FI124308B - Reduce peak to average power ratio - Google Patents

Description

Reduce peak-to-average power ratio

Cross reference to relatives application

This application claims priority over U.S. Provisional Application No. 61 / 050,604, filed May 5, 2008, the disclosure of which is expressly incorporated herein by reference in its entirety.

Technical field

The system and method described herein relates to the field of telecommunication, and in particular to a system and method that reduces the peak power ratio of a communication system to the average power (PAR).

Description of the Related Art

The communication system facilitates data exchange between various electronic devices such as mobile station (MS), base station (BS), access point, cellular telephone, personal digital assistant (PDA), radio, 15 personal computer, laptop, workstation, GPS device, server and other devices that may be used for transmitting and / or receiving data. Communication systems are widely used to provide a variety of communication services, such as speech, video, packet data, messaging, broadcast, etc. These systems may employ various multiplexing methods, such as orthogonal frequency division multiplexing (OFDM), various space-time interleaving, and multiplexing, input and multiple-output, ΜΙΜΟ).

From the space-time codes implemented in many transmitting antennas? they, as well as the inverse Fourier transform used in OFDM systems, generally result in a high peak power to average power ε (PAR). PAR is a measure relevant to all multiplexing methods. It is the ratio of the peak power of the signal to the average power of the signal x. A high PAR is undesirable as it may require

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tin (PA) operates at an average output power, which may be much lower than 30p from the peak output power. This action at reduced power is due to the fact that the high peaks in the signal may cause a decrease in PA function.

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in the nonlinear region, or possibly to cut large peaks, which can then cause intermodulation distortion and other errors that can degrade the signal quality. By using a power amplifier PA at a power 2 that is lower than its peak power, when the operating power level may be dependent on the PAR, the power amplifier PA may be able to handle large signal peaks without generating excessive distortion. However, such operation at lower power results in poor power efficiency 5 of the power amplifier PA at times when there are no large peaks in the signal. Thus, it is desirable to reduce the PAR of the signal so that the PA can operate closer to peak-to-peak power, if necessary.

A slowly fading point-to-point channel has a trade-off between error probability and data rate in the form of diversity multiplexing gain (D-MG). However, when multiple antennas are used, the space-time codes that reach the D-M compromise generally result in a larger pair in each antenna.

Constellation shaping is a coding technique that selects pattern points from an expanded pattern by selecting a new border from the lattice.

It can provide a reasonable design gain over the coding gain with reasonable complexity. The basic idea of pattern design is to create a pattern that contains the minimum number of points needed, and by selecting a new boundary that matches a planar surface defined by the energy standard of a pattern that uses only points within this optimized boundary. Proper pattern design can lead to a decrease in PAR.

A method for reducing PAR using pattern design has been proposed by H. Kwok in 'Shape up: Peak-power reduction via constellation shaping', Ph.D. dissertation, University of Illinois, Urbana-Cham-paign, 2001. Kwok describes a method of reducing PAR using Smith 25 Normal Form matrix decomposition. Kwok's method is relatively complex and requires large computational resources. In addition, it appears to be applicable only to OFDM systems.

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Therefore, there is a need for PAR reduction methods suitable for various communication systems, including OFDM, time division coding and MIMO systems, as well as systems that include | Summary of the Invention In one aspect of the present disclosure, methods and apparatus according to the appended independent claims are provided. According to a first aspect of the present disclosure, there is provided a method of transmitting data in a communication system using an encoding method. This method comprises processing the data according to a particular processing method so as to provide a plurality of information symbols; shaping the pattern of these plurality of information symbols so as to obtain a plurality of formatted symbols; processing the plurality of shaped symbols 5 according to an encoding method to obtain a plurality of converted signals such that the peak power ratio of these plurality of converted symbols to an average power (PAR) is lower than the PAR that would have been provided if the information symbols had not been formatted symbols; the encoding-10 method may be expressed in the form *, where x is the isomorphic vector representation of the transformed signals, G is the inverse NxN generator matrix and N is an integer> 0, s is a vector of multiple information symbols selected from the n-dimensional integer lattice ZN represents real space; and transmitting the plurality of converted signals over the communication network.

According to another aspect of the present disclosure, there is provided a method of receiving data in a communication system using an encoding method, the method comprising receiving a plurality of transmitted signals having a pattern of received signals preformed before transmission, processing the plurality of received signals in an estimator; and decoding the decoded symbols so as to obtain information symbols when the pattern of the transmitted signals has been processed before transmission so that the peak power ratio of the transmitted signals is less than PAR if the transmitted signals were not formatted before transmission, and

__ / “* r ^ NxN

according to a method which may be expressed in the form A

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According to a third aspect of the present disclosure, is

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an apparatus for transmitting data in a communication system using an encoding method, the apparatus comprising a processor for processing data according to a particular processing method 30, so as to produce a plurality of information symbols | and; a shaping unit for shaping a pattern of these plurality of information symbols so as to obtain a plurality of shaped symbols; an encoder for encoding these plurality of shaped symbols according to the encoding method so as to obtain a plurality of transformed signals such that the peak power ratio of these plurality of transformed symbols is lower than the PAR if the information symbols were not present. would have been formatted into 4 formatted symbols before processing the converted symbols, where the encoding method may be expressed as Λ; and a transmitter for transmitting these multiple converted signals over the communication network.

According to a fourth aspect of the present disclosure, there is provided an apparatus for receiving data in a communication system using an encoding method, the apparatus comprising a receiver for receiving a plurality of transmitted signals as received signals, wherein the pattern of the transmitted signals was shaped prior to transmission; a processor for processing the plurality of received signals 10 in the estimator to obtain decoded symbols; and a despreading unit for despreading the decoded symbols so as to obtain information symbols wherein the pattern of the transmitted signals has been processed prior to transmission so that the peak power ratio of the transmitted signals is lower than the PAR if the transmitted signals were not formatted;

__ / * -> _ c pj / Vx / V

according to a method that may be expressed as Ä

It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not limiting of the claimed invention.

