U.S. patent application number 12/780692 was filed with the patent office on 2010-12-16 for method for generating a data block for transmission using a cpm scheme.
This patent application is currently assigned to IMEC. Invention is credited to Andre Bourdoux, Wim Van Thillo.
Application Number | 20100316166 12/780692 |
Document ID | / |
Family ID | 40622559 |
Filed Date | 2010-12-16 |
United States Patent
Application |
20100316166 |
Kind Code |
A1 |
Van Thillo; Wim ; et
al. |
December 16, 2010 |
METHOD FOR GENERATING A DATA BLOCK FOR TRANSMISSION USING A CPM
SCHEME
Abstract
A method for generating a data block for transmission using a
continuous phase modulation scheme is disclosed. In one aspect, the
method includes inserting payload data in the data block, the
payload data having a plurality of payload symbols, each involving
an state change in a continuous phase modulation waveform generated
from the data block in one of two opposite directions. It may
include inserting state compensation data in the data block for
cancelling out the state changes, such that the waveform has an end
state at the end of the data block equal to a begin state at the
beginning of the data block. The state compensation data is
determined by determining from the state changes an overall state
change caused by the payload data over the waveform and by
selecting a set of compensation symbols for the state compensation
data on the basis of the overall state change.
Inventors: |
Van Thillo; Wim; (Deurne,
BE) ; Bourdoux; Andre; (Esneux, BE) |
Correspondence
Address: |
KNOBBE MARTENS OLSON & BEAR LLP
2040 MAIN STREET, FOURTEENTH FLOOR
IRVINE
CA
92614
US
|
Assignee: |
IMEC
Leuven
BE
Katholieke Universiteit Leuven
Leuven
BE
|
Family ID: |
40622559 |
Appl. No.: |
12/780692 |
Filed: |
May 14, 2010 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
PCT/EP2008/066010 |
Nov 21, 2008 |
|
|
|
12780692 |
|
|
|
|
60989763 |
Nov 21, 2007 |
|
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|
Current U.S.
Class: |
375/308 |
Current CPC
Class: |
H04L 25/03159 20130101;
H04L 25/0244 20130101; H04L 25/0224 20130101; H04L 25/03254
20130101; H04L 27/22 20130101; H04L 2025/03407 20130101; H04L
2025/03522 20130101 |
Class at
Publication: |
375/308 |
International
Class: |
H04L 27/20 20060101
H04L027/20 |
Claims
1. A method of generating a data block for transmission using a
continuous phase modulation scheme, the method comprising:
inserting payload data in the data block, the payload data
comprising a plurality of payload symbols, each involving a state
change in a continuous phase modulation waveform generated from the
data block; and inserting state compensation data in the data block
for cancelling out the state changes, such that the waveform has an
end state at the end of the data block equal to a begin state at
the beginning of the data block, wherein the state compensation
data is determined by a) determining from the state changes an
overall state change caused by the payload data over the waveform,
and b) selecting a set of compensation symbols for the state
compensation data on the basis of the overall state change, the
compensation symbols each involving a state change in the waveform
and collectively cancelling out the overall state change.
2. The method according to claim 1, wherein the state compensation
data is placed on predetermined positions in the data block.
3. The method according to claim 1, wherein the continuous phase
modulation scheme comprises predetermined modulation parameters and
wherein the state compensation data is organized as a subblock
having a minimum required length which is determined on the basis
of at least one of the modulation parameters.
4. The method according to claim 3, wherein one of the
predetermined modulation parameters is a modulation index.
5. The method according to claim 1, wherein each of the state
changes comprises a phase rotation.
6. The method according to claim 5, wherein each of the state
changes further comprises a correlative state change.
7. The method according to claim 1, wherein the continuous phase
modulation scheme is a precoded continuous phase modulation scheme,
the data block forming part of a larger data structure in which the
data block is sandwiched between an equal cyclic pre- and
postfix.
8. The method according to claim 7, wherein the cyclic pre- and
postfixes also comprise the payload data and the state compensation
data.
9. The method according to claim 1, wherein the continuous phase
modulation scheme is a precoded continuous phase modulation scheme,
the data block forming a cyclic pre- and postfix provided on
opposite sides of another data block in a larger data
structure.
10. The method according to claim 1, wherein the data block is
preceded by a training sequence.
11. A communication system implementing the method of claim 1, the
system comprising a transmitter having a block for determining and
inserting the state compensation data in the data block and a
receiver having a block for detecting and removing the state
compensation data from the data block.
12. A device for generating a data block for transmission using a
continuous phase modulation scheme, the device comprising: means
for inserting payload data in the data block, the payload data
comprising a plurality of payload symbols, each involving a state
change in a continuous phase modulation waveform generated from the
data block; and means for inserting state compensation data in the
data block for cancelling out the state changes, such that the
waveform has an end state at the end of the data block equal to a
begin state at the beginning of the data block, wherein the state
compensation data is determined by a) determining from the state
changes an overall state change caused by the payload data over the
waveform, and b) selecting a set of compensation symbols for the
state compensation data on the basis of the overall state change,
the compensation symbols each involving a state change in the
waveform and collectively cancelling out the overall state
change.
