Title: Methods and apparatus of signal demodulation combining with different modulations and coding for wireless communications
Abstract: According to an embodiment of the invention, the information is transmitted in symbols encoded at a source to a destination. A log likelihood ratio is respectively calculated for each of the encoded symbols. The calculated log likelihood ratios for the information bits are accumulated where the contribution from each of the encoded symbols is accounted for in the accumulating step. Each of the information bits is decoded according to the accumulated log likelihood ratios. An acknowledgment (ACK) is sent to the source for each block of the decoded information bits that passed the error check. A negative acknowledgment (NACK) is sent to the source for each block of the decoded information bits that did not pass the error check. After the source receives the negative acknowledgment (NACK), the encoded symbols are retransmitted to the destination.
Patent Number: 6,996,762 Issued on 02/07/2006 to Kuo, et al.
| Inventors:
|
Kuo; Wen-Yi (Morganville, NJ);
Kamel; Raafat (Little Falls, NJ);
Lai; Jie (Belle Mead, NJ)
|
| Assignee:
|
Intel Corporation (Santa Clara, CA)
|
| Appl. No.:
|
125644 |
| Filed:
|
April 19, 2002 |
| Current U.S. Class: |
714/749; 714/755; 714/794 |
| Current Intern'l Class: |
H04L 1/18 (20060101); H03M 13/00 (20060101); G06F 11/08 (20060101) |
| Field of Search: |
714/748,749,750,755,758,786
|
References Cited [Referenced By]
U.S. Patent Documents
Primary Examiner: Decady; Albert
Assistant Examiner: Kerveros; James C
Attorney, Agent or Firm: Wisor; Rita M.
Parent Case Text
RELATED APPLICATIONS
The present invention relates to and claims priority of U.S. Provisional Patent
Application 60/286,157 filed on Apr. 24, 2001, having common inventorship and assignee,
which is incorporated herein by reference.
Claims
We claim:
1. A method for encoding and decoding data comprising the steps of:
(a) encoding information bits at the source into symbols;
(b) transmitting the encoded symbols from a source to a destination;
(c) respectively calculating a log likelihood ratio for each of the information
bits based on the encoded symbols received at the destination;
(d) recursively accumulating the calculated log likelihood ratios for the information
bits wherein contribution from each of the encoded symbols is factored into the
accumulating step;
(e) decoding each of the information bits according to the accumulated log likelihood
ratios;
(f) respectively conducting an error check for a block of decoded information
bits;
(g) determining if the error check is passed for the block of decoded information
bits;
(h) if it is determined in step (g) that the error check is passed, sending an
acknowledgment (ACK) to the source for the block of decoded information bits that
passed the error check;
(i) if it is determined in step (g) that the error check is not passed, sending
a negative acknowledgment (NACK) to the source for the block of decoded information
bits that did not pass the error check; and
(j) after the source receives the negative acknowledgment (NACK) sent in step
(i), retransmitting the encoded symbols to the destination.
2. The method of claim 1 wherein the error check is a cyclical redundancy check (CRC).
3. The method of claim 1 wherein the encoding is turbo coding.
4. The method of claim 1 further comprising the step of resetting the log likelihood
ratios to zero if it is determined in step (g) that the error check is passed.
5. The method of claim 1 wherein the encoded symbols are transmitted in spatial diversity.
6. The method of claim 1 wherein the encoded symbols are transmitted in time diversity.
7. The method of claim 1 further comprising the steps of:
modulating the information bits; and
demodulating the information bits.
8. The method of claim 1 further comprising receiving the encoded symbols at
the destination.
9. The method of claim 8 further comprising the step of calculating a posteriori
probability (APP) for the encoded information bits according to an equation
##EQU18##
wherein P represents a posteriori probability, b represents one of the transmitted
information bits, X represents one received encoded symbol, Y represents another
received encoded symbol.
10. The method of claim 1 further comprising the step of calculating a posteriori
probability (APP) for the information bits.
11. The method of claim 10 further comprising the step of selecting the information
bit b by maximizing the a posteriori probability.