20 Brief Description of the Drawings

The accompanying drawings, which are incorporated herein and form part thereof, illustrate various embodiments. In the drawings:

Figure 1 shows an exemplary communication system; Figure 2 shows a block diagram of a user station and a node:

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Fig. 3 shows an encoding unit; ™ Figures 4A-4C show signal patterns; Fig. 5 shows a process of a forming unit according to the first embodiment; ir 30 Figure 6 shows a decoding unit;

Fig. 7 shows the process of the S shaping removal unit according to the first embodiment; Fig. 8 shows a process of an encoding unit according to another embodiment; Figure 9 illustrates a process of a mold removal unit according to a second embodiment; 5

Fig. 10 shows a process of an encoding unit according to a third embodiment;

Figure 11 illustrates the process of a mold removal unit according to a third embodiment; Figures 12A-12C show simulation results.

DESCRIPTION OF EMBODIMENTS

In the following description, certain techniques and embodiments, such as certain sequence sequences, interfaces and configurations of process steps, are provided for explanation and not for purposes of limitation, in order to provide a sufficient understanding of the techniques disclosed herein. While these techniques and embodiments are primarily described in connection with the accompanying drawings, those skilled in the art will further appreciate that these techniques and embodiments may also be implemented in other communication systems.

Reference will now be made in detail to an exemplary embodiment of the invention, examples of which are illustrated in the accompanying drawings. Wherever possible, the same reference numerals will be used throughout the drawings to refer to the same or similar parts.

The methods, apparatus, and systems disclosed herein are configured to reduce PAR without affecting code structures and without transmitting additional information so that the modified space-time codes still achieve the desired D-MG compromise.

Figure 1 shows a wireless communication system 100 including a plurality of nodes 110 and a plurality of user stations 120. Each node 110 is generally a fixed station that communicates with the user stations and may also be referred to as a base station, an access point, etc.

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The node 110 provides communication coverage over a specific geographic area and supports communication between user stations 120 located within this coverage area. System controller 130 may connect to node 110 and provide T-coordination and control of these nodes. System Controller 130 | 30 may be a single network unit or a collection of network units, e.g., an Access Gateway (AGW), a Radio Network Controller (RNC), etc.

User stations 120 may be scattered throughout the system 100 and each user station 120 may be stationary 35 or mobile. Each user station 120 may also be referred to as a mobile station, mobile equipment, terminal equipment, access terminal, subscriber unit, station, etc. Each user station 120 may be a cellular telephone, a personal digital assistant (PDA), a wireless communication device, a handheld device, laptop computer, etc. User station 120 may communicate with zero, one or more nodes 110 downlink 5 and / or uplink at any particular time. Downlink (or forward link) refers to a communication link from one node 110 to one user station 120. Uplink (or reverse link) refers to a communication link from one user station 120 to one node 110. In addition, system 100 may utilize OFDM, ΜΙΜΟ, status coding, 10 and / or other multiplexing methods.

Fig. 2 shows an exemplary block diagram of a communication system 200 including a user station 202 and a node 204, which may be one of the user stations 120 and nodes 110, respectively, in Fig. 1. For simplicity, only the uplink transmission processing units are shown in Fig. 2.

As shown in Figure 2, the user station 202 and the node 204 of the communication system 200 may use the communication network 206 to transmit and / or receive data over channels 208. Communication network 206 may include one or more types of networks, such as wide area network (WAN), local area network (LAN), 3G network, Worldwide Interoperability for Microwave Access (WiMAX) network, Long Term Evolution ( LTE) network, Code Division Multiple Access (CDMA) network, Broadband CDMA (WCDMA) network, or any other suitable protocol to facilitate communication between user station 202 and node 204. Communication network 206 may operate on wire line and / or wire tower techniques and may, but need not, operate according to the protocols defined in IEEE 802.11, 802.11a, 802.11b, ™ 802.11e, 802.11g, 802.11 h, 802.11 i, 802.11 n, 802.16, 802.16d, 802.16e and / or ° 802.16m. Network connections between or among the nodes of the communication system 200 may be established over Ethernet, telephone line, cellular channels | or any other transfer medium.

The user station 202 may include a transmission (TX) process [£ Sorin 210, an encoding unit (s) 212, a transmitter (s) 214, memory device (s) 216, and TX antenna (s). The node 204 may include a receive (RX) processor 220, a decoding unit (s) 222, a receiver (s) 224, a memory device 226, and an RX antenna (s) 228.

In connection with user station 202, TX processor 210 receives traffic data and signaling for transmission to node 204, processes 5 (e.g., interleaves, symbol mapping, modulates, etc.) traffic data, signaling and / or pilot symbols and outputs the modulated symbols. The encoding unit 212 encodes the modulated symbols and generates the converted signals for transmission, and may include its own processor. The transmitter 214 further processes (e.g., converts, amplifies, filters and converts to a higher frequency) 10 these converted signals and generates an uplink signal which is transmitted via the TX antenna 218. The memory device 216 may store data that may be retrieved and used when the user station 220 performs various processing tasks, including those performed by the encoding unit 212. The memory device 216 may also store predetermined values such as addresses, channel 15 en 208 transmissions / reception capacity, as well as information related to the properties of the communication network 206 and the node 204.