13. A device for generating a data block for transmission using a
continuous phase modulation scheme, the device comprising: a
payload insertion module configured to insert payload data in the
data block, the payload data comprising a plurality of payload
symbols, each involving a state change in a continuous phase
modulation waveform generated from the data block; and a state
compensation insertion module configured to insert state
compensation data in the data block for cancelling out the state
changes, such that the waveform has an end state at the end of the
data block equal to a begin state at the beginning of the data
block, wherein the state compensation data is determined by a)
determining from the state changes an overall state change caused
by the payload data over the waveform, and b) selecting a set of
compensation symbols for the state compensation data on the basis
of the overall state change, the compensation symbols each
involving a state change in the waveform and collectively
cancelling out the overall state change.
14. The device according to claim 13, wherein the state
compensation data is placed on predetermined positions in the data
block.
15. The device according to claim 13, wherein the continuous phase
modulation scheme comprises predetermined modulation parameters and
wherein the state compensation data is organized as a subblock
having a minimum required length which is determined on the basis
of at least one of the modulation parameters.
16. The device according to claim 13, wherein each of the state
changes comprises a phase rotation.
17. The device according to claim 17, wherein each of the state
changes further comprises a correlative state change.
18. The device according to claim 13, wherein the continuous phase
modulation scheme is a precoded continuous phase modulation scheme,
the data block forming part of a larger data structure in which the
data block is sandwiched between an equal cyclic pre- and
postfix.
19. The device according to claim 13, wherein the continuous phase
modulation scheme is a precoded continuous phase modulation scheme,
the data block forming a cyclic pre- and postfix provided on
opposite sides of another data block in a larger data
structure.
20. The device according to claim 13, wherein the data block is
preceded by a training sequence.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation of PCT Application No.
PCT/EP2008/066010, filed Nov. 21, 2008, which claims priority under
35 U.S.C. .sctn.119(e) to U.S. provisional patent application
60/989,763 filed on Nov. 21, 2007. Each of the above applications
is incorporated herein by reference in its entirety.
BACKGROUND OF THE INVENTION
[0002] 1. Field of the Invention
[0003] The present invention relates to a method for generating a
data block for transmission using a continuous phase modulation
(CPM) scheme.
[0004] 2. Description of the Related Technology
[0005] There is an explosive growth in the demand for wireless
connectivity. Short ranges wireless links will soon be expected to
deliver bit rates of over 2 Gbit/s. Worldwide, recent regulation
assigned an at least 3 GHz-wide frequency band at 60 GHz to this
kind of applications. Chips for mobile consumer devices need to be
power efficient; hence a suitable modulation technique for 60 GHz
transceivers should allow an efficient operation of the power
amplifier (PA). Moreover, these chips need to be cheap so the
modulation technique should have a high level of immunity to the
front end nonidealities.
[0006] CPM signals posses these properties. They have a perfectly
constant envelope which makes them much more favorable than
orthogonal frequency-division multiplexing (OFDM) as cheap, power
efficient nonlinear PA's can be used instead or expensive,
inefficient linear ones. They are also more robust against other
front end imperfections such as phase noise and analog-to-digital
converter clipping and quantization. Moreover, they combine
attractive spectral properties with excellent power efficiency.
[0007] It is known that just the insertion of a cyclic prefix (CP)
is not sufficient to make the convolution of a CPM signal with a
linear channel appear to be a cyclic convolution, enabling FDE with
one complex multiplication per sample. An extra subblock has to be
inserted in each block to deal with the memory in the CPM signal.
In WO 2007/068994, a method is presented to append a cyclic
extension to a continuous phase modulation signal. Only N/2 symbols
in a block are used to transmit data, while the other N/2 are
chosen as the inverse of the first N/2. Of course, the block will
satisfy the cyclicity constraints. The overhead is huge, halving
the useful bit rate.
SUMMARY OF CERTAIN INVENTIVE ASPECTS
[0008] Certain inventive aspects relate to a method for generating
a data block for transmission using a continuous phase modulation
scheme with which cyclic continuous phase modulation signals can be
generated with a smaller loss on bit rate.
[0009] In an embodiment, a method for generating a data block for
transmission using a continuous phase modulation scheme is
presented. The method comprises the step of inserting payload data
in the data block. The payload data comprises a plurality of
payload symbols, each involving a state change in a continuous
phase modulation waveform generated from the data block (for
example a phase rotation in one of two opposite directions). The
method further comprises the step of inserting state compensation
data in the data block for cancelling out the state changes, such
that the waveform has an end state at the end of the data block
equal to a begin state at the beginning of the data block. The
state compensation data is determined by determining from the state
changes an overall state change. The overall state change is caused
by the payload data over the waveform. The state compensation data
is determined by selecting a set of compensation symbols for the
compensation data on the basis of the overall state change. The
compensation symbols are selected on the basis of the associated
state change in the waveform, to collectively cancel out the
overall state change. Hence, a cyclic continuous phase modulated
signal is generated.
[0010] In one aspect, the state compensation data is determined on
the basis of the overall state change caused by the payload data
and an appropriate set of compensation symbols is selected to
cancel out this overall state change. In this way, cyclicity of the
generated signal can be achieved with less compensation symbols
than in the prior art, where a complete antipode of the payload
data is required. Hence, more of the data block is available for
the payload data and a higher bit rate can be achieved.
