Hyper Phase Shift Keying Modulation

Transcription

1 Calhun: The NPS Institutinal rchive Faculty and Researcher Publicatins Faculty and Researcher Publicatins Hyper Phase Shift Keying Mdulatin Caldwell, James The United States f merica as represented by the Secretary f the Navy, Washingtn, DC (US)

2 US864541Bl (12) United States Patent Caldwell (1) Patent N.: US 8,64,541 Bl (45) Date f Patent: Nv. 22, 211 (54) HYPER PHSE SHIFT KEYING MODULTION (75) Inventr: James Caldwell, Mnterey, C (US) (73) ssignee: The United States f merica as represented by the Secretary f the Navy, Washingtn, DC (US) ( *) Ntice: Subject t any disclaimer, the term f this patent is extended r adjusted under 35 U.S.c. 154(b) by 528 days. (21) ppl. N.: 15,73 (22) Filed: Jan. 8, 29 Related U.S. pplicatin Data (6) Prvisinal applicatin N ,413, filed n Nv. 13,28. (51) Int. Cl. H4L 2712 (26.1) (52) U.S. Cl /38 (58) Field f Classificatin Search /279, 375/28,281,283,38,322,323,329,33, 375/331,332; 455/23,42,25; 37/215 See applicatin file fr cmplete search histry. (56) References Cited OTHER PUBLICTIONS Caldwell, J.; Tummala, M.;, "Hyper Phase Shift Keying (HPSK) Mdulatin," Signals, Systems and Cmputers, 27, CSSC 27. Cnference Recrd f the Frty-First silmar Cnference n, pp. 14, Nv. 4-7, 27. [retrieved n ug. 1,21]. Retrieved frm the Internet: <URL: jsp?tp~&arnumbef &isnumbef >. Caldwell, J.; Rbertsn, c.;, "Lng Blck Length Reed Slmn Cded M-ary Hyper Phase-shift Keying," Signals, Systems and Cmputers, 28 42ndsiimar Cnference n, pp , Oct ,28. [retrieved n ug. 8, 21]. Retrieved frm the Internet: <URL: Caldwell, J.; Rbertsn, c.;, "Reed Slmn Cded M-ary Hyper Phase-Shift Keying," Military Cmmunicatins Cnference, 28. MILCOM 28. IEEE, pp. 1-6, Nv. 169,28. [retrieved n ug. 9,21]. Retrieved frm the Internet: <URL: rg/stamp/ stampj sp?tp~&arnumber~ 7533&isnumbeF >. Primary Examiner - Sam Khn (74) ttrney, gent, r Firm - Dnald E. Lincln; Lisa. Nrris (57) BSTRCT cmmunicatins system and methd fr transmitting digital infrmatin includes arranging a mdulatr t have an input bit stream f binary data and arranging a signal generatr t generate fur rthnrmal hyper phase shift keying (HPSK) basis functins that are peridic functins with a duratin T. bit t symbl mapper is arranged t cmbine the bit stream and the HPSK basis functins t frm a successin f 4-bit HPSK symbls fr 16-HPSK, 5-bit HPSK symbls fr 32-HPSK r 6-bit HPSK symbls fr 64-HPSK, and a transmitter is arranged t transmit signals indicative f the HPSK symbls. receiver is arranged t receive the signals frm the transmitter and the HPSK symbls are demdulated with the HPSK basis functins t reprduce the bit stream f binary data. 1 Claims, 7 Drawing Sheets {,1} Bit Stream l : / : ~:=~:_--~~$~:n~ ~, Serial-t- Parallel Cnverter 12 HPSK / Mdulatr 1 HPSK mdulated signal 17

3 u.s. Patent Nv. 22, 211 Sheet 1 f7 US 8,64,541 Bl {,1} Bit Stream 11 Serial-t Parallel Cnverter r ~ , I I I $n1 I HPSK / Mdulatr 1 Basis Functins Generatin Transmitter 16 HPSK mdulated signal 17 FIG. 1