12. The method of claim 10 further comprising the step of selecting the information
bit b by maximizing the a posteriori probability (APP) wherein the maximized APP
is equivalent to, according to an equation:
##EQU19##
wherein P(b|X) provides extrinsic information regarding the transmitted information
bit b from the received encoded symbols X and P(Y|b) is the probability to receive
encoded symbols Y on the hypothesis that b is the embedded transmitted information bit.
13. The method of claim 10 further comprising the steps of:
expanding the encoded symbols into a series of mathematical observations; and
obtaining the APP according to contribution of each of the observations.
14. The method of claim 10 further comprising the steps of:
expanding the encoded symbols into a series of mathematical observations;
separately calculating a log of conditional probability for each of the observations;
and
summing the calculated logs of conditional probability for the observations to
obtain the APP.
15. A system for encoding and decoding data comprising:
a source transmitting information bits in encoded symbols;
a destination receiving the encoded symbols from the source;
an encoder at the source encoding the information bits:
a calculator at the destination respectively calculating a log likelihood ratio
for each information bit based on the received encoded symbols;
an accumulator at the destination recursively accumulating the calculated log
likelihood ratios for the information bits and factoring in contribution from each
of the received encoded symbols;
a decoder at the destination decoding the transmitted encoded symbols;
an error checker at the destination respectively conducting an error check for
a block of the decoded information bits;
wherein an acknowledgment (ACK) is sent to the source for each block of the decoded
information bits that pass the error check, and a negative acknowledgment (NACK)
is sent to the source for each block of the decoded information bits that do not
pass the error check.
16. The system of claim 15 wherein the source retransmits the encoded symbols
to the destination after receiving the negative acknowledgment (NACK) from the destination.
17. The system of claim 15 wherein the source further comprises a plurality of
transmitters and the destination further comprises a plurality of receivers.
18. The system of claim 17 wherein each transmitter further comprises a decision
logic for receiving the ACK and NACK from the destination.
19. The system of claim 17 wherein each transmitter further comprises a coder
for encoding, modulating and interleaving the information bits for transmission
by the transmitter.
20. The system of claim 17 wherein each receiver further comprises a demodulator
for demodulating the information bits received at the receiver.
21. The system of claim 17 wherein each receiver further comprises a calculator
respectively calculating a log likelihood ratio for each of the information bits
based on the encoded symbols received at the receiver.
22. The system of claim 17 wherein each receiver further comprises an accumulator
accumulating the calculated log likelihood ratios for the information bits received
at the receiver and factoring in contribution from each of the encoded symbols
received at the receiver.
23. The system of claim 17 wherein each receiver further comprising a re-initializing
switch for summing the log likelihood ratios for the encoded information bits received
at the receiver.
24. The system of claim 15 further comprising a re-initializing switch for summing
the log likelihood ratios.
25. The system of claim 15 wherein the error check is a cyclical redundancy check (CRC).
26. The system of claim 15 wherein the encoding is turbo coding.
27. The system of claim 15 wherein the log likelihood ratios are reset to zero
if it is determined that the error check is passed.
28. The system of claim 15 wherein the information bits are transmitted in spatial diversity.
29. The system of claim 15 wherein the information bits are transmitted in time diversity.
30. The system of claim 15 further comprising a calculator for calculating a
posteriori probability (APP) for the encoded information bits.
31. The system of claim 30 further comprising a processor for maximizing the
a posteriori probability (APP) by respectively selecting the encoded information bits.
32. The system of claim 30 further comprising:
a processor expanding the encoded information bits into a series of mathematical
observations; and
wherein the APP is obtained according to contribution of each of the observations.
33. The system of claim 30 further comprising:
a processor expanding the encoded information bits into a series of mathematical
observations;
another calculator separately calculating a log of conditional probability for
each of the observations; and
a summer summing the calculated logs of conditional probability for the observations
to obtain the APP.