[0011] The way in which the state compensation data is determined
according to one inventive aspect clearly some advantages. Less
compensation symbols are needed in comparison to the prior art,
reducing the overhead. The state compensation data can be
calculated based on just the symbols of the current data block so
the algorithm can work on a per-block basis, without knowledge of
previous blocks. Moreover it is compatible with differential
precoding of a popular class of CPM signals, which approximately
halves the bit error rate compared to uncoded CPM without any extra
overhead or complexity increase.
[0012] In one embodiment, the state compensation data is placed on
predetermined positions in the data block, which can facilitate
detection and removal of the state compensation data on receiver
side. Alternatively, the state compensation data can also be
grouped and preceded by a predetermined identifier.
[0013] In one embodiment where the continuous phase modulation
scheme comprises predetermined modulation parameters (such as for
example a modulation index, a number of symbol levels, length of
the pulse shaping filter or other), the state compensation data is
organized as a subblock having a minimum required length which is
determined on the basis of at least one of the parameters of the
CPM scheme, preferably at least the modulation index. This has the
advantage that each generated data block contains a subblock of the
same length in the same position, so that the detection and removal
of the state compensation data on receiver side can be facilitated.
As used herein, this subblock is called "intrafix". It can be
inserted after the payload data, before or somewhere in between.
Its minimum length is always sufficient if a certain relation to
the total block length is respected. In alternative embodiments,
the state compensation data can also be uniformly spread over the
payload data, for example each third, fourth, . . . n-th symbol
being a compensation symbol.
[0014] In one embodiment, the state changes are phase rotations. In
other embodiments, the state changes may further comprise
correlative state changes. Phase state and correlative state are
known terms in the field of CPM, so that they require no further
explanation here.
[0015] In one embodiment, the continuous phase modulation scheme is
a precoded continuous phase modulation scheme in which the data
block is part of a larger data structure in which the data block is
sandwiched between an equal cyclic pre- and postfix. These cyclic
pre- and postfixes may also comprise payload data and state
compensation data determined by the method according to one aspect.
In general, the method can be applied on the data block alone, on
the cyclic pre/postfix alone or on both, the latter being preferred
for reasons of achieving cyclicity while maximizing bit rate.
[0016] In one embodiment, a training sequence (TS) is used instead
of a cyclic prefix (CP). A TS offers additional known symbols and
therefore can enhance synchronization and--potentially--channel
estimation, while keeping the same performance as with a CP.
[0017] Another inventive aspect relates to a device for generating
a data block for transmission using a continuous phase modulation
scheme. The device comprises a payload insertion module configured
to insert payload data in the data block, the payload data
comprising a plurality of payload symbols, each involving a state
change in a continuous phase modulation waveform generated from the
data block. The device may further comprise a state compensation
insertion module configured to insert state compensation data in
the data block for cancelling out the state changes, such that the
waveform has an end state at the end of the data block equal to a
begin state at the beginning of the data block, wherein the state
compensation data is determined by a) determining from the state
changes an overall state change caused by the payload data over the
waveform, and b) selecting a set of compensation symbols for the
state compensation data on the basis of the overall state change,
the compensation symbols each involving a state change in the
waveform and collectively cancelling out the overall state
change.
[0018] Another inventive aspect relates to a system implementing
the method above. The system may comprise a processor configured to
execute instructions and perform the method above. The method may
be a general purpose, or a special purpose processor, and may be
for inclusion in a device, e.g. a chip that has other components
that perform other functions. Thus, one or more aspects of the
present invention can be implemented in digital electronic
circuitry, or in computer hardware, firmware, software, or in
combinations of them. Furthermore, aspects of the invention can be
implemented in a computer program product tangibly embodied in a
transitory or non-transitory computer-readable medium carrying
machine-readable code for execution by a programmable processor.
Method steps in the foregoing embodiments may be performed by a
programmable processor executing instructions to perform functions
of those aspects of the invention, e.g. by operating on input data
and generating output data.
BRIEF DESCRIPTION OF THE DRAWINGS
[0019] The invention will be further elucidated by means of the
following description and the appended drawings.
[0020] FIG. 1 shows structures of possible overall data structures
which can be generated with the embodiments of method.
[0021] FIG. 2 shows schematically possible communication system
models for implementing embodiments of the method.
[0022] FIG. 3 shows examples of possible cumulative state
constellations.
[0023] FIG. 4 plots the BER performance as a function of Eb/No for
some illustrative examples.
DETAILED DESCRIPTION OF CERTAIN ILLUSTRATIVE EMBODIMENTS
[0024] The present invention will be described with respect to
particular embodiments and with reference to certain drawings but
the invention is not limited thereto but only by the claims. The
drawings described are only schematic and are non-limiting. In the
drawings, the size of some of the elements may be exaggerated and
not drawn on scale for illustrative purposes. The dimensions and
the relative dimensions do not necessarily correspond to actual
reductions to practice of the invention.