4 u.s. Patent Nv. 22, 211 Sheet 2 f7 US 8,64,541 Bl S dt 28 Receiver X(t) S dt ~ Minimum Euclidean Detectr 36 HPSK I demdulatr 2 26 S dt <1>3(t) 3 <1>4(t) S dt 31 Sample at time T {-l,l} Bit Stream 38 FIG. 2

5 u.s. Patent Nv. 22, 211 Sheet 3 f7 US 8,64,541 Bl P b Eb. db -In N FIG. 3 J-. E :. ' 1-3. : «:$.. J tit- Upper bund 32-HPSK ~ Simulatin 32-HPSK Lwer bund 32-HPSK -+- pprximatin 32-HPSK 1-7L- ~ ~ ~L- ~ ~ ~ Energy per bit t nise PSD in db FIG. 4

6 u.s. Patent Nv. 22, 211 Sheet 4 f7 US 8,64,541 Bl ;... t:: 11) ; G J -4 c!j.. l-. P Simulatin 64-HPSK -e- 64--HPSK Upper bund ~ 64-HPSK Lwer bund -a- Theretical 64-HPSK Energy per bit t nise PSD in db FIG. 5

7 u.s. Patent Nv. 22, 211 Sheet 5 f7 US 8,64,541 Bl l:: Q).t:: '+-<.f'... r ~ pprximatin 32-HPSK -Ir- pprximatin 64-HPSK PSK -e- 16-HPSK ~ 16-PSK -e-l6-qm Eb. db -Ill N FIG Encde Mdulatin l Channel Decde Demdulatin * FIG. 7

8 u.s. Patent Nv. 22, 211 Sheet 6 f7 US 8,64,541 Bl ~... : "-' g : c:!..d... c <l Eb. db -In N FIG. S 8.2 -Ir- 64-HPSK RS (495,3685) --e- Uncded 64-HPSK --e- 16-QM LDPC r =.9... Uncded 16-QM v..- : "-' E' : c:!..d... c O-<l L-...l..--L.---L_.l--..~~~_.l--...L Eb. db -In N FIG. 9 -t:r- 64-HPSK RS (495,3685) --e- Uncded 64--HPSK -e- 8-PSK LDPC r =.9... Uncded 8-PSK

9 u.s. Patent Nv. 22, 211 Sheet 7 f7 US 8,64,541 Bl HPSK mdulated signal 17 HPSK Mdulatr 1 HPSK '-- I Demdulatr 2 {,1 } Bit Stream 1 1 I HPSK mdulated cmmunicatins system 1 {-l,l} Bit Stream 38 FIG. 1