34. A base station transmitting information bits in encoded symbols to a device
receiving the encoded symbols from the base station wherein the base station further comprises:
an encoder encoding the information bits;
wherein the mobile device further comprises:
a calculator respectively calculating a log likelihood ratio for each information
bit based on the received encoded symbols;
an accumulator recursively accumulating the calculated log likelihood ratios
for the information bits and factoring in contribution from each of the received
encoded symbols:
a decoder decoding the transmitted encoded symbols;
an error checker respectively conducting an error check for a block of the decoded
information bits;
wherein an acknowledgment (ACK) is sent to the source for each block of the decoded
information bits that pass the error check, and a negative acknowledgment (NACK)
is sent to the source for each block of the decoded information bits that do not
pass the error check.
35. The base station and the mobile device of claim 34 wherein the base station
retransmits the encoded symbols to the mobile device after receiving the negative
acknowledgment (NACK) from the mobile device.
36. The base station and the mobile device of claim 34 wherein the base station
further comprises a plurality of transmitters and the mobile device further comprises
a plurality of receivers.
37. The base station and the mobile device of claim 36 wherein each receiver
further comprising a re-initializing switch for summing the log likelihood ratios
for the encoded information bits received at the receiver.
38. The base station and the mobile device of claim 36 wherein each transmitter
further comprises a decision logic for receiving the ACK and NACK from the mobile device.
39. The base station and the mobile device of claim 36 wherein each transmitter
further comprises a coder for encoding, modulating and interleaving the information
bits for transmission by the transmitter.
40. The base station and the mobile device of claim 36 wherein each receiver
further comprises a demodulator for demodulating the information bits received
at the receiver.
41. The base station and the mobile device of claim 36 wherein each receiver
further comprises a calculator respectively calculating a log likelihood ratio
for each of the information bits based on the encoded symbols received at the receiver.
42. The base station and the mobile device of claim 36 wherein each receiver
further comprises an accumulator accumulating the calculated log likelihood ratios
for the information bits received at the receiver and factoring in contribution
from each of the encoded symbols received at the receiver.
43. The mobile device of claim 34 further comprising a re-initializing switch
for summing the log likelihood ratios.
44. The base station and the mobile device of claim 34 wherein the error check
is a cyclical redundancy check (CRC) and the encoding is turbo coding.
45. The base station and the mobile device of claim 34 wherein the log likelihood
ratios are reset to zero if it is determined that the error check is passed.
46. The base station and the mobile device of claim 34 wherein the information
bits are transmitted in spatial diversity.
47. The base station and the mobile device of claim 34 wherein the information
bits are transmitted in time diversity.
48. The mobile device of claim 34 further comprising a calculator for calculating
a posteriori probability (APP) for the encoded information bits.
49. The mobile device of claim 48 further comprising a processor for maximizing
the a posteriori probability (APP) by respectively selecting the encoded information bits.
50. The mobile device of claim 48 further comprising:
a processor expanding the encoded information bits into a series of mathematical
observations; and
wherein the APP is obtained according to contribution of each of the observations.
51. The mobile device of claim 48 further comprising:
a processor expanding the encoded information bits into a series of mathematical
observations;
another calculator separately calculating a log of conditional probability for
each of the observations; and
a summer summing the calculated logs of conditional probability for the observations
to obtain the APP.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention generally relates to encoding and decoding in data communications
and more particularly, to a novel encoding and decoding method and associated architectures
for processing information bits with different modulation and coding.
2. Description of the Related Art
In wireless communications, dynamic adjustment or switching of modulation schemes
and channel coding can yield better performance or system throughput when channel
(or data path) conditions vary. When channel conditions are relatively adverse,
modulation and coding are respectively adjusted to lower-order modulation schemes
and lower-rate coding. Conversely, when channel conditions are relatively favorable,
modulation and coding are respectively adjusted to higher-order modulation schemes
and higher-rate coding. Exemplary lower-order modulation schemes in the art include
quaternary phase shift keying or QPSK. Exemplary higher-order modulation schemes
include quadrature amplitude modulation or QAM. As information are being transmitted
between a source (e.g., a base station) and a destination (e.g., a mobile device),
the channel conditions are monitored for determining whether adjustment of the
modulation and coding is needed.