[0025] Furthermore, the terms first, second, third and the like in
the description and in the claims, are used for distinguishing
between similar elements and not necessarily for describing a
sequential or chronological order. The terms are interchangeable
under appropriate circumstances and the embodiments of the
invention can operate in other sequences than described or
illustrated herein.
[0026] Moreover, the terms top, bottom, over, under and the like in
the description and the claims are used for descriptive purposes
and not necessarily for describing relative positions. The terms so
used are interchangeable under appropriate circumstances and the
embodiments of the invention described herein can operate in other
orientations than described or illustrated herein.
[0027] The term "comprising", used in the claims, should not be
interpreted as being restricted to the means listed thereafter; it
does not exclude other elements or steps. It needs to be
interpreted as specifying the presence of the stated features,
integers, steps or components as referred to, but does not preclude
the presence or addition of one or more other features, integers,
steps or components, or groups thereof. Thus, the scope of the
expression "a device comprising means A and B" should not be
limited to devices consisting only of components A and B. It means
that with respect to the present invention, the only relevant
components of the device are A and B.
[0028] Below, methods are described for generating a data block for
transmission using a continuous phase modulation (CPM) scheme. In
addition to a cyclic prefix, state compensation data in the form of
a so-called intrafix of payload data-dependent symbols is inserted
in each block to cope with the memory of the CPM signal, i.e. for
cancelling out overall or cumulative state change caused by the
payload data, such that the waveform becomes cyclic. Methods are
proposed for constructing such an intrafix, yielding a CPM signal
with properties enabling frequency domain equalization (FDE) on
receiver side. The intrafix and its minimum required length are
determined on the basis of the parameters of the CPM signal, such
as for example the modulation index, the number of symbol levels
and the length of the pulse shaping filter.
[0029] FIG. 1 shows data structures containing data blocks
according to one embodiment. "Data" is used to refer to payload
data, "Intrafix" is used to refer to a subblock containing state
compensation data. The combination of a "Data" sequence and an
"Intrafix" forms an embodiment of a "data block" as defined in the
claims. FIG. 1a shows a data block sandwiched between an equal
cyclic pre- and postfix, FIG. 1b shows a data block preceded by a
training sequence (on which the method according to various
embodiments can be applied as well), FIG. 1c shows a data structure
in which a data block sandwiched between an equal cyclic pre- and
postfix in which a second intrafix is inserted.
[0030] FIG. 2 a-c shows the corresponding communication system
schemes respectively corresponding to the data structures of FIG. 1
a-c. The top parts each time represent the transmitter side, which
comprises a block for intrafix insertion; the bottom parts each
time represent the receiver side, which comprises a block for
intrafix deletion.
[0031] In general, a transmitted CPM signal has the form:
s ( t , a ) = 2 E S T j .phi. ( t , a ) ( 1 ) ##EQU00001##
Where a contains the sequence of M-ary data symbols
a.sub.n.epsilon.{.+-.1,.+-.3, . . . , .+-.(M-1)}.The symbol
duration is T and E.sub.S is the energy per symbol, here normalized
to E.sub.S=1. The transmitted information is contained in the
phase:
.phi. ( t , a ) = 2 .pi. h n a n q ( t - nT ) ( 2 )
##EQU00002##
where h is either a single modulation index or is drawn from a
predetermined set of parameters of the CPM scheme. In the latter
case, the method can then be used for each group of symbols
corresponding to the same modulation index. q(t) is the phase
response, related to the frequency response f(t) by the
relationship q(t)=.intg..sub.-.infin..sup.tf(.tau.)d.tau. The pulse
f(t) is a smooth pulse shape over a finite time interval
0.ltoreq.t.ltoreq.LT and zero outside, where L is an integer. The
function f(t) is normalized such that
.intg. - .infin. .infin. f ( t ) t = 1 2 . ##EQU00003##
It can be seen that the phase .phi.(t,a) during interval
nT.ltoreq.t.ltoreq.(n+1)T can then also be written as:
.phi. ( t , a ) = h .pi. i = 0 n - L a i + 2 .pi. h i = n - L + 1 n
a i q ( t - iT ) ( 3 ) ##EQU00004##
[0032] We distinguish two types of memory in the CPM signal: the
phase state
.theta. n = h .pi. i = 0 n - L a i mod 2 .pi. ( 4 )
##EQU00005##
where .=. mod x is the modulo x operator which applies to both
sides of the equation, and the correlative state
.sigma..sub.n=(a.sub.n-1,a.sub.n-2, . . . , a.sub.n-L+1) (5)
Together, they form the "state" of the CPM signal .chi..sub.n
(.theta..sub.n,.sigma..sub.n) which captures all the memory. Taking
this memory into account has the advantage that FDE can be
enabled.
[0033] We consider a block-based communication system as explained
in [1]. Parameters with respect to the l.sup.th block are denoted
with a superscript (l). The last N.sub.P symbols a.sub.s.sup.(l) of
each block a.sup.(l) of length N are copied in front of the block,
creating blocks of length N.sub.T=N+N.sub.P, see FIG. 1a. Attaching
this CP a.sub.p.sup.(l) in the transmitter and discarding it in the
receiver makes the convolution with the channel appear to be a
cyclic convolution. The channel can then be equalized in the FD
with one complex multiplication per sample.