In connection with node 204, the RX antenna 228 receives an uplink signal from the user station 202 and outputs the received signal to the receiver 224. The receiver 224 processes (e.g., filters, amplifies, downgrades, and digitizes) the received signal and outputs the received samples. Decoding unit 222 performs symbol estimation and decoding of received samples. The RX processor 220 further processes (e.g., deletes the symbol mapping, de-interleaves) these symbol estimates and outputs the information symbols. The memory device 226 stores information taken from the received data and / or data that may be retrieved and used when node 204 performs various processing tasks. Additionally, the memory device 5,226 may store predetermined values that facilitate communication

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between user station 202 and node 204. In general, the processes performed by the RX processor 220 and the decoding unit 222 at node 204 are complementary to the processes performed by the TX processor 210 and the encoding | unit 212 performs at user station 202.

The TX and RX processors 210 and 220 may be media access controllers (MAC) and / or physical layer processing circuits, and the memories 216 and 226 may include any or all of 00 Non-volatile or volatile memory formats including, for example, semiconductor storage devices such as EPROM, RAM, ROM, DRAM, EEPROM and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical discs; and CD-ROMs. The memory devices 216 and 226 may include a computer readable storage medium containing application programs, code and / or instructions that may be executed by processors 5 210 and 220, respectively, in performing various processing tasks performed by user station 202 and node 204.

Embodiments consistent with the present invention may be practiced in communication systems using any of a variety of encoding methods, including those that achieve a D-MG compromise as previously described. Such en-coding methods may be expressed in the following general form (1):

X = Gs seZN Gg RNxN (1) wherein x is an isomorphic vector representation of either space-time code, symbols transformed with the inverse Fou-15 rier transform in OFDM systems, or other similarly transformed signals; G is a reversible NxN generator matrix (where N is an integer); s is a vector of information symbols selected from the N-dimensional integer lattice ZN, where Z represents a set of integers; and R represents a real number level. For example, the QAM-20 pattern is simply a translation of the integer lattice ZN.

Many encoding methods may be expressed in the general form of equation (1). For example, the nxn space-time code X could be expressed in the form of n vectors x (l) of length n when i = 1.2, ..., n, xw = G (,) sw SWeZ [i] n, G (0eC ™ nc \ j δ 25 where Z [i] represents Gaussian integers (i.e. a + bi, a, b eZ), C represents

CM

At the complex level, sw is a vector containing n information symbols and Gw is a corresponding generator matrix. An isomorphic representation of each of s (l) and G (l) may be obtained by separating their real and imaginary parts, as follows,

X

£ s' ^ Re ^ Y), lm ((s {Y)] rm S 30 | £, (/) _ Γ Re (G0>) Im (G (0) I and L-Im (Gw) Re (G (0) _ where vT denotes transpositions of vector v.

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As a result, x (l) = G (l) s (l), where x '(l), s (l) and G (l) respectively represent the vectors x (l), s (l) and G ( (l) an isomorphic representation. This expression corresponds to the general form (1).

FIG. 3 shows an exemplary block diagram 300 of the encoding unit 52. The shaping unit 310 receives information symbols s, i.e., symbols that undergo modulation, either from the TX processor 210 or from the memory device 216. The shaping unit 310 performs pattern shaping on the information symbols s and to generator 320. In one embodiment, the information symbols s are quadrature amplitude modulation (QAM) symbols and the shaping unit 310 performs the shaping of the information symbols s such that the shape of the converted symbols x is substantially cubic. Generator 320 may be an encoder or an IDFT matrix that produces converted symbols for x transmission. The shaping unit 310 performs pattern shaping on the information symbols s such that the converted PAR x symbols are reduced.

The pattern generally consists of a set of points in an m-dimensional complex lattice or in an M-dimensional real lattice (where M = 2m) enclosed within a finite region. At any given transmitted data rate, the signal pattern boundary determines its average power and PAR. The PAR of the symbol stream transmitted at a given 20 antenna is defined as the maximum of the instantaneous transmitted power and the average transmitted power. This definition of PAR can be represented as: PAR s max PAR (x,) where PAR (x, -) - (IW |) J / (E [|| x, || 2]), cm 25 X, is the x of the transmitted signal element and "|| || "represents the L2 standard.

° The average power and PAR vary depending on the shape of the selected signal pattern. As the size of the pattern approaches an infinite, M-dimensional pattern o consisting of dots enclosed within an M-dimensional cube or cube, x results in a PAR value of 3. Embodiments consistent with the present invention are described to implement an asymptotic PAR 0 value obtained in cube design. However,

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g mate understands that different formatting methods may alter o PAR in different ways, some of which may be more advantageous than others, depending on the specific coding methods and desired PAR values.

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Figure 4A shows an exemplary two-dimensional representation of the signal pattern of information symbols s. Fig. 4B shows a pattern of x resulting from information symbols s processed by generator unit 320 without being processed by styling unit 310, e.g., x = Gs.

As shown in Figure 4B, the pattern of x is no longer cubic and consequently the PAR of the pattern is larger. Figure 4C shows the converted symbols x after the pattern has been formed, i.e. x = Gs'. As shown in Figure 4C, the shaping unit 310 converts the information symbols s into symbols s' such that the resulting pattern of x is cubic, resulting in an asymptotic PAR value of 3.

Approximal cube design HNF (Hermite Normal

Form) by disintegration

As shown in Figure 3, the shaping unit 310 generates the shaping symbols s' from the information symbols s, which are then used by the generator 320 to produce the converted symbols x. The shaping unit 310 generates the symbols s 'such that the output symbols x, obtained from the equation x = Gs', are approximately cubic and have a low PAR, and the generator 320 generates the output symbols x.

Figure 5 illustrates a process unit 310 for applying process 500 approximation cube design using HNF decomposition in accordance with the first embodiment of the invention. The process 500 may be performed by the design unit 212 as an ASIC or may be performed by the processor 210.

