Pulse or digital communications – Receivers – Particular pulse demodulator or detector
Reexamination Certificate
2000-02-04
2004-04-27
Ghayour, Mohammad H. (Department: 2731)
Pulse or digital communications
Receivers
Particular pulse demodulator or detector
C714S791000
Reexamination Certificate
active
06728322
ABSTRACT:
TECHNICAL FIELD
The present invention relates to a sequential decoder and a receiver using a sequential decoder, and more particularly to a sequential decoder which can be applied to broadband mobile communications and reduces the computational efforts of a sequence estimation, and a receiver equipped with the same.
BACKGROUND ART
There are a block code and a convolutional code as error correction codes. There are Viterbi decoding and sequential decoding as decoding of the convolutional code. The Viterbi decoding is a method of decoding which utilizes a repetition structure of the convolutional code and efficiently performs maximum likelihood decoding. The sequential decoding utilizes a tree structure and approximately performs maximum likelihood decoding with a given memory capacity and a limited number of computations.
However, the Viterbi decoding handles equal-length paths at each time, while the sequential decoding handles a variable-length path. Thus, the sequential decoding does not use a metric used in the Viterbi decoding. For example, although the Hamming distance in a binary symmetric channel takes a metric of the Viterbi decoding, it is not suitable for a case where paths having different lengths are objects to be compared. That is, the Hamming distance of even the maximum likelihood path from a received sequence increases as it becomes longer, and thus the maximum likelihood path has a metric greater than any paths shorter than the same.
Thus, let us consider the following branch metric &mgr;(y
t
,w
t
) with respect to a q-ary convolutional code (code rate k
) in which the length of the information block is k and the length of the encoded block is n:
μ
(
y
t
,
w
t
)
=
-
log
P
(
y
t
❘
w
t
)
P
(
y
t
)
+
k
log
q
(
1
)
where y
t
and w
t
respectively denote a received block and encoded block (a branch in the trellis diagram) at time t. Also, P(y
t
) denotes a probability that the received block at time t is y
t
. Further, P(y
t
|w
t
) denotes a conditional probability that the received block at time t is y
i
when the encoded block at time t is w
t
.
A metric between a received sequence Y
L
=y
0
y
1
y
2
. . . y
L−1
and an encoded sequence (path) W
L
=w
0
w
1
w
2
w
3
. . . w
L−1
is defined by the following equation:
μ
(
y
L
,
w
L
)
=
∑
i
=
0
L
-
1
μ
(
y
t
,
w
t
)
(
2
)
It is assumed that the communication channel is a memoryless, stationary channel. The metric thus defined above is called a Fano metric (sometimes, an expression obtained by multiplying equation (2) by −1 is defined as the Fano metric).
When an information sequence is random, in the normal convolutional code, all patterns of a length n appear in the code block at each time with an equal probability except for a few times in the commencement of encoding. Now, it is further assumed that the communication channel is a q-ary symmetric communication channel. In this case, all patterns of length n appear in each block of the received sequence except for a few times in the commencement. Thus, P(y
i
)=q
−n
. By substituting this into equation (1), the following is obtained:
&mgr;(
y
t
,w
t
)=
P
(
y
t
|w
t
)−(
n−k
)log
q
(3)
The first term of equation (3) is no more than the branch metric in the Viterbi decoding. Thus, the Fano metric is biased with −(n−k)log q which is not involved in the branch metric of the Viterbi decoding. The metric of the maximum likelihood does not increase even if it is longer, and does not have any disadvantage as compared to short paths.
A description will now be given of computation of the Fano metric in the sequential decoding by exemplarily describing a case where the sequential decoding is applied to a sequence estimation in mobile communications. A feature of mobile communications is that the radio propagation environment is a multipath propagation. When considering an up (transmission from a mobile station, reception in a base station) communication channel, a bundle of transmitted element waves which have been subject to scatter, diffraction and reflection around the mobile station arrives at the base station directly or after it is reflected at a great distance. Hence, the base station receives the transmitted signal in such a fashion that a plurality of components resulting from the transmitted signal have different incoming angles. These respective paths are subject to independent fading.
When a communication takes place in the mobile communication environment as described above, phenomena different from each other due to the bandwidths of the signals appear in the received signals. In a case where the transmitted signal has a low bit rate and the bandwidth thereof is much narrower than a coherence bandwidth in the channel, the differences in propagation delay time among the signals propagated through the above-mentioned paths are much smaller than the symbol time length (which is normally equal to the reciprocal number of the symbol rate) of the signals. In this case, the same information symbol is received on the reception side, and a waveform distortion due to intersymbol interference does not occur in the received signals.
When the bit rate of the transmitted signals increases and the bandwidth of the signals becomes approximately equal to the coherence bandwidth in the channel, information symbols different from each other in the respective paths are received. In this case, a waveform distortion due to intersymbol interference over a few past and future symbols occurs in the received signals. Since the paths are subject to the respective, independent fading as has been described above, the intersymbol interference over a few past and future symbols is a time-varying intersymbol interference in which the intersymbol interference varies with time.
Thus, an equalizer which eliminates the intersymbol interference is required to estimate a channel impulse response (which is equivalent to an arrangement in which the complex amplitudes of the paths are arranged in the order of arrival time) and to thus estimate the transmitted sequence. An algorithm based on the maximum likelihood sequence estimation theory (MLSE theory) can be applied to estimation of the transmitted sequence. When the intersymbol interference results from a few past and future symbols, the joint signal processing of channel estimation and MLSE can be achieved with reasonable complexity. This is described in detail in, for example, a literature: Fukawa, Suzuki, “Recursive Least Squares Adaptive Maximum Likelihood Sequence Estimation (RLS-MLSE)—An Application of Maximum Likelihood Estimation Theory to Mobile Radio”, The Transaction of the Institute of Electronics, Information and Communication Engineers (B-11), J76-B-II, No. 4, PP. 202-214, April 1993.
As the transmission bit rate increases, the received signal is affected by an increased amount of intersymbol interference. Theoretically, the above-mentioned joint signal processing of the channel estimation and the MLSE can be applied to equalization of the intersymbol interference. However, the number of states in the Viterbi algorithm used in the MLSE increases exponentially with respect to the length of the intersymbol interference (equal to the channel memory length). For example, in a case where binary phase shift keying (BPSK) is used as a modulation method, if there is a channel memory length of 11 symbols, the number of states (involved in a 12-path channel) is 2048, which exceeds the practical complexity limit.
It will be seen from the above consideration, it can be said that technical drawbacks to be solved in order to achieve an adaptive equalizer in high-bit-rate channels on the megabit order are involved in the sequence estimation and channel estimation corresponding to the above sequence. Of the above drawbacks, an adaptive equalizer using a sequential sequence estimation instead of
Asai Takahiro
Matsumoto Tadashi
Ghayour Mohammad H.
NTT Mobile Communications Network Inc.
Oblon & Spivak, McClelland, Maier & Neustadt P.C.
Williams Demetria
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