[0034] To construct a data block which yields a cyclic CPM signal
we also take the memory introduced by the CPM modulation into
account. This memory is reflected by the state .chi..sub.n.sup.(l)
of the modulator at symbol interval n in block l. From FIG. 1a it
can be seen that the condition to get a cyclic CPM signal with
period NT after discarding the CP is
.chi..sub.N.sub.P.sup.(l)=.chi..sub.N.sub.T.sup.(l) (6)
or equivalently:
.theta..sub.N.sub.P(l)=.theta..sub.N.sub.T.sup.(l) (7)
and
.sigma..sub.N.sub.P.sup.(l)=.sigma..sub.N.sub.T.sup.(l) (8)
Note that we use index N.sub.P and N.sub.T to indicate the state
after the last symbol of the CP (index N.sub.P-1) and of the
complete block (index N.sub.T-1) respectively.
[0035] To avoid interblock interference, the length N.sub.P of the
CP is chosen such that N.sub.P>L.sub.C+L where L.sub.CT is the
length of the channel delay spread. Because
a.sub.p.sup.(l)=a.sub.s.sup.(l), condition (8) is then
automatically satisfied. As we show now, condition (7) can be
satisfied by inserting an intrafix a.sub.i.sup.(l) of K
data-dependent symbols in each block. We assume the modulator
remembers its state after modulating block l-1, and starts from
that state modulating block l:
.chi..sub.0.sup.(l)=.chi..sub.N.sub.T.sup.(l-1) (9)
This is done to guarantee phase continuity between blocks. Again we
use index N.sub.T to indicate the state after the last symbol of
block l-1. We now define
.xi. n ( I ) = [ h .pi. i = 0 n a i ( I ) + k = 0 I - 1 .xi. N T -
1 ( k ) ] mod 2 .pi. ( 10 ) ##EQU00006##
and call it the cumulative state. It is very similar to the phase
state, but it includes all symbols up to the current interval n in
block l. With this new concept, and because we know condition (8)
is always satisfied, condition (7) is equivalent to
.xi..sub.N.sub.P.sub.-1.sup.(l)=.xi..sub.N.sub.T.sub.-1.sup.(l)
(11)
or
.xi..sub.N.sub.T.sub.-1.sup.(l)-.xi..sub.N.sub.P.sub.-1.sup.(l)=0
mod 2.pi. (12)
Inserting definition (10) this becomes
[ h .pi. i = 0 N T - 1 a i ( I ) + k = 0 I - 1 .xi. N T - 1 ( k ) -
h .pi. i = 0 N P - 1 a i ( I ) - k = 0 I - 1 .xi. N T - 1 ( k ) ] =
h .pi. i = N P N T - 1 a i ( I ) = 0 mod 2 .pi. . ( 13 )
##EQU00007##
We thus have to choose the symbols of the intrafix such that (11)
is satisfied. Equivalently, as
a.sub.d2.sup.(l)=a.sub.p.sup.(l):
h .pi. [ i = 0 N - K - 1 a i ( I ) + i = N - K N - 1 a i ( I ) ] =
0 mod 2 .pi. . ( 14 ) ##EQU00008##
[0036] This result can be interpreted as follows. The intrafix (in
(14) the second term) forces the CPM modulator after the N.sup.th
symbol into the same cumulative state as where it was after the
previous block, by cancelling the rotation caused by the symbols of
the current block (in (14) the first term). It is not relevant
which particular state this is, as long as it is the same at both
instants. We therefore do not need any information on the previous
blocks, enabling us to work on a per-block basis.
[0037] The length of the intrafix is determined so that (14) can
always be satisfied, i.e. a minimum required length is determined.
It obviously needs to be long enough to return to a certain state
from any other possible state. Moreover, the physical trellis of a
CPM scheme is sometimes time-dependent, which brings an additional
constraint on the length of the block and the intrafix. For FDE,
the Discrete Fourier Transform (DFT) of the block needs to be
taken, so we want to choose N a power of 2. We first do the
reasoning for M=2 and generalize afterwards.
[0038] Although CPM signals are in principle conceivable for any
value of the modulation index h, a key to the development of
practical maximum likelihood detectors is to consider schemes with
rational values of h. We therefore choose h=m/p where m and p have
no common factors. Three possible situations can occur, depending
on whether m and p are odd or even.
[0039] a) Even m, odd p: If m is even and p is odd, (14) is
satisfied if
i = 0 N - K - 1 a i ( I ) + i = N - K N - 1 a i ( I ) = 0 mod p (
15 ) ##EQU00009##
Below we suppose that N-K>p. By choosing N-K even, the first
term in (15) can then take the values
-p+1, . . . , -2,0,2, . . . , p-1=0,1,2,3, . . . , p-1 mod p.
(16)
Remembering that a.sub.n .epsilon.{1,-1}, it can be easily seen
that an intrafix of length p-1 (in this case an even number) can
also take all these values and is sufficiently long.
[0040] Note that this case (even m, odd p) is the only one where
CPM sheme has p phase states. This explains why (15) has to be
evaluated modulo p. In the next two cases (odd m and odd or even
p), the CPM scheme will have 2p phase states, and the respective
equations will have to be evaluated modulo 2p.