Similar to the data transmission via the wireline, wireless transmission
of a particular packet or data may not succeed at the first instance due to interference
in the channel. Multiple transmissions of the same data can improve system performance
particularly if the receiver can combine multiple transmissions for demodulating
and decoding the signals. However, such combining in the prior art only applies
to signals with the same modulation and channel coding schemes. Thus there exists
a dilemma that either 1) the transmitter will have to change the modulation and/or
coding according to the channel conditions with the receiver abandoning previously
received signals of the same information, or 2) the transmitter will have to maintain
the same modulation and coding until the packet or burst of data is successfully received.
There is therefore a need for a novel encoding and decoding method and associated
architectures for processing data with different modulation and coding that advantageously
overcome the signal combining problems and other problems in the art as set forth herein.
SUMMARY OF THE INVENTION
The present invention provides a novel encoding and decoding method and associated
architectures for processing data with different modulation and coding. According
to a particular embodiment of the method of the invention, the data are transmitted
in encoded symbols from a source to a destination. The information bits are encoded
at the source, which may be a single transmitter or a plurality of transmitters.
The encoded symbols can be transmitted with spatial diversity (i.e., from a plurality
of transmitters at the source) or without spatial diversity (i.e., from a single
transmitter at the source). The encoded symbols can also be transmitted at different
time intervals, i.e., in time diversity. A log likelihood ratio is respectively
calculated for each of the information bits based on the received encoded symbols.
The calculated log likelihood ratios for the information bits are accumulated where
the contribution from each of the encoded symbols is accounted for or factored
into the accumulating step. Each of the information bits is decoded according to
the accumulated log likelihood ratios. An error check (e.g., a cyclical redundancy
check) is respectively conducted for a block of the decoded information bits. If
it is determined that the error check is passed, an acknowledgment (ACK) is sent
to the source for the block of the decoded information bits that passed the error
check. If it is determined that the error check is not passed, a negative acknowledgment
(NACK) is sent to the source for the block of the decoded information bits that
did not pass the error check. After the source receives the negative acknowledgment
(NACK), the encoded symbols are retransmitted to the destination.
BRIEF DESCRIPTION OF THE DRAWINGS
The foregoing and other advantages and features of the invention will become
more apparent from the detailed description of the preferred embodiments of the
invention given below with reference to the accompanying drawings (not necessarily
drawn to scale) in which:
FIG. 1 is a flow diagram generally illustrating the method for encoding and
decoding data according to an embodiment of the method of the invention;
FIG. 2 is a block diagram generally illustrating a receiver architecture for
receiving and decoding the data according to a particular embodiment of the invention;
FIG. 3 is a block diagram illustrating an exemplary embodiment of an architecture
at the source having a plurality of transmitters for transmitting and encoding
the data according to the invention; and
FIG. 4 is a block diagram illustrating an exemplary embodiment of an architecture
at the destination having a plurality of receivers for receiving and decoding the
data according to the invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
FIGS. 1 and 2 are respectively a flow diagram and a block diagram generally
illustrating the method and receiver architecture for transmitting data according
to an embodiment of the method of the invention. As the information bit b is transmitted
from a source to a destination (step
101), the information bit is encoded
at the source into encoded symbols X
1, X
2, X
3,
. . . X
k (step
102). At the calculator or processor
201
in the receiver, the log likelihood ratios Λ
b(X
k) for
each information bit b based on the received encoded symbols are respectively calculated
(step
103). At the accumulator
202, the log likelihood ratios Λ
b(X
1,
X
2, X
3, . . . X
k) calculated at processor
201
for the information bit b are accumulated and stored (step
104). At the
decoder
203, the information bit b is decoded according to the accumulated
log likelihood ratios (step
105). The accumulation of the log-likelihood
ratios is done recursively so that the demodulation of information bit b can utilize
the received multiple transmissions of encoded symbols that have embedded information
on information bit b. Once the information block containing data bit b passed the
error checking (CRC), where an ACK will be sent, the log-likelihood ratios are
thus reset to zero and is ready to decode new sets of data.