Initially, the shaping unit 310 determines whether the encoding method can be expressed in the general form described above (1) (520). If it cannot be expressed in this way, formatting is not performed (530). If the encoding method can be expressed in generic form (1), then formatting unit 310 determines the o relation matrix Q (540). Q is a relational matrix that defines the relation between the symbols s and s ', where s'eS + QZ ^ and s + QZN is a set of equivalent points, i.e. an adjacent set such that x = Gs', where x has the desired approximation

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30 cubic pattern represented by the following expression (2): x = Gs \ s'es + QZw (2)

Lo Therefore, S xeG (s + QZw) σ> § xeGs + GQZn and GQsal · 11 where σ is chosen such that σΝ is the total number of possible transmitted pixels and I is the identity matrix.

In FIG. 5, the shaping unit 310 selects the values of the symbols s' in the above equation (2) from within the shaped pattern having a boundary parallelepiped 5 defined by the columns (540) of the matrix Q. As a result, the signal limit in the x plane of the transformed symbols becomes approximately hypercube.

Q is determined by the ratio:

| Det (Q)!> Aw 10 where [] denotes the rounding function, σ 'is a constant that ensures that | det (Q) | > σΝ, oN is the number of possible transmitted points, and | det (Q) | is the volume of the parallelogram defined by the matrix Q or, equivalently, the number of points in the parallelogram. Since the number of subgroups, ie | det (Q) | must be large enough to support the desired number of transmitted points, the selected o'value is the smallest value that ensures that | det (Q) | > oN. In the case of a substantially hexagonal design, Q may be selected as a non-unit matrix.

When the matrix Q (540) is determined by the shaping unit 310, it indexes each auxiliary group s + QZN for encoding. In doing so, the design unit 310 assigns a group of subgroup leaders to represent the subgroups from among the subgroups s + QZN. The s + QZN side group leaders meet the following equation (3):

Her s' * ^

So s' ^ + Qz, all || a z e ZN

g 25 where s1, sj are respectively the co-leaders of two different subgroups s' + QZN, sj + QZN, to ensure that no ambiguity arises in the demodulation.

? For example, in the case where Q = D = diag (d1, d2, ..., dN), the group of sub-group leaders denoted by S may be chosen as follows:

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30 ra m m S S = {s = [Si, s2, sNy | 0 <Si <di, / = 1,2, ..., A /},

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o Here the subgroup leaders s e S satisfy equation (3) and S contains all subgroup group leaders.

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As explained above, the number of side group leaders is equal to | det (D) |. For example

F \ 0Λ D = 0 2 S = {[0,0] r, [0,1] r} if νυ Δ), min 5 and the number of side group leaders in group S is det (D) which is 2.

According to one embodiment of the invention, for a general case where Q is not a diagonal matrix, Q can be decomposed as follows.

Q = RV, <4) 10 where V is a unimodular matrix and R is a lower triangle integer matrix. The HNF Theorem, published by C. Hermite in "Sur I'introduction of Variables in Theorie des Nombres" (J. Reine Angew. Math., Pp. 191-216, 1851) and summarized below in Theorem 1 and In Theorem 2, the quotient Q = RV exists.

Theorem 1: Any inverse N x N integer matrix Q can be decomposed to Q = RV, where V is a unimodular matrix and R is a lower triangle integer matrix.

Let rN ^ 0 be the diagonal elements of the matrix R. The group S of adjacent group leaders may be formed as follows 20 S = {s | 0 <s, <η). (5) where s ~~ S1 'Sz' Sf ^ 'The validity of this group of subgroup leaders can be verified by the cm theorem 2 below.

Theorem 2: For a given matrix Q = RV, the group S defined in equation (5) contains all set s + QZN subgroup leaders.

Therefore, by performing HNF decomposition of the matrix Q on the lower triangle matrix R and the unimodular matrix V, the design unit 310 is able to * obtain the subgroup leaders from the s + QZN by first obtaining the subgroup § 30 leaders from the matrix R (550).

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Next, to ensure that each subgroup leader o of the set S is within the parallelogram enclosed by the columns of the matrix Q, the shaping unit 310 performs the modulo Q operation expressed in equation (13) below to insert s' into the shaped pattern before being transmitted. x = Gs '(560): Y - LQ "1sJ (6) s' = s-Qy where LJ denotes the floor function.

Alternatively, the shaping unit 310 may invert s' to minimize the average transmit power of x (570). Finally, when s' is defined, generator 320 receives the converted signals x based on equation (2) above.

FIG. 6 shows an exemplary block diagram of a decode unit 222 of node 10204 of 600. Received symbols y are processed by estimator 610 to obtain an estimate of s'. Estimator 610 may employ a number of available methods including, but not limited to, maximum likelihood and spherical demodulation. The despreading unit 620 processes the estimate of s' to produce information symbols s.

Figure 7 illustrates the process of a defrosting unit 620 according to a first embodiment of the invention. In this embodiment, the de-shaping unit 620 decodes symbols processed by HNF decomposition. First, the decoder unit 620 receives the decoded s' from the estator 610 and determines whether the decoder is necessary and / or desirable (710). 20 If formatting is not required or desired, formatting is not performed (720). If despreading is needed and / or desired, the despreading unit 620 determines s based on the decoded s' and r 1, where n is the i th column (730) of the lower triangular integer matrix R using the following algorithm: ^ 25 si = s'i mod m (si = s'i + q ^) c \ j

9 for i-2 \ N

o

En S '= s' + <? M Γη

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g s, = s'm modra (s, · = s'f + qfa) m o) 30 end o o ^ where Sj is the i th element in s; qj is the modulo quotient; and η, is the ith diagonal element of the matrix R. Because the generator matrix G is fixed for each particular application, n is pre-computed and stored 14 as part of the application system settings and is therefore known to both the transmitter and the receiver.