[0041] b) Odd m, even p: If m is odd and p is even, (14) is
satisfied if
i = 0 N - K - 1 a i ( I ) + i = N - K N - 1 a i ( I ) = 0 mod 2 p (
17 ) ##EQU00010##
By choosing N-K odd, the first term in (17) can take the values
-2p+1, . . . , -3,-1,1,3, . . . , 2p-1=1,3, . . . , 2p-1 mod 2p
(18)
It can be seen that also in this case an intrafix of length K=p-1
(an odd number this time) can take on all these values and is
therefore sufficiently long. For instance, the largest value (2p-1
mod 2p) can be seen to equal -1 mod 2p. The remaining (even) number
of elements in the term can then be chosen alternatively as 1 and
-1 so that they always cancel out each other. We have thus taken
into account all available knowledge about h and S to show that the
first term in (17) can only take a restricted number of values
between 0 and 2p. This allows us to choose the smallest possible
value for K.
[0042] c) Odd m, odd p: If m is odd and p is odd, finally, the
condition for (14) to be satisfied remains (17). Like in the two
previous cases, we choose K=p-1. As p is now odd, K and N-K are
even. The first term in (17) can then take on the values
-2p+2, . . . , -2,0,2, . . . , 2p-2=0,2, . . . , 2p-2 mod 2p
(19)
An intrafix of length K=p-1 can take on all these even values and
is therefore again sufficiently long. For binary signaling (M=2),
we can conclude that if we choose N even and K=p-1, (14) can always
be satisfied. We can now easily generalize this result towards
M-ary signaling.
[0043] With M-ary signaling, we can move `M-1 times faster` to a
certain state, so the general constraint becomes
K = p - 1 M - 1 ( 20 ) ##EQU00011##
Where .left brkt-top.x.right brkt-bot. is the smallest integer
greater than or equal to x. Of course the odd/even constraints on K
discussed above, still have to be respected.
[0044] These three cases will be discussed with one example each,
illustrated by FIG. 3. Without loss of generality, suppose that we
start in cumulative state 1 at the beginning of the block, and we
want to return to this state after the intrafix. The reasoning is
done for binary signaling to keep the examples simple, but it is
also valid for M-ary signaling.
[0045] a) Even m, odd p: When h=2/3, there are three possible
cumulative states. With N-K even, we can end up in any state before
the intrafix. We can indeed always return to state 1 with p-1=2
symbols. Note that 1 symbol would not be enough to `return` to
state 1 coming from state 1.
[0046] b) Odd m, even p: When h=1/2, there are four possible
cumulative states. With N-K odd, we can end up in states 2 or 4
right before the intrafix. We can thus always return to state 1
with p-1=1 symbol.
[0047] c) Odd m, odd p: When h=1/3, there are six possible
cumulative states. With N-K even, we can end up in states 1, 3 or 5
before the intrafix. With p-1=2 we can always return to state 1.
Note that with 2 symbols we can also `stay` in state 1.
[0048] In another embodiment, the method for generating a data
block uses a precoded continuous phase modulation scheme.
Differential encoding can be applied to the class of binary CPM
signals with
h=1/(2Q) (21)
Where Q .epsilon. to annihilate the inherent differential decoding
of CPM signals and thus improve error performance for coherent
detection. This precoding halves the BER compared to nonprecoded
CPM without any overhead or complexity increase. However, it also
imposes additional constraints on the block structure. These
constraints have to be taken into account to enable FDE.
[0049] Before calculating the intrafix, we explain how the sent
symbols a can be extracted from the received CPM waveform.
Exploiting the Laurent decomposition [2], (1) can be written as a
sum of P=2.sup.L-1 linearly modulated signals:
s ( t ) = p = 0 P - 1 n b p , n I p ( t - nT ) ( 22 )
##EQU00012##
Where pseudocoefficients b.sub.p,n are given by:
b p , n = exp [ j .pi. h ( i = 0 n a i - i = 1 L - 1 a n - i .beta.
p , i ) ] ( 23 ) ##EQU00013##
With .beta..sub.p,i the i.sup.th bit in the binary representation
of p (p=.SIGMA..sub.i=1.sup.L-12.sup.i-1.beta..sub.p,i). The
Laurent pulses l.sub.p(t), p=0, . . . , P-1 are real, with
l.sub.p(t)=0 for t<0 and t>(L+1)T. Using (22), a Viterbi
processor can generate an estimate of {circumflex over (b)}.sub.0,
both in the nonprecoded and in the precoded case.
[0050] A Viterbi receiver can be used to generate a maximum
likelihood estimate of the first pseudo-coefficient, from where a
can be uniquely determined by b.sub.0. We can therefore extract the
estimate of the input symbols a from the estimate {circumflex over
(b)}.sub.0 without losing any information:
b ^ 0 , n = exp ( j .pi. h i = 0 n a ^ i ) . ( 24 )
##EQU00014##
[0051] If we do not apply any precoding, the detection goes as
follows. Equation (24) can be written as:
b ^ 0 , n = exp ( j.pi. h i = 0 n - 1 a ^ i ) , exp ( j .pi. h a ^
n ) = b ^ 0 , n - 1 , exp ( j .pi. h a ^ n ) and as b ^ 0 , n - 1 =
1 , b ^ 0 , n - 1 - 1 = b ^ 0 , n - 1 * so ( 25 ) exp ( j.pi. h a ^
n ) = b ^ 0 , n b ^ 0 , n - 1 * ( 26 ) ##EQU00015##
[0052] In the very popular case of h=1/2 for instance, the input
symbols can be estimated as
a.sub.n=-j{circumflex over (b)}.sub.0,n{circumflex over
(b)}.sub.0,n-1* (27)
One error in {circumflex over (b)}.sub.o will on average cause two
errors in a. We want to avoid this by applying a precoding.