10 1 HYPER PHSE SHIFT KEYING MODULTION US 8,64,541 Bl 2 M-ary phase shift keying (MPSK) uses tw rthnnnal basis functins CROSS REFERENCE TO RELTED PPLICTION This applicatin claims the benefit f U.S. Prvisinal pplicatin N ,413, filed Nv. 13, 28 which is hereby incrprated in its entirety by reference. BCKGROUND OF THE INVENTION 1 and (h(t) = ~cs(ilrf,t) ve, (5) (6) 1. Field f the Inventin This inventin relates generally t digital cmmunicatins 15 and particularly t signal mdulatin techniques. Still mre particularly, this inventin relates t phase shift keying, which is a digital mdulatin scheme that cnveys data by changing, r mdulating, the phase f a reference signal. 2. Descriptin f the Related rt In telecmmunicatins, mdulatin is the prcess f varying a peridic wavefrm in rder t use that signal t cnvey a message r t transmit infnnatin. ny digital mdulatin scheme uses a finite number f distinct signals t represent digital data. Phase shift keying (PSK) is a digital mdulatin 25 scheme that cnveys data by changing, r mdulating, the phase f a reference signal (the carrier wave). PSK uses a finite number f phases, each assigned a unique pattern f binary bits. Usually each phase encdes an equal number f bits. Each pattern f bits fnns the symbl that is represented 3 by the particular phase. In digital cmmunicatins, a symbl is the smallest unit f data transmitted at ne time. Traditinal digital mdulatin techniques include binary phase shift keying and quadrature phase shift keying. Binary phase shift keying (BPSK) has nly ne basis functin, which 35 is expressed as!/j(t) = H cs (ilrf,t), where fc is the carrier wave frequency and T represents the symbl duratin and the basis functin is defined nly fr times between and T. The BPSK wavefrms, Sl(t)=-S2(t), are represented as where Eb is the energy per bit. In the presence f zer mean additive white Gaussian nise (WGN) with a variance f Nj2, the prbability f bit errr using maximum likelihd (ML) detectin is where Eb is the energy per bit, and the Q functin is 1 r= Q(x) = {2; J dlx. (1) (2) (3) (4) where is the amplitude, fc =m/t with m being a psitive integer and the basis functins are defined nly fr time values between and T. The cnstraint n the frequency allws the tw basis functins t be rthgnal t each ther. dditinally, Es represents the energy per symbl and 2 equals 2T/2. The signals sn(t), where n=l, 2,..., Mare written as Fr quadrature phase shift keying (QPSK) where M=4, the prbability f bit errr using ML detectin in WGN is the same as is the same as in Equatin (3) because QPSK in effect is tw independent BPSK chaunels. Nte that even thugh the bit errr rates are identical, QPSK has twice the bandwidth efficiency f BPSK. The bit errr prbability fr M-PSK in general is P b = --Q 2 ((") sin - lg2m-. 2Eb) lg2m M N 4 Equatin (8) is accurate when gray cding is used t cde adjacent symbls. nther cmmnly used mdulatin is M-quadrature mdulatin (QM), which is simply amplitude mdulatin ver tw quadrature channels. The bit errr prbability fr 45 M-QM in general is 5 In the simplest mdulatin schemes such as binary phaseshift keying, nly ne bit f data (i.e., a r I) is transmitted at a time depending n the phase f the transmitted signal. 55 Hwever, in a mre cmplex scheme such as 16-QM, fur bits f data are transmitted simultaneusly, resulting in a symbl rate (r baud rate) that is equal t ne quarter f the bit rate. Owing t PSK's simplicity, it is widely used in existing technlgies. The mst ppular wireless lcal area netwrk 6 (LN) wireless standard, IEEE 82.llb uses a variety f different PSK techniques depending n the data-rate required. t the basic-rate f I Mbit/s, it uses differential BPSK. T prvide the extended-rate f 2 Mbitls, DQPSK is used. In reaching 5.5 Mbitls and the full-rate f 11 Mbit/s, 65 QPSK is emplyed cupled with cmplementary cde keying. The higher-speed wireless LN standard, IEEE 82.llg has eight data rates: 6, 9,12,18,24,36,48 and 54 Mbitls. The (7) (8) (9)