Alternatively, the values of s may be pre-computed and stored in a lookup table (not shown) in memory 226, together with the relevant algorithms used to obtain s. If the lookup table is used, the formatting unit 620 obtains s by looking at the lookup table (730). ).

Approximation Cube Design via Variable Integer Matrix Mapping 10 Figure 8 illustrates process 800 of shaping unit 310 according to another embodiment of the invention. Process 800 applies approximately hexadecimal formatting using an Integer Mapping Matrix (Integer Mapping). IRMM can avoid encoding calculations that involve large numbers because the integer constraints on the Q-factors of the relational matrix can be facilitated and non-linear mapping may be utilized. Thus, the IRMM may contribute to a useful encoding mechanism. In addition, the IRMM enables the resulting | det (Q) | expression in 2M format, which resembles the number of points in the pattern of all practical communication systems (Constellation).

Initially, the shaping unit 310 determines whether the encoding method can be expressed in the general form described above (1) (820). If it cannot be expressed, formatting will not be performed (830).

On the other hand, if the encoding method can be expressed in general form (1), the shaping unit 310 calculates the relation matrix Q to be G'1 25 (840) and normalizes (Q) | to be 1 (850). Then cm Q ”G'1,.

TT And CM | det (Q) | = 1.

^ By normalizing | det (Q) | to be 1 encoding unit 212 ensures that the response matrix Q can be processed by IRMM.

| IRMM is described in '' Matrix factorizations for re-

Lo versible integer mapping, "Hao et al. (IEEE trans. Signal Processing, vol. 49, p. 2314-2324, October 2001) (hereinafter referred to as" Hao "), the entire contents of which are incorporated herein.

As Hao suggests, if there is a matrix based 35 inverse elementary structure for a perfectly inverse integer implementation, this matrix is called an elementary reversible matrix (ERM). In the case of the upper triangular elementary reversible matrix (TERM) A, where the elements {amn} contain diagonal elements jm = ± 1, its variable integer fit from input s to output y is defined as y = [As], where

OF

Yin ~ Jiii ^ m ®mn ^ n _; l = A / + 1 y ^ l ”JnSN m = 1,2,3 ... iV-l, and its inverse is

sN ^ yJjN

*. = ('n „{y, - \ Σ>» α1 | (?) 1Q m = N - \, N-2, ... 1.

Similar results can be obtained for lower TERMs.

Single-row ERM (single-row ERM, SERM) is another functional ERM where jm = ± 1 on diagonal and all but one row of non-diagonal elements are zeros. The inverse integer adjustment of SERM is 15 as follows:

OF

Τ „, '= ΛΑ,' + Σβ ^ Λ,> ln * m 'J where m = m', etc. where m 'm' C \ J '° where m' represents a row of non-zero non-diagonal elements; 20 roads. Its inverse operation is i ° sm = y «, U ^ for m = m '£ uv- Σ ^ ά, κλ. ·· ^

V imin 'J

m o m If all the diagonal elements of the TERM are equal to o 1, the TERM is called the unit TERM. Similarly, SERM, whose dia-

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nal elements equal to 1 are called unit SERMs. Hao further states that the matrix has a "PLUS0" factorization if and only if its determinant is ± 1. In PLUS0 factorization, P is a permeation matrix that can shift the negative sign, L and U are respectively lower unit TERM and upper unit TERM, and S0 is a unit SERM, where m '= N.

Accordingly, shaping unit 310 obtains an inverse-to-integer-mapping (860) of its variable direction by decomposing the previously obtained relation matrix Q (850) into Q-PLUS0, (9) where P is a permutation matrix that can carry a negative sign, L and U. are the lower unit TERM and the upper unit TERM, respectively, and S0 is the yk-10 unit SERM.

Finally, the shaping unit 310 receives the symbols s 'via the following algorithm s' = [Qs] or equivalent

], seS

S '= {s' | 0 <, 9, <σ}.

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where [] represents a rounding function, S is a pattern of information symbols s selected from an N-dimensional integer lattice ZN, S 'is a contoured pattern, and o is an integer selected such that o is equal to the total number of possible transmitted pixels (870).

FIG. 9 illustrates a process 900 of a deinterleaving unit 620 according to another embodiment of the invention. The process 900 decodes symbols processed by the IRMM. The despreading unit 620 receives the decoded s' from the estimator 610 and determines whether despreading is necessary and / or desired (910). If de-formatting is not necessary or desired, then de-formatting

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£ 25 to do not run (920). If de-formatting is required and / or desired, the de-formatting unit 620 returns s (930) using decoded s' based on the following 9 ratios ° s-iSoVVpV)]]], cc 1 where [U v] denotes (7). the given upper triangle TERM U: 30 inverse operation for vector v, [L'1v] denotes the lower three TERM L: nm 1 g inverse operation for vector v, and [S0 v] is the inverse operation of SERM S0 given in equation (8) for vector v.

According to an embodiment of the invention, when the complex representation is used for the design, the general form will be (1) 17 x = Gs, setZIi ^ GeC * '4 ", (10) where the rounding function now functions separately for real and imaginary components and corresponding jm = ± 1. The SERM and TERM either become ± 1 or ± i, where i is the imaginary unit The inverse operations (7) and (8) are still valid in the above equation (10).

In this case, Q may be decomposed to Q = PLDrUS0, (11) if and only if det (Q) = det (DR) t 0, where Dr = diag (1,1, ..., 1, e10). , L and U are the lower and upper TERM, respectively, and P is the permutation matrix. If det (Q) = 10 ± 1 or ± i, then a simplified factorization Q = PLUS0 is obtained. In other words, equation (11) is a generalization of equation (9).