[0053] In the precoder, the information bits i, i.sub.n
.epsilon.{0,1} are first differentially encoded to obtain the
sequence p, p.sub.n .epsilon.{0,1}:
p.sub.n=i.sub.n.sym.i.sub.n-1 (28)
Where .sym. represents the modulo 2 addition. This sequence is then
mapped on the CPM symbols a, a.sub.n.epsilon.{-1,1};
a.sub.n=2p.sub.n-1=2(i.sub.n.sym.i.sub.n-1)-1 (29)
Substituting this in (24) yields
b ^ 0 , n = exp ( j .pi. 2 Q i = 0 n 2 ( i ^ i .sym. i ^ i - 1 ) -
1 ) = exp ( - j .pi. 2 Q n ) exp ( j .pi. Q i = 0 n ( i ^ i .sym. i
^ i - 1 ) ) ( 30 ) ##EQU00016##
If we assume (explained below)
.sub.-1=0 (31)
and as i.sub.n.sym.i.sub.n=0, (30) becomes:
b ^ 0 , n = exp ( - j .pi. 2 Q n ) exp ( j .pi. Q i ^ n ) ( 32 )
##EQU00017##
For h=1/2 for instance, it can be seen that
i ^ n = b ^ 0 , n j .pi. 2 n - 1 2 ( 33 ) ##EQU00018##
Contrary to (27), one error in {circumflex over (b)}.sub.o will now
on average cause only one error in the information bits. This is
what we wanted to obtain by precoding the information bits.
[0054] An extra constraint is imposed by the precoding. At the
beginning of each block (i.e. at n=0), we initialize the encoder
(28) by setting i.sub.-1=0, such that assumption (31) is valid. To
be able to start decoding correctly at the receiver after the
deletion of the CP (i.e. at n=N.sub.P), we have to bring the
transmitter in this same state at n=N.sub.P. We therefore also have
to satisfy
.chi..sub.0.sup.(l)=.chi..sub.N.sub.P.sup.(l) (34)
or because a.sub.p.sup.(l)=[a.sub.d2.sup.(l);a.sub.i2.sup.(l)] by
definition
.chi..sub.N.sup.(l)=.chi..sub.N.sub.T.sup.(l) (35)
[0055] We can satisfy both (6) and (35) easily by inserting two
intrafixes into each block as shown in FIG. 1c. We first insert the
second intrafix a.sub.i2.sup.(l) of length
K = p - 1 M - 1 + L - 1 ##EQU00019##
to satisfy (35). This length is needed because both the phase state
and the correlative state have to be compensated to enable correct
decoding at the receiver. The intrafix is therefore calculated such
that
h .pi. ( n = 0 N P - K - 1 a d 2 , n ( I ) + n = 0 K - 1 a i 2 , n
( I ) ) = 0 mod 2 .pi. ( 36 ) ##EQU00020##
Next, the first intrafix a.sub.i1.sup.(l) is calculated to satisfy
(6):
h .pi. ( n = 0 N - N P - K - 1 a d 1 , n ( I ) + n = 0 K - 1 a i 1
, n ( I ) ) = 0 mod 2 .pi. ( 36 ) ##EQU00021##
This intrafix only has to be of length
K = p - 1 M - 1 ##EQU00022##
because only the phase state has to be compensated, as the
correlative state condition is satisfied automatically. Finally,
the CP is inserted. The last N.sub.P symbols [a.sub.d2.sup.(l);
a.sub.i2.sup.(l)] of each block are copied in front of the block,
creating blocks of length N.sub.T=N+N.sub.P at the transmitter. The
complete system model is shown in FIG. 2c.
[0056] The above embodiments use a cyclic prefix. In an embodiment,
a training sequence (TS) is used instead of a cyclic prefix (CP). A
TS offers additional known symbols and therefore enables better
synchronization and--potentially--channel estimation, while keeping
the same performance as with a CP.
[0057] In the case of a TS, also memory can be taken into account
when inserting the TS in the data structure. The condition to get a
cyclic CPM signal with period NT after discarding the CP
becomes:
.chi..sub.0.sup.(l)=.chi..sub.N.sup.(l) (38)
Or equivalently:
.theta..sub.0.sup.(l)=.theta..sub.N.sup.(l) (39)
And
.sigma..sub.0.sup.(l)=.sigma..sub.N.sup.(l) (40)
[0058] In the case of a TS, the previous presented technique can
readily be applied to satisfy (38). However, (39) is not satisfied
automatically, therefore the last L-1 symbols of a.sub.i.sup.(l)
have to chosen such that
(a.sub.N-1.sup.(l),a.sub.N-2.sup.(l), . . . ,
a.sub.N-L+1.sup.(l))=(a.sub.N-1.sup.(l-1), a.sub.N-2.sup.(l-1), . .