11 US 8,64,541 Bl 3 6 and 9 Mbitls mdes use BPSK. The 12 and 18 Mbitls mdes use QPSK. The fastest fur mdes use frms f quadrature amplitude mdulatin. Because f its simplicity BPSK is apprpriate fr lw-cst passive transmitters, and is used in radi frequency identifi- 5 catin (RFID) standards such as Internatinal Organizatin fr Standardizatin (ISO) which has been adpted fr bimetric passprts, credit cards such as merican Express's Express Pay and many ther applicatins. SUMMRY OF THE INVENTION Embdiments in accrdance with the inventin prvide a cmmunicatins system and methd fr transmitting digital data using a mdulatin technique that has a lwer errr prbability than prir art phase shift keying techniques fr the same spectral efficiency. In ne embdiment, a cmmunicatins system includes: a mdulatr arranged t receive a bit stream f binary data 2 input theret, the mdulatr including a signal generatr arranged t generate fur rthnrmal M-hyper phase shift keying (M -HPSK) basis functins that are peridic functins having with a duratin T and a bit t symbl mapper fr cmbining the bit stream and the HPSK basis functins t 25 frm a successin f 4-bit HPSK symbls fr 16-HPSK, 5-bit HPSK symbls fr 32-HPSK, r 6-bit HPSK symbls fr 64-HPSK; a transmitter cnnected t the mapper and arranged t receive the HPSK symbls and transmit signals indicative f the HPSK symbls; a receiver arranged t 3 receive the signals indicative f the HPSK symbls frm the transmitter; and a demdulatr cnnected t the receiver and arranged t demdulate the HPSK symbls with the HPSK basis functins and reprduce the bit stream f binary data. In ne embdiment, a methd fr transmitting digital infr- 35 mati n includes: arranging a mdulatr t receive a bit stream f binary data input theret; prviding a signal generatr arranged t generate fur rthnrmal M-hyper phase shift keying (M -HPSK) basis functins that are peridic functins with a duratin T; prviding a bit t symbl mapper fr 4 cmbining the bit stream and the HPSK basis functins t frm a successin f 4-bit HPSK symbls fr 16-HPSK, 5-bit HPSK symbls fr 32-HPSK, r 6-bit HPSK symbls fr 64-HPSK; cnnecting a transmitter t the mapper and arranging the transmitter t receive the HPSK symbls transmit 45 signals indicative f the HPSK symbls; prviding a receiver arranged t receive the signals indicative f the HPSK symbls frm the transmitter; and demdulating the HPSK symbls with the HPSK basis functins t reprduce the bit stream f binary data. 5 Embdiments in accrdance with the inventin are best understd by reference t the fllwing detailed descriptin when read in cnjunctin with the accmpanying drawings. BRIEF DESCRIPTION OF THE DRWINGS 55 FIG. 1 is a blck diagram f an HPSK mdulatr in accrdance with ne embdiment. FIG. 2 is a blck diagram f an HPSK demdulatr in accrdance with ne embdiment. 6 FIG. 3 graphically illustrates the theretical bit errr prbability and Mnte Carl simulatin results fr 16-HPSK in accrdance with ne embdiment. FIG. 4 graphically illustrates Mnte Carl simulatin results, the upper bund, the lwer bund, and an useful 65 apprximatin fr 32-HPSK in accrdance with ne embdiment. 4 FIG. 5 graphically illustrates Mnte Carl simulatin results, the upper bund, the lwer bund, and an useful apprximatin fr 64-HPSK in accrdance with ne embdiment. FIG. 6 graphically illustrates the theretical bit errr prbabilities fr uncded 16-PSK, 16-QM, 16-HPSK, and 8-PSK and useful apprximatins t theretical bit errr prbabilities fr 32-HPSK and 64-HPSK fr the mdulatin techniques withut using errr crrectin cdes in accr- 1 dance with ne embdiment. FIG. 7 graphically illustrates an errr crrectin cde blck diagram in accrdance with ne embdiment. FIG. 8 graphically illustrates the Mnte Carl simulatin 15 results fr 64-HPSK and 16-QM using errr crrectin cding in accrdance with ne embdiment. FIG. 9 graphically illustrates the Mnte Carl simulatin results fr 64-HPSK and 8-PSK using errr crrectin cding in accrdance with ne embdiment. FIG. 1 illustrates a HPSK mdulated cmmunicatins systems in accrdance with ne embdiment. DETILED DESCRIPTION OF THE INVENTION Hyper Phase shift keying (HPSK) accrding t the present inventin uses fur rthnrmal basis functins t mdulate the infrmatin bits. The basis functins are: (h(t) = ~cs(2.jr(f, + 1/(2T))t) (fj2(t) = ~ sin(2.jr(f, + 1/(2T))t) (/J3(t) = ~sin(2.jr(f, /(2T))t) (fi4(t) = ~cs(2.jr(f, /(2T))t) where T is the symbl duratin, is the energy per symbl transmitted and the basis functins are defined fr time values between and T and with k being a psitive integer. Orthnrmal functins have tw qualities: they are nrmalized t have unit energy and they are mutually rthgnal with each ther. The fllwing derivatin shws the mutual rthgnality f the fur HPSK basis functins f Equatins (1)-(13). The rthgnality f the basis functins <P2 and <PI can be shwn by nting that (1) (11) (12) (13)