The decoding of the information bit b can be performed in accordance with convolutional
coding or turbo coding. Turbo codes allow coded modulation schemes for data communications
capable of operation near Shannon capacity on bandwidth-limited data channels.
Concatenated codes (such as turbo codes) use two constituent codes with some interleaving
processing therebetween. A turbo code is formed by two constituent convolutional
encoders, arranged in parallel, separated by an interleaver or a permuter. A convolution
encoder transforms a stream or block of information bits into a block of coded
bits. The function of the interleaver is to take each incoming block of data or
information bits and rearrange them in a pseudo-random manner prior to encoding
by the second convolutional encoder. For decoding the turbo code, a decoder including
two soft-input soft-output (SISO) modules connected by an interleaver and an iterative
algorithm that swaps from one SISO module to the other SISO module. A SISO algorithm
is one that accepts a priori information at its input and produces a posteriori
information at its output. Iterative decoding requires the individual decoders
to not only determine the most likely transmitted sequence of information bits
but to also yield a soft decision which is a measure of the likelihood or confidence
of each bit in that sequence. A SISO decoder is a soft decision block decoding
algorithm with soft output information. For turbo decoding, multiple iterations
of soft-decision decoding are performed. The first SISO decoder outputs the decoded
data or information bits and a reliability metric associated with each information
bit for the soft decision. The reliability metric determines how reliable the soft
decision on each of the decoded bits. After interleaving or permutation, the reliability
metric is fed to the second SISO decoder for improving the reliability of the decoded
bits. The reliability metric from the second SISO decoder is then fed to the first
SISO decoder, where the process is repeatedly implemented.
At the error checker
204, error checks (e.g., a cyclical redundancy check
or CRC) are performed for a block of information bits (step
106). A CRC
is a mathematical method that permits errors in long runs of data to be detected
with a very high degree of accuracy. According to the CRC, the entire block of
data is treated as a long binary number or polynomial that is divided by a conveniently
small number where the remainder is used as the check value that is tacked onto
the end of the data block. Choosing a prime number as the divisor provides excellent
error detection. The number or polynomial representing the complete block (main
data plus CRC value) is always a multiple of the original divisor, so using the
same divisor always results in a new remainder of zero. This means that the same
division process can be used to check incoming data as is used to generate the
CRC value for outgoing data. At the transmitter, the remainder is (usually) non-zero
and is sent immediately after the real data. At the receiver, the entire data block
is checked and if the remainder is zero, then the data transmission is confirmed.
At the logic control
205, it is determined whether an error check is passed
or failed (step
107). If the error check is passed, an acknowledgment (ACK)
is sent from an ACK sender
206 (step
108). Pursuant to the ACK sent
from the ACK sender
206, the switch S′ re-initializes or sets to
zero for adding or summing with the log likelihood ratios. If the error check failed,
a negative acknowledgment (NACK) is sent from a NACK sender
207 (step
109).
After the NACK is received at the source, the encoded symbols are retransmitted
to the destination (step
110).
FIG. 3 is a block diagram that illustrates an exemplary embodiment of an architecture
at the source having a plurality of transmitters for transmitting and encoding
the data according to the invention. FIG. 4 is a block diagram that illustrates
an exemplary embodiment of an architecture at the destination having a plurality
of receivers for receiving and decoding the data according to the invention. As
the data are transmitted in encoded symbols X
1, X
2, X
3,
. . . X
k from a source with data source
301 to a destination
having a plurality of transmitters Tx
1, Tx
2, . . . Tx N, the information
bits are encoded at the coder
302 into encoded symbols for transmission
303 coupled with the transmitters (Tx
1, Tx
2, . . . Tx N)
to the destination having a plurality of receivers Rx
1, Rx
2, .
. . Rx M. For turbo coding, the coding, modulation and interleaving can be performed
at the decoder
302 in conjunction with decision logic
304 for coding,
modulation, transmission timing and duration processing. The decision logic
304
also receives the ACK and NACK messages from the destination.