In the case where det (Q) = e10 and is not equal to ± 1 or ± i, complex rotation e10 can be performed using the real and imaginary components of the complex number factorized into three unit TERMs as follows: 'cosG - sinθ ^ | f I OVl -sinG ^ jf 1 O'1 ^ sinG cosG J [(l-cosG) / sinG lJ [o 1 J [(1-cosG) / sinG \} (cosG) / sinGV 1 {Λ p (cosG- lj / sinG '' v0 1 J ^ sinG 1) (o 1 y This equation may also be used when Q is a Fourier transform matrix, as in the OFDM signal, where all coefficients have the form e10.

In one embodiment, the values and algorithms used to obtain s 'in process 800 may be pre-computed and stored in a lookup table (not shown) in memory 216, and the values and algorithms used to obtain s' in process 900 may be pre-calculated and stored in the io lookup table (not shown) in memory 226. If the lookup tables are used, the formatting unit 310 obtains a s' in process 800 by looking at the lookup table x 25 in memory 216, and the despreading unit 620 receives the ss in process 900 from the lookup table in memory 226 .

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Figure 10 illustrates process 1000 of forming unit 310 according to a third embodiment of the invention and selectively applies either HNF decomposition or IRMM.

18

Initially, the shaping unit 310 determines whether the encoding method can be expressed in the general form given above (1) (1020). If it cannot be expressed, formatting is not performed (1030).

If the encoding method can be expressed in general form (1), then the shaping unit 310 determines whether HNF decomposition or IRMM (1040) is desired. If HNF decomposition is desired, then shaping unit 310 performs the operations described in steps 540-570 in process 500 using HNF decomposition to obtain s' (1050). On the other hand, if IRMM is desired, then shaping unit 310 performs operations corresponding to steps 840 to 870 10 in process 800 using IRMM to obtain s' (1060).

Fig. 11 shows a decoder unit 610 according to a third embodiment of the present invention for decoding symbols 1100. Initially, the decoder unit 620 receives the decoded s' from the estator 610 and determines whether the decoder is necessary and / or desirable (1110). If de-formatting is not required or desired, de-formatting is not performed (1120). If despreading is required and / or desired, the despreading unit 620 determines whether the received symbols have been processed by HNF spreading or IRMM (1130).

If the despreading unit 620 determines that the symbols 20 have been processed by HNF decomposition, it performs an operation corresponding to step 730 in process 700 to obtain s from the decoded s' (1140). On the other hand, if the decompression unit 620 determines that the IRMM was used, it performs an operation corresponding to step 930 of the process 900 to obtain s from the decoded s' (1150).

Figs. 12A-12C show simulation results for exemplary space-time codes that achieve an optimal D-o MG compromise using 106 randomly generated symbols. Because

CVJ

The signals transmitted by the antennas have similar statistical distributions, the simulation results are presented as the mean complementary cumulative density function (CCDF) of the signals PAR of each antenna i expressed as follows: o CCDF {PAR (x /), p} = P {PAR (x, ·)> p}. (12) m O) § where p is the value of the abscissa. Equation (12) can be interpreted as the probability that the symbols PAR (Xj) transmitted by the antenna i exceed p at any given time.

19

In FIG. 12, an exemplary 4x4 mode time code comprising 4 transmission antennas and 4 symbol durations, designed to achieve an optimal D-MG compromise, was used to generate the simulation. Figure 12A shows the average CCDF {PAR (Xj), p} for four antennas using the HNF and IRMM type approximation cube design shown above. The horizontal axis represents the parameter p in dB (dB) and the vertical axis represents the mean CCDF {PAR (Xj), p}. The effect of the pattern size is also included in the simulation. As shown in Figure 12A, when the pattern is a reasonable size (64 QAM), the HNF formatting method provides a roughly 1.3 dB increase in PAR small-10 compared to the IRMM formatting method (denoted by "a" in Figure 12A), which gives approximately 2 dB PAR reduction compared to the unformatted method (denoted by "b" in Figure 12A). This increase in PAR reduction may be due to the fact that the HNF design places each transmitted point in a precisely parallelepiped, which is roughly a hypercube, while the IRMM design provides an exact hexagonal pattern with a few points outside the hypercube. As a result, the IRMM design generates certain points with higher PARs. However, as the size of the pattern becomes larger, both methods result in nearly equal PAR reductions and the PAR approaches its optimum value in cubic design, namely 10 log 3, or about 4.78 dB, as illustrated in Fig. 12A.

Fig. 12B is an exemplary 5x5 space-time code used for simulation generation, comprising 5 transmit antennas and 5 symbol durations, designed to achieve an optimal D-MG

25 missions. The axes of Figure 12B show the same dimensions as the axes of Figure 12A. Since Figure 12B shows the average CCDF of the PAR for 5 antennas using HNF and IRMM type, approximately cubic design, Figure 12A

CM

In comparison to showing the average CCD of PAR for 4 antennas, FIG. 12B demonstrates that greater PAR reduction is achieved as the number of antennas increases.

Finally, Figure 12C shows the probability of a frame error

Lo (frame error probability, FEP) for communication systems having 4 or 5 transmitting antennas and 4 or 5 receiving antennas in channels of pseudo-static Rayleigh fading, plotted as a function of average signal-to-noise ratio (SNR).

™ 35 Exemplary complete space-time codes that achieve optimal D-MG compromise are used for 4x4 and 5x5 channels. The state decoder is used for lattice decoding. As shown in Fig. 12C, the state-time codes transmitted after formatting give almost indistinguishable error performance compared to the codes transmitted without formatting. In other words, the PAR subtraction methods consistent with the present invention do not affect the performance of the space time codes.