12 5 2i T cs(2tr(f, + 11 (2T»t)sin(2Tr(f, + 11 (2T»t) dlt, which, using sme trignmetric identities, may be written as T 2iT sin(4tr(f, + 1/2T)t) (h(t)(fi2(t) dlt = dlt = O. i 2, US 8,64,541 Bl Equatin (15) equals zer (i.e. the functins <P2 and <PI are 15 rthgnal) under the cnditin that (14) (15) 6 Hwever, in HPSK the symbls are cded at varius phases spaced arund the surface f a fur dimensinal hypersphere. Fr example, the wavefrm is determined by a basis functin weighting values where Snl' Sn2' Sn3' and Sn4 cnvey the infrmatin t be transmitted as shwn in Table 1 fr M=16, Table 2 fr M=32, 1 and Table 3 fr M=64. The vim is apprximated as in Table 2. The v'24/9 is apprximated as in Table 3. Bit Stream TBLE 1 16-HPSK Bit t Symbl Mapping Values (22) where k is a psitive integer. Even if the carrier frequency des nt exactly meet the cnditin, the first tw basis functins are still apprximately rthgnal. In a similar manner the rest f the basis functins are shwn 25 t be rthgnal. T 2iTCOS(4Tr/,tJ+COS(2TrtIT) (h(t)cp3(t)dlt= dlt=o i 2, rr J CPl (t)cp4(t) dlt = J 2, dlt = 2 (Tsin(4Tr/,tJ-sin(2TrtIT) (16) 2 3 (17) TBLE 2 T 2 it sin(4tr/,tj - sin(2mit) CP2(t)CP3(t)dlt=- dlt=o i, 2 T 2iTcS(2mIT)-COS(4Tr/,tJ CP2(t)CP4(t) dlt = - dlt = i, 2 (18) (19) 4 Equatins (16) thrugh (2) als equal zer under the same carrier frequency cnditin specified abve. HPSK has a psitive frequency magnitude respnse that is prprtin t tw sin c functins sin c(x) centered at the carrier frequency minus half the symbl rate and the carrier 5 frequency plus half the symbl rate where sin(trx) sinc(x) = --, TrX and the null-t-null bandwidth f a sin c functin is 2 - =2R. T s a result, HPSK requires a null-t-null bandwidth f3r. HPSK takes k=lg2m bits at a time and passes them 65 thrugh a serial t parallel cnverter. Just as in MPSK, the symbls are cded at varius phases in the signal space. (2) (21) Bit Stream Bit-t-symb1 mapping values fr 32-HPSK