At the calculator or processor (
401,
411 . . . ) corresponding
to
each receiver (Rx
1, Rx
2, . . . Rx M), the log likelihood ratio
Λ
b(X
k) for each information bit b are respectively
calculated. At the accumulator (
402,
412, . . . ) corresponding to
each receiver (Rx
1, Rx
2, . . . Rx M), the log likelihood ratio
Λ
b(X
1, X
2, X
3, . . . X
k)
calculated at the calculator or processor (
401,
411 . . . ) for the
information bit b are accumulated and stored. At the decoder
403, the information
bit b is decoded according to the accumulated log likelihood ratios. The accumulation
is done in a recursive manner where the log likelihood ratios, as they are calculated
and accumulated, are added or summed, corresponding to each receiver (Rx
1,
Rx
2, . . . Rx M), with the incoming log likelihood ratios from the corresponding
processor (
401,
411 . . . ). The decoding of the information bit
b can be performed in accordance with convolutional coding or turbo coding at the
decoder
403.
At the error checker
404, error checks (e.g., a cyclical redundancy check
or CRC) are performed for each block of the decoded information bits. At the logic
control
405, it is determined whether an error check is passed or failed.
If the error check is passed, an acknowledgment (ACK) is sent from an ACK sender
406 and the decoded information bits can be output to a voice decoder or
other data applications
408 for further data processing. Pursuant to the
ACK sent from the ACK sender
406, the switch (S′, S" . . . ) corresponding
to the particular receiver re-initializes or sets to zero for adding or summing
with the log likelihood ratios. If the error check failed, a negative acknowledgment
(NACK) is sent from a NACK sender
407. After the NACK is received at the
decision logic
304 of the source, the encoded symbols are retransmitted
to the destination.
A preferred embodiment of the method of the invention is described in further
detail
below with mathematical representations in conjunction with FIGS. 1 and 2.
Assume the information bit b be embedded in the encoded symbols and transmitted,
the encoded (and modulated, if needed) symbol X be received at one receiver and
another encoded symbol Y are received at the same receiver at a different time
or at a different receiver at the same time or at a different time. The received
encoded symbol Y can have the same or different encoding and/or modulation as the
received encoded symbol X. Moreover, the received encoded symbol Y can be transmitted
from the same or different transmitter or a plurality of transmitters at the source,
e.g., in spatial diversity. For spatial or space diversity, if a receiver provides
multiple antennas, the distance between the receiving antennas is made large enough
to ensure independent fading where a plurality of transmission paths or channels
are available for carrying and receiving uncorrelated and generally the same message
or information with independent fading characteristics.
A posteriori probability (APP) of for the information b is calculated for the
basis
of the maximum a posteriori probability (MAP) therefor. MAP is an estimation of
the most likely information bit to have been transmitted in a coded sequence of
information. A posteriori information is the soft output of a SISO decoder. The
a posteriori probability or APP, the base for MAP, can be described as follows:
##EQU1##
The information b is selected out of the received encoded symbols X and Y such
that the APP or P(b|X,Y) is maximized, which is mathematically represented in the
following Equation 2:
##EQU2##
where the first term P(b|X) provides the extrinsic information regarding the
information b via the encoded symbol X, and the second term P(Y|b) is the probability
to receive encoded symbol Y given the hypothesis that b is transmitted.
The received encoded symbols can be further expanded into a series of mathematical
observations for obtaining the APP according to contribution of each of the observations.
As the received encoded symbols are expanded into a series of mathematical observations,
a log of conditional probability is separately calculated for each of the observations.
The calculated logs of conditional probability for the observations are summed
or accumulated to obtain the APP which is the base for MAP. That is, the received
encoded symbols X can be expanded into a series of observations X
1,
X
2, . . . , X
M to obtain the MAP in the following mathematical
representation in Equation 3:
##EQU3##
where
##EQU4##
The final two forms of Eq. 3 represent two implementation methodologies according
to the invention. According to the summation
##EQU5##
the log of the conditional probability of the mathematical observations with
the given information b, ln[P(X
k|b)], is calculated for each observation
X
k, which are then summed together. Accordingly, the contribution from
each observation X
k can be separately calculated. The summation ln[P(b|X
1,
. . . , X
M-1)] and ln[P(X
M|b)] provides that the log for
the a posteriori probability (APP) can be calculated in an accumulated fashion
by adding the contribution from each new mathematical observation into the accumulated sum.