Compared to existing PAR subtraction methods, the methods described herein significantly reduce the computational complexity. In addition, the methods provided herein work for any non-unit matrix type generator / modulation matrix while achieving a better PAR reduction. Furthermore, the embodiment of the present invention is not limited to OFDM and space-time coded systems; embodiments consistent with the present invention may be applied in virtually any system having encoding methods that may be expressed in general form (1).

The above description is presented for purposes of illustration. It is not exhaustive and does not limit the invention to the precise forms or embodiments disclosed. Variations and adaptations of the invention will become apparent to those of ordinary skill in the art upon consideration of the specification and upon the practical application of the disclosed embodiments of the invention.

Other embodiments of the invention will be apparent to those skilled in the art from consideration of the disclosure and from the practice of the invention disclosed herein. It is intended that the specification and examples be considered to be exemplary only, with the true scope and spirit of the invention as set forth in the following claims.

25

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δ c \ j i o o

X

cc

CL

m o m m O) o o c \ j

Claims (34)

21 A method for transmitting data in a communication system (100, 200) using an encoding method, characterized in that the method comprises: shaping (540-570) a pattern of a plurality of information symbols into a cubic pattern such that s' = s-Qy ,. > where s 'is these plurality of shaped symbols, Q is a relational matrix and y = Le ~' 4 where L J is a floor function and s is information symbols so that a plurality of shaped symbols are obtained; processing the plurality of shaped symbols according to the encoding method to obtain a plurality of converted signals such that the peak power ratio of the plurality of converted symbols is lower than the average PAR that would be if the information symbols 15 were not formatted to form symbols , where the encoding method may be expressed in the form x = Gs, seZ, GeR where x is the isomorphic vector representation of the transformed signals, G is the inverse NxN generator matrix, and N is an integer> 0, s is a vector of multiple information symbols selected in the N dimension -20 of the integer lattices ZN, and R represents a real plane; and transmitting the plurality of converted signals over the communication network (206). The method of claim 1, wherein performing the cube shaping comprises performing matrix decomposition. The method of claim 1, further comprising: generating a plurality of formatted symbols such that s e S + Q 1 where O s' is a plurality of formatted symbols and Q is a relational matrix; and ^ generating a plurality of modified signals such that x = Gs'. i The method of claim 1, wherein Q satisfies ^ 30 Q = [o'G'1], | det (Q) | > oN o where [] represents the rounding function, σ 'is a constant that ensures § | det (Q) | > oN, oN is the number of possible transmitted pixels and 00 | det (Q) | represents the absolute value of the determinant of the matrix Q. 22 The method of claim 1, further comprising decomposing the matrix Q into the form Q = RV, where R is a lower triangle integer matrix and V is a unimodular matrix. The method of claim 2, wherein the cube shaping comprises performing a normal matrix decomposition of Hermite. The method of claim 1, wherein Q satisfies GQ = ^ I where o is selected such that oN is the total number of possible path pixels transmitted and I is the identity matrix. The method of claim 2, further comprising performing non-linear mapping. The method of claim 8, wherein performing the non-linear mapping comprises performing an inverse integer rice mapping. 10 Q = [o'G'1], | det (Q) | > oN, where [] represents the rounding function, σ 'is a constant that ensures | det (Q) | > σΝ, oN is the number of possibly transmitted pixels and | det (Q) | represents the absolute value of the determinant of the matrix Q. The method of claim 9, further comprising treating these plurality of information symbols such that s '= [Qs], and Q = G'1 20 where s' is a plurality of shaped symbols, Q is a relational matrix, and [] represents a rounding function. The method of claim 10, further comprising: normalizing an absolute value of the determinant of the matrix Q to 1; and C 1 J 2 is decomposed Q such that Q = PLUS 0, ° where P is the permutation matrix, L and U are respectively the lower inverse unit triangle in the basic matrix and the upper inverse unit | triangle matrix S0 is a single row inverse unit base matrix. The method of claim 11, further comprising obtaining a plurality of shaped symbols s 'such that s' = P [L [U [SO (s)]]]. o The method of claim 10, further comprising decomposing the matrix Q such that 23 Q = PLDr10IS0, if det (Q) = det (DR) Φ 0, where P is a permutation matrix, L and U are respectively lower inverse the unit triangle basic matrix and the upper inverse unit triangle basic matrix, Dr = diag (1,1, ..., 1, e'e) and S0 is the single row inverse unit base matrix. A method of receiving data in a communication system (100, 200) using an encoding method, the method comprising: receiving a plurality of transmitted signals, characterized in that the pattern of the received signals is shaped (540-570) into an auditory pattern prior to transmission such that s' = s -Qy ,. ? where s' is these plurality of shaped symbols, Q is a relational matrix and y = \ qM where | J is a floor function and s is information symbols; processing the plurality of received signals in an estimator 15 (610) to obtain decoded symbols; and removing (730) decoding the decoded symbols to provide information symbols wherein the pattern of the transmitted signals is processed prior to transmission such that the peak power ratio of the transmitted signals to the average power 20 (PAR) is lower than the PAR that would be if the transmitted signals were not formatted before transmission. , and according to the encoding method, which can be expressed as x = Gs, seZw, GeRNxN ^ where x is an isomorphic vector representation of the transmitted signals before transmission, G is an inverse NxN generator matrix and N is an integer> 0, s is a vector of their plurality of information symbols, selected from the N-dimensional integer lattice ZN, and R represents a real plane. o C \ J The method of claim 14, further comprising performing a maximum likelihood estimation or balloon demodulation / decoding. X £ 30 The method of claim 14, further