Multiplex communications – Generalized orthogonal or special mathematical techniques
Reexamination Certificate
1998-01-30
2001-11-13
Vu, Huy D. (Department: 2664)
Multiplex communications
Generalized orthogonal or special mathematical techniques
C370S480000, C375S340000
Reexamination Certificate
active
06317409
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to a multiplexing system and multiplexing and demultiplexing apparatuses for telecommunication, capable of transmitting a number of parallel signals (hereinafter referred to as subchannel signals) through a single transmission channel. The multiplexing system, more particularly, includes the multiplexing apparatus that converts subchannel signals into a single signal (hereinafter referred to as a multiplexed signal) at a transmitter, and a demultiplexing apparatus that recovers the subchannel signals from the received multiplexed signal at a receiver.
2. Description of Related Art
Frequency division multiplexing (FDM) and time division multiplexing (TDM) represent conventional primary multiplexing techniques for dividing a single transmission channel into a number of virtual subchannels. The TDM is a multiplexing system that assigns samples of subchannel signals into nonoverlapping time slots. The FDM, on the other hand, achieves the multiplexing by dividing an available channel frequency bandwidth into a number of nonoverlapping frequency subbands, each of which is assigned to a single channel. A special type of the FDM, known as multicarrier modulation (MCM), fully utilizes the channel frequency band by allowing the subchannel frequency bands to overlap. Such multiplexing systems can be used not only for communication among multiple users, but also for one-to-one communication. The MCM, in particular, can be applied to a modem where a multiplexing apparatus and a demultiplexing apparatus are formed in a unit ( Bingham, J. A. C., “Multicarrier modulation for data transmission: an idea whose time has come,” IEEE Communication Mag., pp. 5-14, May 1990).
Another type of multiplexing system that has received increasing attention in recent years is a code division multiple access (CDMA) system using spread spectrum (SS) communication techniques. In spread spectrum communications, the transmitting bandwidth of the transmitted subchannel signal is much broader than the required bandwidth for information to be sent. The CDMA enables a number of subchannel signals to occupy an overlapping frequency band by encrypting distinct codes in the process of spreading the subchannel signals. At the receiver side, each of the subchannel signals is recovered first by concentrating the spread subchannel signal energy into a narrow frequency band while correlating it with the corresponding code, and then filtering it to pass only the narrow frequency band signal. Since the other subchannel signal energy remains in wideband after the correlation, most of the energy is removed by the filtering process. By this method, the CDMA can spread subchannel signals by assigning a different code sequence to each for implementing a multiplexing communication.
The CDMA has two well-recognized advantages. First, the CDMA offers strong protection against jamming and interference. Jamming signals, regardless of a narrow or wide band, will remain as spreading in broad bands after completion of the despreading operation upon correlation, whereas the desired subchannel signal energy is concentrated in a narrow band, so that a filter can extract the subchannel signals with a high signal-to-noise (S/N) ratio. The CDMA also achieves a higher message privacy in the presence of other listeners. If code sequences in use are maintained in secrecy, unauthorized listeners cannot extract the subchannel signals' components. The CDMA has been applied historically to military communications because of its anti-jamming, anti-interference, and privacy capabilities, but it has recently gained interest for civil applications.
The TDM suffers from interchannel interference if there is a linear distortion in the channel. In contrast, the FDM raises a problem that transmission bandwidth cannot be efficiently used though interchannel interference rarely occurs due to such a linear distortion. In the MCM, subchannel independence is guaranteed by the orthogonal principle whereby the transmission channel bandwidth is efficiently used. However, when there is a linear distortion in the transmission channel, the orthogonal property may not hold, and it generally causes interchannel interference.
The CDMA using a spread spectrum communication technique has excellent anti-jamming property and privacy capability. Applications for commercial telecommunications using the CDMA have been researched these days upon higher demands for communications having such features even for civil use. It is therefore important to devise an alternative CDMA type multiplexing system that is simple and inexpensive.
SUMMARY OF THE INVENTION
It is an object of the invention to provide a multiplexing apparatus and a multiplexing system (which refers to a combination of the multiplexing apparatus and a demultiplexing apparatus) for discrete-time signals that can efficiently use a transmission channel bandwidth without inducing interchannel interference even though a linear distortion exists in the transmission channel.
It is another object of the invention to provide a multiplexing apparatus and a multiplexing system providing virtual subchannels, in which the well-accumulated conventional technology for the linear distortion channel such as channel equalizer or the pulse waveform design methods of digital communication can be utilized easily.
It is a further object of the invention to provide a multiplexing system, having an effect similar to that of the CDMA, built cost-effectively with a relatively simple structure in use of FFT processors or the like.
A multiplexing system according to the invention as applied to a typical communication setting is briefly described using the following relations. Let sequences {x
m
(n)}, m=0, 1, . . . , M−1, of length K be M discrete-time subchannel signals to be transmitted in parallel. Their z-transform representations are defined by
X
m
(
z
)
=
∑
n
=
0
K
-
1
x
m
(
n
)
z
∼
n
(
1
)
For the following discussion, the sequences and their z-transforms are used interchangeably under the relation of (1). The z-transforms are interpreted as polynomials in z
−1
, and simply referred to as polynomials. The Msubchannel signals are first supplied to the multiplexer which produces the multiplexed signal X(z) as its output. This multiplexed signal is then converted to the carrier frequency signal by conventional modulation, and transmitted by the carrier frequency transmission. At the receiver side, the received carrier frequency signal is demodulated to produce the receiver side multiplexed signal Y(z). The receiver side multiplexed signal is then supplied to the demultiplexer which recovers the receiver side subchannel signals as its outputs.
The proposed multiplexing system is based on the Chinese remainder theorem for polynomials, which states: For given relatively prime polynomials P
m
(z), m=0, 1, . . . , M−1, there exist polynomials Q
m
(z), m=0, 1, . . . , M−1, that satisfy the congruencies
Q
k
(
z
)
mod
(
P
m
(
z
)
)
≡
1
,
k
=
m
≡
0
,
k
≠
m
.
(
2
)
Let P(z) be defined by
P
(
z
)
=
∏
m
=
0
M
-
1
P
m
(
z
)
.
(
3
)
Then, for arbitrary given polynomials X
m
(z), m=0, 1, . . . , M−1, there exists a polynomial X(z) on mod(P(z)) that satisfies the congruency X
m
(z)≡X(z)mod(P
m
(z)), m=0, 1, . . . , M−1. This polynomial on mod(P(z)) is given by
X
(
z
)
≡
∑
m
=
0
M
-
1
Q
m
(
z
)
X
m
(
z
)
mod
(
P
(
z
)
)
.
(
4
)
The proposed multiplexing system uses the Chinese remainder theorem for multiplexing subchannel signals; that is, we regard X
m
(z), m=0, 1, . . . , M−1 as subchannel signals, and X(z) as the multiplexed signal in the interpretation of the theorem. As for demultiplexing, the receiver side subchannel signals are recovered as the residue pol
Harper Kevin C.
Rabin & Berdo P.C.
Vu Huy D.
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