In the case that the prior knowledge of information b, i.e., P(b), is unknown
or the information b is equally probable, the MAP is thus obtained as
##EQU6##
In digital communications, binary representation is often used. The log likelihood
ratio of information b with the mathematical observation X
k can be obtained
as, in binary representation:
##EQU7##
where, in code division multiple access or CDMA, a rake receiver is used with
L paths or multiple antennas(or fingers) using the same modulation and coding,
x
k,l is the received signal at the l
th path
in observation X
k and X
k =[x
k,l, . . . , x
k,l]
w
k,l is the multiplicative distortion (i.e., fade) at
the l
th path associated with observation X
k and ŵ
k.t
is its estimate,
N
T is the spreading factor (chips per symbol),
A
T(k,l) is the transmitted amplitude at the l
th
path associated with observation X
k and Â
T(k,l)
is its estimate
Q
j is the hypothesized modulated symbol (e.g., 3-j in 16QAM)
which belongs to the set determined by a hypothesized bit b,
S
b=1 , is the hypothesized set of modulated symbols whose
associated bit b=1,
S
b=-1 , is the hypothesized set of modulated symbols
whose associated bit b=-1,
V
k,l is the variance at the l
th path associated
with observation X
k,
##EQU8##
J(k,l) is the per chip interference density at the l
th path associated
with observation X
k and is equal to
##EQU9##
l
oc(k) is the per chip interference density of the transmission
from the source (e.g., base stations) associated with observation X
k,
##EQU10##
represents the interference power from other paths (but the same source
or base station) associated with observation X
k.
Since the summation in Eq. 6 is based on exponential terms, an approximation
of the log-likelihood ratio associated with observation X
k can be obtained
as
##EQU11##
Further simplification of Eq. 9 can also be implemented. As the channel estimation
is of high quality, V
k,l in Eq. 8 can thus be approximated as
Vk,l=NTJ(
k,l)
where:
##EQU12##
For soft decision combining in the rake receiver, generally only the multiple
antennas or fingers within a few decibels (dB) of the strongest finger are combined
so J(k,l) is relatively close for all l, as follows:
##EQU13##
where C
x(k) is a weighting coefficient for observation X
k,
and is inversely proportional to J(k,l) in Eq. 8. For instance, assuming the L
paths be of roughly equal average power, one can obtain
##EQU14##
Note that the ratio l
oc(k)/l
or(k), where l
or(k)
denotes the received power from the serving base station, discloses the major interference
scenario at time of observation X
k.
The resultant log-likelihood ratio with all the observations (X
1,
X
2, . . . , X
M) can then be obtained as
##EQU15##
where both the individual summation and accumulation forms can be implemented.
In case the second strongest term is so close to the strongest term such that
the approximation in Eq. 9 cannot be used, a 2-term solution can then be used as
follows:
##EQU16##
where
max 2
nd is the function yields the second largest term in a series,
min 2
nd is the function yields the second smallest term in a series,
N is the number of Taylor series truncation for exponential terms,
##EQU17##
Similarly, approximations using multiple terms (more than 2 terms) that
are very close to the strongest term can be derived from Eq. 14. Also note that
the approximation using
Vk,l=NTJ(
k,l)
and the approximation using C
x(k) can also be applied to Eq. 14 and
Eq. 15.
Although the invention has been particularly shown and described in detail
with reference to the preferred embodiments thereof, the embodiments are not intended
to be exhaustive or to limit the invention to the precise forms disclosed herein.
It will be understood by those skilled in the art that many modifications in form
and detail may be made without departing from the spirit and scope of the invention.
Similarly, any process steps described herein may be interchangeable with other
steps to achieve substantially the same result. All such modifications are intended
to be encompassed within the scope of the invention, which is defined by the following
claims and their equivalents.
*