13 Bit Stream TBLE 3 Bit-t-symbl mapping values fr 64-HPSK US 8,64,541 Bl The binary bit stream values are either ne r minus ne. The bits that are minus ne crrespnd t zers, and the bits 6 that are plus ne crrespnd t nes. Then all fur basis functins weighted accrding t Equatin (22) are multiplexed tgether t frm the first symbl using either Table 1, Table 2, r Table 3 fr M=16, 32, r 64, respectively (i.e. summed tgether). This multiplexing apprach wrks 65 because all fur basis functins are mutually rthnrmal. The prcess is repeated fr each symbl. 8 n example f hw an HPSK mdulatr 1 accrding t the present inventin is implemented is shwn in FIG. 1. bit stream 11 is input t a serial t parallel cnverter 12. The utput f serial t parallel cnverter 12 is input t a bit t symbl mapper 14 that weights the fur HPSK basis functins, shwn in FIG. 1 as basis functin generatrs 18, 2, 22, and 24 representing basis functins <PI thrugh <P4' respectively, t frm symbls that represent the bit stream accrding t either Table 1, Table 2, r Table 3. fter the summing f the 1 weight basis functins in symbl mapper 14, the symbls are transmitted via a transmitter 16. FIG. 2 is a blck diagram f an HPSK demdulatr 2 that may be included in the present inventin. receiver 22 utputs a signal x(t) t an array f multipliers that multiply 15 x(t) by the basis functins <PI thrugh <P4' respectively. The functins X(t)<PI(t), X(t)<P2(t), X(t)<P3(t) and x(t)<pit) are input t an array f crrelatrs 28-31, respectively. The crrelatrs prvide their respective integrated signals t a switch array 34, which clses at time T t prvide the fur signals t a minimum Euclidean distance detectr 36. The minimum 2 Euclidean distance detectr 36 selects the signal input that is clsest t the received signal and frms a bit stream 38. t the demdulatr 2 each symbl is crrelated with all fur basis functins (i.e. there are fur crrelatrs, althugh 25 fur matched filters wuld functin in the same way) and sampled at time T. The minimum Euclidean distance (MED) detectr estimates the signal that is sent based n the principle that the received signal shuld be clsest t the sent signal. Therefre, the MED detectr estimates the transmitted sym- 3 bl that is clsest in the fur-dimensinal Euclidean space t the received signal. The prcess then repeats itself fr the next symbl and s n. This MED detectin prcedure results in the lwest bit errr prbability fr WGN. T determine the bit errr prbability, the prbability f 35 crrect symbl estimatin is derived first. Fr M=16, the prbability f estimating the crrect symbl i given that symbl i was transmitted is where the prbability density functin f the WGN is 1 f(n;)=--e {;N; Since the nise is independent between the fur rthgnal demdulatr channels, the cnditinal prbability f estimating the crrect symbl is 4 lg2 MEb P(c Is;) = 1 - Q v:;;-. ( ( )) The prbability f estimating a crrect symbl is 1 M P(C)=M~ p(cls;) (21) (22) (23) (24)