comprising obtaining the information symbols s by the equations mg Si = s'j mod n, (Si = s'i + qirn) ooc \ js = s + qj-irj-24 where Sj is the information symbol s the ith element in order; s' is said plurality of decoded symbols; γν is the ith diagonal element of the order R of the lower triangle integer R; qj is the modulo quotient; and rj is the i th column of the lower triangular integer matrix R. The method of claim 14, further comprising obtaining the information symbols s by the equation s = [So'1 [U'1 [L'1P'1 (s')]]], wherein P is a permutation matrix, L and U are respectively lower the inverse triangle base matrix and the upper inverse triangle base matrix-10 rice, S0 is the one-row inverse base matrix, [U'1v] denotes the inverse operation of the upper inverse triangle base matrix (TERM) U for the vector v, [L'1v] denotes the lower matrix TER, S0'1v] is the inverse operation of a single-row inverse basic matrix S0 An apparatus (202) for transmitting data in a communication system (100, 15,200) using an encoding method, characterized in that the apparatus comprises: a shaping unit (212) for shaping a plurality of information symbols into a cubic pattern such that s' = s-Qy. > where s' is these plurality of shaped symbols, Q is a relational matrix and 20 y = \ qM where L J is a floor function and s is information symbols so as to obtain a plurality of shaped symbols; an encoder (212) for encoding these plurality of shaped symbols according to the encoding method so as to obtain a plurality of transformed signals such that the peak power ratio of these plurality of converted symbols has a mean power (PAR) lower than PAR 0 if the information symbols were not formatted where x is the isomorphic vector representation of the transformed x signals, G is the inverse NxN-CC 30 generator matrix, and N is an integer> 0, s is the vector of the plurality of information symbols selected from the N-dimensional integer lattice ZN, and R m 1 represents a real plane; and o a transmitter for transmitting these plurality of converted signals over the communication network (206). 25 The device (202) of claim 18, further configured to perform cube design through matrix decomposition. The apparatus (202) of claim 18, further configured to produce said plurality of shaped symbols such that the 5 es + QZ, mSa s' are said plurality of shaped symbols and Q is a relational matrix, and wherein the plurality of transforms produces said plurality of transformed symbols signals such that x = Gs'. The device (202) of claim 18, wherein Q fills the ratios The apparatus (202) of claim 18, further configured to decompose Q into the form Q = RV, wherein R is a lower triangle integer matrix and V is a unimodular matrix. The device (202) of claim 19, further configured to perform normal matrix decomposition of Hermite. The device (202) of claim 18, wherein Q satisfies the ratio GQsa /, mjSA where σ is selected such that oN is the total number of transmitted ^ pixels, and I is the identity matrix. The device (202) of claim 19, further configured to perform non-linear mapping. The device (202) of claim 19, further configured to perform mapping of the inverse integer matrix. CL The device (202) of claim 26, further configured to process said plurality of information symbols such that CD130 S = [Qs], and Q = G'12 26 where s' is said plurality of formatted symbols, Q is a relational matrix and [] denote the rounding function. The device (202) of claim 27, further configured to normalize the absolute value of the determinant of the matrix Q to 15 and decompose Q such that Q = PLUS0, where P is a permutation matrix, L and U are respectively a lower inverse triangle base matrix and an upper inverse triangular base matrix and S0 is a single row inverse unit base matrix. The device (202) of claim 28, further configured to obtain said plurality of shaped symbols s 'such that s' = P [L [U [SO (s)]]]. The device (202) of claim 27, further configured to decompose Q such that Q = PLDrUSo, if det (Q) = det (DR) Φ 0, 15 where Ρ is a permutation matrix, L and U are respectively lower alternate the triangular base matrix and the upper inverse triangular base matrix, Dr = diag (1,1, ..., 1, e10) and S0 is the single row inverse unit base matrix. An apparatus (204) for receiving data in a communication system 20 (100, 200) using an encoding method, the apparatus comprising: a receiver (224) for receiving a plurality of transmitted signals as received signals, characterized in that the pattern of transmitted signals is cube-shaped (540-570); pattern such that 5 25 s' = S-QY>; where s' is the plurality of shaped symbols, Q is a relational matrix, and 9 y = where Q is a floor function and s is information symbols; a processor (220) for processing the plurality of received signals in the estimator to obtain decoded symbols; and g 30 a decoding unit (222) for decoding these decoded symbols so as to obtain information symbols, O) where the pattern of the transmitted signals is processed before transmission so that the peak power ratio of the transmitted signals is lower than PAR, if the transmitted signals were not formatted, and according to the 27 encoding method which can be expressed as x-Gs, $ eZN, GeRN * N t where x is the isomorphic vector representation of the converted signals before transmission, G must be inverted NxN generator matrix and N is an integer> 0, s is the vector of the plurality of information symbols selected from the N-dimensional integer lattice ZN, and R represents a real plane. The device (204) of claim 31, further configured to perform maximum likelihood estimation or balloon modulation / decoding. The device (204) of claim 31, further configured to obtain information symbols s by the equations s, = s', mod η, (s, = s'i + qirn) s' = s' + qMrM where s, is the information symbol s the i th element; s' is said plurality of decoded symbols; η, is the ith diagonal element of the lower triangle integer-15 rice; q, is the modulo quotient; and η is the diagonal element of the i th column of the lower triangle integer matrix. The device (204) of claim 31, further configured to obtain information symbols s by 20 s = [S0'1 [U'1 [L'1P'1 (s')]]], wherein P is a permutation matrix, L and U are respectively a lower inverse triangle base matrix and an upper inverse triangle base matrix, S0 being a single row inverse unit base matrix; [U'1v] denotes the inverse operation of the cvi upper inverse triangle basic matrix (TERM) U for vector v, [L'1v] denotes the inverse operation of the lower TERM L, and [S0'1v] is the inverse operation of the single row inverse basic matrix S0. o X X Q. m o m m σ> o o C \ J 28