. , a.sub.N-L+1.sup.(l-1)). (41)
If these symbols are chosen in this way,
a.sub.n.sup.(l)=a.sub.n.sup.(l') for all l,l' and for n=N-L+1 . . .
N-1. Therefore, the intrafix is independent of the block index and
information about previous blocks is not needed. The total length
of the intrafix in the case of a TS then becomes:
K = p - 1 M - 1 + L - 1 ( 42 ) ##EQU00023##
Where
[0059] p - 1 M - 1 ##EQU00024##
symbols are used to satisfy (38) and the remaining L-1 symbols are
chosen to satisfy (39).
[0060] It can be desirable--though not necessary to guarantee
cyclicity of the block--that the TS is designed such that
.chi..sub.0.sup.(l)=.chi..sub.N.sub.P.sup.(l). This can be
satisfied by including an additional intrafix TS.sub.i in the TS
itself, as shown in FIG. 1b. As the whole TS is composed of known
symbols, this does not entail a loss of net data rate.
[0061] One embodiment of the method will be illustrated in a 60 GHz
environment, but can be used in any other occurrence where CPM is
used. The 60 GHz channel is severely frequency-selective for the
targeted signal bandwidth. Equalizing such channels in the
frequency domain rather than in the time domain can sufficiently
lower the computational complexity of the system. Simulations were
performed with the proposed method and a CPM-FDE. A linear
equalizer is first applied to cancel the intersymbol interference
(ISI) introduced by the channel. The minimum mean square error
(MMSE) channel equalizer is chosen. The systems are shown in FIG.
2. The binary 3-RC CPM scheme
( M = 2 , f ( t ) = ( 1 - cos 2 .pi. t LT ) / 2 LT ##EQU00025##
with L=3) is used. Modulation index h=0.5 and h=0.25 are chosen.
The former scheme closely resembles Gaussian Minimum Shift Keying
(GMSK). The latter scheme uses a smaller bandwidth, at the expense
of an increased Bit Error rate (BER). As a huge bandwidth is
available at 60 GHz, the bit rate is R.sub.b=1 Gbits/s. A blocksize
N=256 and CP or TS length N.sub.P=64 are chosen. The receiver
lowpass filter is modelled as a raised cosine filter with roll-off
factor R=0.5.
[0062] FIG. 4 shows the BER performance in the 60 GHz environment
both with a CP and a TS. To verify the simulation framework, a
reference curve in additive white Gaussian noise (AWGN) is also
provided for the h=0.5 case. Comparing the TS and CP curves, it can
be seen that the CP performance is slightly better. This is because
in the case of a CP,
N N + N P ##EQU00026##
of the total available energy is available for useful bits, whereas
in the case of a TS this is only
N - N P N . ##EQU00027##
For N=256 and N.sub.P=64, this yields 80% for the CP, and only 75%
for the TS. This "loss" explains the small gap between the CP and
TS curves. For two reasons we can conclude that both the CP and the
TS constructions satisfy all requirements, both for the h=0.5 and
the h=0.25 cases. First, the CP or TS is sufficiently long.
Otherwise interblock interference (IBI) would not be mitigated,
causing BER flooring. Second, the intrafix is correctly calculated
in both cases, yielding a cyclic CPM signal. This can again be seen
from the fact that no BER flooring occurs, so that we can conclude
that the FD equalizer operates correctly.
[0063] FIG. 4 also shows the BER of the precoded h=0.25 and h=0.5
CPM schemes in the 60 GHz environment. As can be seen, precoding
approximately reduces the BER by half. We can therefore conclude
that the precoding and the FDE cooperate correctly.
[0064] The foregoing description details certain embodiments of the
invention. It will be appreciated, however, that no matter how
detailed the foregoing appears in text, the invention may be
practiced in many ways. It should be noted that the use of
particular terminology when describing certain features or aspects
of the invention should not be taken to imply that the terminology
is being re-defined herein to be restricted to including any
specific characteristics of the features or aspects of the
invention with which that terminology is associated.
[0065] While the above detailed description has shown, described,
and pointed out novel features of the invention as applied to
various embodiments, it will be understood that various omissions,
substitutions, and changes in the form and details of the device or
process illustrated may be made by those skilled in the technology
without departing from the spirit of the invention. The scope of
the invention is indicated by the appended claims rather than by
the foregoing description. All changes which come within the
meaning and range of equivalency of the claims are to be embraced
within their scope.
REFERENCES
[0066] References, hereby incorporated by reference in their
entirety: [0067] [1] F. Pancaldi and G. M. Vitetta, "Equalization
algorithms in the frequency domain for continuous phase
modulation," IEEE Trans. Commun., vol. 54, no. 4, pp. 648-658,
April 2008. [0068] [2] P. A. Laurent, "Exact and approximate
construction of digital phase modulations by superposition of
amplitude modulated pulses (AMP)," IEEE Trans. Commun., vol. 34,
no. 2, pp. 150-160, February 1986.
* * * * *