14 US 8,64,541 Bl 9 fr equally likely symbls. Due t symmetry in the HPSK signal cnstellatin, all f the cnditinal crrect prbabilities are equal and P(c)=P(cI s,). The prbability f a symbl errr is ne minus the prbability f estimating a crrect symbl. Therefre, the bit errr prbability using a gray cde 5 fr 16-HPSK is 1 T determine the prbability f bit errr fr M=64, first the prbability f symbl errr is apprximated by the first term in a tight unin bund (3) 1 ( ( (1 g 2 MEb ))4) P b = Q ---. lg 2 M 2N (25) 1 This is the 16-HPSK prbability f errr shwn in FIG. 3 using the demdulatr shwn in FIG. 2 using gray cding as 15 in Table I. T determine the prbability f bit errr fr M=32, first the prbability f symbl errr is apprximated by the first term in a tight unin bund 2 where N n is the number f nearest symbls in the cnstellatin, d 2 is the Euclidean distance squared between a symbl and its nearest neighbrs, and N is the ne-sided nise PSD. Fr 64-HPSK, each symbl has three nearest neighbrs with a Euclidean distance fy8e b l3 between each symbl. Hwever, each symbl als has three mre neighbrs that are nly slightly farther away, s gray cding is still nt pssible. The upper bund fr 64-HPSK is, therefre, (31) (26) 25 The crrespnding lwer bund fr 64-HPSK is where N n is the number f nearest symbls in the cnstellatin, d 2 is the Euclidean distance squared between a symbl and its nearest neighbrs, and N is the ne-sided nise PSD. Fr 32-HPSK, gray cding is nt pssible because each sym- 3 bl has six nearest neighbrs, and there are nly five bits per symbl. Therefre, an upper bund and a lwer bund are derived using (26). Simulatin results fall apprximately halfway between these tw bunds. The Euclidean distance 35 between each f the symbls and its nearest neighbrs is YIOE b I3. Therefre, an upper bund fr 32-HPSK is useful apprximatin fr 64-HPSK is the average f (31) and (32): (32) (33) n apprximate lwer bund fr 32-HPSK is achieved if gray 45 cding were pssible, and this lwer bund is Therefre, a useful apprximatin fr 32-HPSK is the average f (27) and (28): Thus (29) is an accurate apprximatin f the prbability f bit errr fr 32-HPSK when cmpared t Mnte Carl simulatin results where each value f EblN in db is simulated fr 1 bit errrs in FIG. 4 using the bit t symbl mapper values shwn in Table 2. Ntice that the apprximatin is accurate as the prbability f bit errr appraches 1-5. (27) 4 Thus (33) is an accurate apprximatin f the prbability f bit errr fr 64-HPSK when cmpared t Mnte Carl simulatin results where each value f EblN in db is simulated fr 1 bit errrs in FIG. 5 fr the bit t symbl mapper values shwn in Table 3. Ntice that the apprximatin is (28) (29) extremely accurate fr the prbability f bit errr <1-2. The 8-PSK, 16-PSK, 16-QM, 16-HPSK, 32-HPSK, and 64-HPSK mdulatin techniques are cmpared using theretical and Mnte Carl analysis fr prbability f bit errr versus energy per bit t nse pwer spectral density rati in 5 FIG. 6. Mnte Carl analysis simulates the prbability f bit errr many times and averages the results t predict mdulatin perfrmance. The 64-HPSK mdulatin technique is shwn t have far superir bit errr rates than 16-PSK and 16-QM versus energy per bit t nise pwer spectral density 55 rati while having the same spectral efficiency. Nte that HPSK can perfrm well even when the nise and signal pwers are f the same magnitude with the use f errr crrecting cdes. Errr crrectin cdes refer t the rdering f input infrmatin bit streams s that redundancy is intr- 6 duced int the infrmatin data and errrs can be self-crrected after the demdulatr. n errr crrectin cde blck diagram is shwn in FIG. 7. HPSK is an excellent mdulatin technique fr energylimited scenaris like satellite cmmunicatin. This is 65 because due t the great distances invlved between cmmunicatin satellites and earth statins, the signal is ften received with a degraded signal pwer. dditinally, HPSK

