDG 1, OPDG 2, [Re (OPDG 1) + Im (OPDG 1)] and [Re (OPDG 2) + Im (OPDG

2)] are proportional to a unit impulse of Dirac. This is not the case with Golay's complementary code pairs (Golay 1 and Golay 2).

Figure 10 - Periodic cross-correlation functions for various codes - represents the periodic cross-correlation functions for various codes. The complementary sequences Re (OPDG 1) and Im (OPDG 1) are orthogonal for any cyclic shifts 0 <i <L. The same is true for the sequence pair Re (OPDG 2) and Im (OPDG 2), but not with the complementary pairs of Golay (Golay 1 and Golay 2). In this last property lies the great difference between the Golay codes and the OPDG codes of the present invention.

Figure 11 - Aperiodic Cross-Correlation Functions for Multiple Codes - represents aperiodic cross-correlation functions for multiple codes. A pair of complementary sequences Re (OPDG 1) and Im (OPDG 1) have low correlation values for any cyclic shifts 0 <i <L. The same is true of sequence pair Re (OPDG 2) and Im (OPDG 2), but it is not

Checks (Golay 1 so efficiently with pairs Golay's complementary and Golay 2) . Figure 12 features values absolute functions in autocorrelations aperiodic for four Bipolar codes. At

Bipolar sequences derived from the OPDG sequences show lower absolute, lagged absolute values than Golay sequences.

Figure 13 - presents absolute values of the periodic autocorrelation functions for four bipolar codes. The bipolar sequences derived from the OPDG sequences have lower absolute, lagged absolute values than the Golay sequences.

Bipolar codes derived from OPDG sequences have a low detection error rate when used in a BPSK modulated DS-CDMA system.

Figure 14 - Probability of error as a function of signal to noise ratio (Eb / No) when four codes are used simultaneously Shows the probability of error as a function of signal noise ratio (Eb / No) when four codes are used simultaneously. The mathematical model Probability of error used in figures 14 and 15 was previously presented in the article: Pereira, J .; .P.ÉZÉU ..... 4 ° ..... 4 /. ' Orthogonal perfect discrete Fourier sequences, IET

Signal Processing, Vol. 6, No. 2, pp. 107-113, April, 2012.

Figure 15 - Error probability as a function of the number of codes used simultaneously - It is possible to view graphs of error probability as a function of the number of codes used simultaneously.

The two previous figures show the superiority of the bipolar codes derived from the OPDG sequences over the orthogonal Gold codes for the same lengths and quantities.

Considerations

According to the invention, autocorrelation and cross correlation of the codes thereof are particularly favorable for use in CDMA communication systems.

In addition, the invention allows the generation of optimal code sets in an amount equal to the length L.

In a part of the invention a set of 2 ^W codes, of length 2 ^W , may be constructed. For example, in a specific electronic CODEC application, each code may be assigned to a user of a CDMA communication cell (geographical area). Each user will use their code to transmit their information, on a transmission medium shared by 2 ^W users, in each of the CDMA communication cells, that is, a typical scenario of an asynchronous transmission system where each user is identified by a single code and the polarity of that code is related to the binary information transmitted by that code / user.

Because codes have low cross-correlation values, it will be possible for a specific user receiver to be able to extract their code and binary information, despite receiving all other codes simultaneously. In other words, the codes generated by the new CODEC are very tolerant to interference caused by the code itself (multiple paths) and other codes (adjacent communication channels).

It should be noted that the object of the invention may be implemented using specific hardware or electronics such as application specific integrated circuit (ASIC), programmable electronic devices such as FieldProgrammable Gate Array (FPGA) or Complex Programmable Logic Device (CPLD) and programmable logic devices such as gate arrays, and firmware running on computational devices such as microcontroller microprocessors or digital signal processing devices (DSP).

Also, it should be noted that while OPDG CODECs can be deployed on a single device, such as an ASIC, they can be distributed across multiple devices.

The invention is not limited to the device for implementing electronic OPDG CODECs. The method used in OPDG CODEC may include different implementations or a mix of low-level hardware, firmware and software technologies (examples of languages: Java, C, C ++, Mathlab ™, LabView, Verilog, VHDL, and other assembly languages). processor or machine specific).

