Pulse or digital communications – Equalizers – Automatic
Reexamination Certificate
1998-08-17
2002-04-30
Pham, Chi (Department: 2631)
Pulse or digital communications
Equalizers
Automatic
C375S262000, C375S341000, C375S346000, C375S350000
Reexamination Certificate
active
06381271
ABSTRACT:
BACKGROUND
The present invention relates to Decision Feedback Sequence Estimation.
In a cellular Time Division Multiple Access (TDMA) system, Inter-Symbol Interference (ISI) introduced by bandwidth limited modulation and a multipath radio channel is removed by a channel equalizer. The radio channel in such a system (including the transmitter and receiver filter) can usually be modeled by:
b
(
k
)
=
∑
j
=
0
L
a
(
k
-
j
)
·
h
(
j
)
+
n
(
k
)
,
(
1
)
where b(k) are the received symbol spaced signal samples and h(j) are the taps of a time discrete baseband model of the multipath channel, that is, a model of the ISI introduced by the channel and filters. The variable a(k−j) represents the transmitted symbols and n(k) is additive white Gaussian noise. The channel influence on h will change with time, but can be modeled to be constant under a short enough time interval.
Between the time that symbols, a(k) are generated at a transmitter and the time they are recreated (estimated) at a receiver, they may be altered by various mechanisms. For example, as illustrated in
FIG. 1
a,
at the transmitter the symbols a(k) may first be modified by a transmitter filter
101
. The transmitted signal may then undergo further modification by means of a multipath channel
103
, before it is received by a receiver filter
105
. The received signal, b(t) must then be converted into digital form by a sampling circuit
107
, which generates distorted samples b(k). The distorted samples b(k) are then supplied to an equalizer
109
, which finally generates the estimated symbols â(k).
At the receiver, the transmitter filter
101
, multipath channel
103
, receiver filter
105
and sampling circuit
107
are usually modeled as a time discrete finite impulse response (FIR) filter
111
, as illustrated in
FIG. 1
b.
The FIR filter
111
is estimated to have an estimated response, ĥ, that operates on the transmitted symbols, a(k), in accordance with equation (1). The estimated response, ĥ, is used by the succeeding equalizer
109
in a process that generates estimated symbols, â(k), based on the received distorted samples, b(k).
FIGS. 1
a
and
1
b
illustrate a linear modulation scheme, but continuous phase modulations, such as that used in GSM systems, can as well often be interpreted this way by the receiver.
The equalizer
109
may operate in accordance with any of a number of known symbol estimation techniques. If the goal is to minimize symbol sequence error, a Maximum Likelihood Sequence Estimator (MLSE) provides optimum performance. In the MLSE, the symbol sequence which minimizes the Euclidean distance between the symbol sequence filtered through the channel, and the received sample sequence is found. Assuming white Gaussian noise, this symbol sequence is the most probable one. If the Viterbi algorithm is used to implement the MLSE, the sequence is found in a step-by-step iterative technique that involves calculating metrics. Some of the components in these metrics only depend on the symbol alphabet and the channel estimate. Since these components are used many times in the Viterbi algorithm and are independent of the received samples, they can be pre-calculated once per channel estimate, and stored in tables, thus saving complexity. This is described, for example, in U.S. Pat. No. 5,091,918, which issued to Wales on Feb. 25, 1992. The same approach is possible for a Maximum A Posteriori (MAP) equalizer since the same metrics are needed. It is noted that a non-simplified MAP symbol-by-symbol equalizer can offer lower symbol error rate, and can also provide somewhat better soft values and hence improve the decoded performance.
Examined more closely, conventional MLSE techniques operate by hypothesizing candidate sequences, and for each candidate sequence calculating metrics in the form
dM
=
|
y
(
k
)
-
∑
j
=
0
L
MLSE
a
(
k
-
j
)
·
h
^
(
j
)
|
2
,
(
2
)
where y(k) are the received samples, a(k) are the symbols of a candidate sequence, L
MLSE
+1 is the number of MLSE taps in the equalizer window, and ĥ(j) is the channel estimate. Since a(k−j) and ĥ(j) are independent of the received signal, it is possible to reduce the number of computations for a given channel estimate by calculating the hypothesized received sample values (i.e., the sum in equation 2, henceforth referred to as a hypothesis) for all possible hypothesized symbols, and storing these precalculated sums in a memory. These precalculated values, which are retrieved as needed to determine a branch metric (dM) for a particular received sample y(k), are used many times in the equalization process. Since all M
L
MLSE
+1
branch metrics (dM) are needed per sample, computations are always saved using precalculation.
An example is shown below in Table 1. In this example, let the channel be h=[2 j], and let L
MLSE
+1=2. Assume that the symbol alphabet is a(k)={−1,1,−j,j} (e.g., Quadrature Phase Shift Keying, or QPSK). The possible hypotheses, A(k), then become those shown in Table 1:
TABLE 1
A(k) =
h(0)*a(k) + h(1)*a(k − 1) =
a(k)
a(k − 1)
2*a(k) + j*a(k − 1)
−1
−1
−2 − j
−1
+1
−2 + j
−1
−j
−1
−1
+j
−3
+1
−1
2 − j
+1
+1
2 + j
+1
−j
3
+1
+j
1
−j
−1
−3j
−j
+1
−j
−j
−j
1 − 2j
−j
+j
−1 − 2j
+j
−1
3j
+j
+1
1 + 2j
+j
−j
−1 + 2j
+j
+j
j
It will be observed that A(k) is independent of k, and can be re-used for all samples. It is apparent that complexity can be saved by setting up this table once per channel estimate.
Despite the complexity savings from using precalculated hypotheses in a look-up table, the MLSE algorithm can become computationally intense as the size of the equalization window (i.e., the number of taps in the channel model) grows, and also as higher order modulation is used, because the complexity is proportional to (#Symbols in modulation alphabet)
Window Size
. The need for such growth is driven by the evolution into higher symbol transmission rates, which are being proposed in order to offer high bit rates in future communications systems. The Enhanced Data rates for Global Evolution (EDGE) cellular telecommunications standard is one such system in which higher level modulation (HLM) is proposed. A known alternative equalization technique that requires fewer computations, and which therefore may be suitable for use in such new communications standards, is Decision Feedback Estimation (DFE). Unlike MLSE, which uses a sequence detection strategy, DFE detects symbols on a symbol-by-symbol basis. This is accomplished by first estimating a value that represents the signal energy presently experienced from previously decoded symbols. This energy value is then subtracted from a current received sample, in order to cancel out ISI. Because the energy value is determined from an estimate of the channel response and from previously decoded symbols, the form of energy value computation resembles that of the MLSE's hypothesis computation. However, because calculating the energy value for DFE need only be performed for previously decoded symbols (i.e., the previously generated final output symbols from the DFE), as opposed to a complete set of hypothesized symbol sequences in the case of MLSE, computational complexity of the DFE approach is substantially less than that for MLSE.
As one would expect, the relatively lower computational complexity of DFE is accompanied by a relatively higher symbol error rate, when compared to the MLSE approach. It is nonetheless preferable to MLSE in some cases because the total storage (complexity) of the MLSE algorithm is proportional to the number of states of the trellis which grows exponentially with the channel memory
Burns Doane Swecker & Mathis L.L.P.
Nguyen Dung X.
Pham Chi
Telefonaktiebolaget LM Ericsson (publ)
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