Pulse or digital communications – Receivers – Interference or noise reduction
Reexamination Certificate
1999-11-12
2003-07-29
Emmanuel, Bayard (Department: 2631)
Pulse or digital communications
Receivers
Interference or noise reduction
Reexamination Certificate
active
06600796
ABSTRACT:
FIELD OF THE INVENTION
The invention relates to wireless, radio-frequency communication systems. More particularly, the invention relates to methods for receiving signals in digital wireless communication systems that use multiple-antenna arrays.
ART BACKGROUND
According to information-theoretic predictions, the factors determining the ultimate bit rate at which a digital wireless communication system may communicate data include: the total radiated power at the transmitter, the number of antenna elements at the transmitting and receiving sites, the bandwidth, the noise power at the receiver, and the characteristics of the propagation environment.
Most conventional systems use a single transmitting antenna element and a single receiving element. However, practitioners have recognized that substantial improvements in bit rate can be achieved by using multiple-antenna arrays for transmission, reception, or both. Such use of multiple-antenna arrays is discussed, for example, in the co-pending U.S. patent application Ser. No. 08/673981 by G. J. Foschini, commonly assigned herewith.
One known scheme for using multiple-antenna arrays is illustrated in FIG.
1
. This scheme is meant to operate in a so-called “rich scattering environment,” i.e., a signal-propagation environment in which the elements H
ij
of the channel matrix H may, to a reasonable approximation, be assumed statistically independent.
As shown in
FIG. 1
, transmitted signals s
1
, . . . , s
M
are respectively transmitted from M distinct antenna elements 10.1, . . . , 10.M. The corresponding received signals x
1
, . . . , x
N
are respectively collected from N distinct antenna elements 15.1, . . . , 15.N. In his scheme, the number M of transmitting antenna elements is at least 2, and the number of receiving elements is at least M. The transmission antenna elements 10.1, . . . , 10.M ay represent a single array of elements that are driven in unison, or they may be independently driven antennas.
The channel matrix H is an N×M matrix in which the element in the ith row and jth column represents the coupling, through the propagation channel, between the ith receiving antenna element and the jth transmitting element.
The received signals x
1
, . . . , x
N
are processed in digital signal processor
20
to produce recovered signals ŝ
1
, . . . , ŝ
M
. In effect, the processing in processor
20
inverts the coupling between the transmitting and receiving antennas as mediated by the propagation channel. The manner in which this inversion is carried out is described below. However, a perfect reconstruction of the transmitted signals is not generally possible. Therefore, it is typical to decode each of the recovered signals by seeking a best match (but not, generally, a perfect match) between the recovered signal and one of a predetermined constellation of possible symbol values. Practitioners sometimes refer to this decoding procedure as “slicing.”
The flowchart of
FIG. 2
summarizes an exemplary, known signal-detection procedure. At block
25
, an estimate of the channel matrix elements is obtained by transmitting a sequence of known signals. Typically, a sequence of approximately 2M training vectors is transmitted. Each training vector consists of a respective signal value for transmission from each of the M transmission antenna elements. As will be appreciated by those skilled in the art, the rows of FFT (Fast Fourier Transform) matrices of appropriate dimension, for example, are useful as training vectors.
With further reference to
FIG. 2
, at block
30
a matrix denominated the pseudoinverse is derived from the channel matrix H. The pseudoinverse here corresponds to an augmented matrix that contains H as a sub-matrix. This derivation is described in further detail below. From the pseudoinverse, a further matrix, denominated the error covariance matrix, is derived. The error covariance matrix provides an indication of which is the strongest (as received) of the transmitted signals. If the strongest signal is detected first, the probability of error in detecting subsequent signals is reduced. Thus, it is optimal to detect first the strongest of all remaining undetected signals. Accordingly, the strongest signal is selected for detection.
At block
35
, a vector denominated the nulling vector is derived from the pseudoinverse. The nulling vector is derived from that specific row of the pseudoinverse that corresponds to the signal selected for detection.
At block
40
, the received signal vector {tilde over (x)}=(x
1
, . . . ,x
N
) is left-multiplied by the nulling vector. (It should be noted that {right arrow over (x)} is a column vector.) The result is the recovered signal, representing a least-mean-squares estimate of the corresponding transmitted signal. Those skilled in the art will recognize that this procedure applies the principles of MMSE (Minimum Mean-Square Error) signal detection.
The procedure of block
40
is denominated nulling. The reason for this is that if there were no additive noise present at the receiver, left-multiplying {right arrow over (x)} by the nulling vector would theoretically produce an exact replica of the desired signal. Thus, the effect of the other M−1 signals would have been nulled out.
At block
45
, a slicing procedure is performed to identify the recovered symbol with a member of a symbol constellation.
At block
50
, the effect of the detected signal is cancelled from the detection problem. The result of this step is a reduced-order problem, in which there is one fewer transmitted signal to be recovered. The procedure of blocks
30
to
50
is then iterated until all of the transmitted signals have been recovered and decoded. In each iteration, the optimal signal to be detected is the strongest of the remaining signals, as determined at block
30
. It should be noted in this regard that the computational complexity of the procedures of blocks
30
and
35
scales as M
3
. Due to the iterative loop, these procedures are iterated M times, leading to a total complexity that scales as M
4
.
Although useful, the process of
FIG. 2
, as conventionally practiced, suffers certain limitations. One such limitation is that the computational complexity of the procedures of blocks
30
and
35
, i.e., of determining the nulling vectors and optimal ordering, scales as the fourth power of the number M of transmitting antennas. For large transmitting arrays, e.g. for M of ten or more, these procedures may dominate the computation time, and may even lead to computation times that are prohibitive for real-time processing.
The process of
FIG. 2
, as conventionally practiced, contains numerous matrix squaring operations (e.g., products of a matrix and its conjugate transpose) and inversions that tend to increase the dynamic range of the quantities involved in the computations. As a consequence, these computations are prone to truncation error and may be numerically unstable. To minimize truncation error, it is preferable to carry out these computations in floating point arithmetic rather than fixed point arithmetic. On the other hand, fixed point arithmetic is advantageous in practical applications because it is compatible with fast and relatively inexpensive digital signal processors. Thus, a further limitation of conventional methods for carrying out the process of
FIG. 2
is that they are not well-suited for implementation in processors using fixed point arithmetic.
SUMMARY OF THE INVENTION
I have discovered a new procedure for determining the nulling vectors and optimal ordering. My new procedure has a computational complexity that scales only as the third power of the number M of transmitting antennas. Moreover, matrix squaring operations and inversions are avoided completely in the new procedure. Instead, unitary transformations are heavily used. Those skilled in the art will appreciate that unitary transformations are among the most numerically stable operations used in numerical analysis. As a consequence of this shift from squaring and inversion operations to
Emmanuel Bayard
Finston Martin I.
Lucent Technologies - Inc.
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