Firmware computer programs may incorporate the CODEC OPDG method based on a memory medium and should be within the spirit of the invention.

All firmware-related programming languages referred to herein have a pedagogical purpose to help the reader understand the principle of the invention.

Additionally, any equivalent implementation elements of the present invention should go beyond the equivalent structure and functionality that can be implemented in future systems (technology not currently available).

It should be noted, for those skilled in the art of skill, that the present invention incorporates any equivalent representation types such as block diagrams, illustrative circuits, algorithms, functional steps, flow diagrams, flow graphs, signal diagrams, systems of diagrams, codes and representations of various processes that can be inserted into the memory of one or more computerized systems and executed.

computerized term shall cover other terms of the type

processor, controller and should not refer solely to to hardware, but also to the storage media of information from type ROM (read-only memory), RAM (random access)

memory) or other non-volatile memory types.

Claims (6)

1. Electronic orthogonal and perfect signal encoder (101) (601) characterized in that it consists of: The. code generator with N basic modules each consisting of two inputs, two outputs, an adder (201) (202) (203) (204) (205) (206) (207) (208) (209), a differentiator ( 221) (222) (223) (224) (225) (226) (227) (228) (229), a multiplier (211) (212) (213) (214) (215) (216) (217) (218) (219) and a twiddle factor signal generator interconnected as follows in each basic module: i. the second input and the twiddle factor generator element are connected to the multiplier inputs; ii. The output from multiplied r and the first input They are linked to inputs from adder; iii. The first input and multiplier output They are linked to inputs from differentiator; iv. The first exit is linked directly to first floor entrance next and the Monday exit is directly connected to the second entrance of the next floor; Inputs and outputs are adapted for input and output signals of 2 ^N length; B. top floor of the DAC encoder consisting of a extracting signal memory i (302) (312), one signal (304) (305 ) (306) (314: (307) (317 ) and (308) (309 ) (318) (319: complex converter adders (301) (311), components in a bipolar analog digital multiplexer signal as follows: 1/3 i. one output is coupled to a complex signal extractor and its output is coupled to a memory component that implements temporally delayed sequences of a value equal to the index i of a sequence Im {} with respect to the sequence Re {}; ii. the memory component output and one of the complex signal extractor outputs are connected to the inputs of a adder, the output of that adder being connected to the input of a multiplexer; iii. The multiplexer inputs are connected to all of the above outputs and their output is connected to one or more digital analog converters. Encoder according to claim 1, characterized in that each of the implemented multiplier, adder and differentiator stages comprises XOR, AND, INVERTER and OR logic gates. Encoder according to claim 1, characterized in that the single-stage outputs can be connected to the two inputs of a memory component, where two memory component outputs connect to the two single-stage inputs in a recursive process. 4. Electronic decoder (105) for perfect orthogonal signals, characterized in that it consists of: The. squared module extractor (433) and circuit (432) that electronically implements the real part of an FFT; B. N floors each constituted per two inputs and two outputs, an adder (401) (402) i (403 ) (404 ) (405) (406) (407) (408) (409), a differentiator (421 ) (422 ) (423) (424) (425) (426) (427) (428) (429) and a multiplier (411) (412) (413) 2/3 (414) (415) (416) (417) (418) (419), and a twiddle factor signal generator interconnected as follows, on each stage: i. the first two exits connected directly to the first entrances of the next floor; ii. the inputs and outputs are adapted for input and output signals of 2 ^N length; iii. both inputs of each floor are connected to both the adder and the differentiator; iv. the differential output is connected to the second floor output; v. the adder output and the generator of a twiddle factor signal are connected to the multiplier inputs; saw. the multiplier output is connected to the first floor output. Decoder according to Claim 4, characterized in that it comprises multipliers, adders and differentiators implemented with XOR, AND, INVERTER and OR logic gates. Decoder according to Claim 4, characterized in that the single-stage outputs can be connected to the two inputs of a memory component, where two memory component outputs connect to the two single-stage inputs in a recursive process.