15 US 8,64,541 Bl 11 has equal energy symbls, unlike 16-QM that might cause a satellite amplifier t vary back and frth between saturatin and ver-saturatin, which results in inter-mdulatin nise. FIG. 6 shws the theretical bit errr prbabilities fr uncded 16-PSK, 16-QM, 16-HPSK, 8-PSK, 32-HPSK, 5 and 64-HPSK. HPSK clearly perfrms much better than the ther traditinal mdulatin techniques. This imprvement in bit errr prbability ccurs because f the fur degrees f freedm that are pssible using HPSK. Having fur degrees f freedm des hwever result in increased receiver/de- 1 mdulatr cmplexity as shwn in FIG. 2. FIG. 6 shws bit errr prbabilities fr the mdulatin techniques withut using errr crrectin cdes. Further imprvements in pwerlimited envirnments can be achieved using errr crrectin 15 cding. FIG. 8 shws the Mnte Carl simulatin results fr 64-HPSK and 16-QM using errr crrectin cding. The tremendus imprvements in prbability f bit errr shwn by 64-HPSK ver 16-QM are btained at the same spectral 2 efficiency. FIG. 9 shws the Mnte Carl simulatin results fr 64-HPSK and 8-PSK using errr crrectin cding. The tremendus imprvements shwn by 64-HPSK ver 8-PSK are btained bth in terms f prbability f bit errr and spectral efficiency. 25 FIG. 1 illustrates an HPSK mdulated cmmunicatins system 1 in accrdance with ne embdiment. In ne embdiment, HPSK mdulated cmmunicatins system 1 includes an HPSK mdulatr 1 earlier described that receives an input signal 11. HPSK mdulatr 1 generates 3 and transmits an HPSK mdulated signal 17 as earlier described herein ver a transmissin channel. In ne embdiment' HPSK mdulated signal 17 is received by HPSK demdulatr 2 and demdulated t btain an utput signal 38 as earlier described herein. What is claimed is: 1. cmmunicatins system cmprising: a mdulatr arranged t receive a bit stream f binary data input theret, the mdulatr cmprising: a signal generatr arranged t generate fur rthnrmal hyper phase shift keying (HPSK) basis functins that are peridic functins having with a duratin T, and a bit t symbl mapper fr cmbining the bit stream and the HPSK basis functins t frm a successin f 4-bit 45 HPSK symbls fr 16-HPSK, 5-bit HPSK symbls fr 32-HPSK, and 6-bit HPSK symbls fr 64-HPSK; a transmitter cnnected t the bit t symbl mapper and arranged t receive the HPSK symbls and t transmit signals indicative f the HPSK symbls; a receiver arranged t receive the signals indicative f the HPSK symbls frm the transmitter; and a demdulatr cnnected t the receiver and arranged t demdulate the HPSK symbls with the HPSK basis functins and reprduce the bit stream f binary data, wherein the HPSK basis functins are cntinued (P,(t) = ~ sin(2.jr(f, /(2T))t) (fi4(t) = ~cs(2.jr(f, /(2T))t) where is the amplitude and is the energy per symbl. 2. The cmmunicatins system f claim 1 wherein the data input t the mdulatr is a serial bit stream, the HPSK mdulatr further cmprising: a serial t parallel cnverter arranged t prvide a parallel bit stream t the bit t symbl mapper. 3. The cmmunicatins system f claim 2 wherein the demdulatr cmprises: fur crrelatrs fr crrelating each received HPSK symbl with the fur HPSK basis functins. 4. The cmmunicatins system f claim 3 wherein the demdulatr further cmprises: a sampler that samples signals utput frm the crrelatrs at time intervals equal t the duratin T f the basis functins. 5. The cmmunicatins system f claim 4, wherein the demdulatr further cmprises: a minimum Euclidean distance detectr arranged t and estimate which f the crrelatr utput signals is clsest t the signal received by the receiver. 6. methd fr transmitting digital infrmatin cmprising: arranging a mdulatr t receive a bit stream f binary data input theret; prviding a signal generatr arranged t generate fur rthnrmal hyper phase shift keying (HPSK) basis functins that are peridic functins with a duratin T; frming the HPSK basis functins as (h(t) = ~cs(2.jr(f, + 1/(2T))t) (fj2(t) = ~ sin(2.jr(f, + 1/ (2T))t) (P,(t) = ~ sin(2.jr(f, /(2T))t) (fi4(t) = ~cs(2.jr(f, /(2T))t) where is the amplitude and (h(t)= ~cs(2.jr(f,+i/(2t))t) (fj2(t) = ~ sin(2.jr(f, + 1/(2T))t) 6 65 is the energy per symbl; prviding a bit t symbl mapper accrding t Table 1, Table 2, r Table 3 fr cmbining the bit stream and the HPSK basis functins t frm a successin f 4-bit HPSK symbls fr 16-HPSK, 5-bit HPSK symbls fr 32-HPSK, r 6-bit HPSK symbls fr 64-HPSK;

16 13 cnnecting a transmitter t the mapper and arranging the transmitter t transmit signals indicative f the HPSK symbls; prviding a receiver arranged t receive the signals indicative f the HPSK symbls frm the transmitter; and demdulating the HPSK symbls with the HPSK basis functins t reprduce the bit stream f binary data. US 8,64,541 Bl 7. The methd f claim 6 wherein the data input t the mdulatr is a serial bit stream, the methd further cmpris- 1 ing: prviding a serial t parallel cnverter arranged t prvide a parallel bit stream t the bit t symbl mapper The methd f claim 6 further cmprising: frming the demdulatr t include fur crrelatrs fr crrelating each received HPSK symbl with the fur HPSK basis functins and able t decde errr crrectin cdes. 9. The methd f claim 6 further cmprising: sampling signals utput frm the crrelatrs at time intervals equal t the duratin T f the basis functins. 1. The methd f claim 6 further cmprising: prviding a minimum Euclidean distance detectr arranged t and estimate which f the crrelatr utput signals is clsest t the signal received by the receiver. * * * * *