TWI601392B - He set orthogonal communication method and device - Google Patents

Description

He sets orthogonal communication technology method and device thereof

Digital communication

Communication technology is primarily a technique in which a message is correctly transmitted by the sender to the recipient. In many real-world environments, we often cannot send messages directly, so we must first convert them beforehand, and the work of the solution is the responsibility of the receiver.

Recently developed orthogonal coding (OFDM) communication technology is one of the prior conversion and de-conversion techniques of the above information, and another main purpose of this conversion is to save bandwidth. It is outlined below:

(1) Assuming that there are n messages D ₁ , D ₂ , ..., D _n to be transmitted, we can select n signals g ₀ that are approximately orthogonal in the transmission period [0, T] in advance ( 1, t), g ₀ (2, t), ....g ₀ (n, t), so that they can represent (or bear) D _i (i = 1, 2, .... ., n); So I can order:

The above formula SM(t) is the actually transmitted signal, and the receiver receives the approximate orthogonality of g ₀ ( i , t ) to demodulate D _i .

In general g ₀ ( i , t ) is a sampling function (or a sampling function with a curve shape similar to a sampling function) that selects phase differences of different time periods. When the minimum time phase difference is large enough, the sampling function is in the period of transmission [0, T] can be approximately orthogonal to each other; but if the time phase difference is too small, the orthogonality is gradually lost. Therefore, the period [0, T] of the transmission cannot be too short, which means that the bandwidth saving is limited.

(b) The choice of g ₀ ( i , t ) also makes it truly orthogonal (non-approximate orthogonal) in [0, T], where g ₀ ( i , t ) is not necessarily a sampling function (or Similar to the sampling function). Now we represent G ={ g ( i , t )| i =1,2,..... n } as the true orthogonal set, ie each g ( i , t ) in its set is at t [0, T ] is orthogonal to each other, which is what the author calls "this set of orthogonal".

To select a G set, you must first select another function set U = { u ( i , t )| i =1, 2, ..... n }. After normalizing and regularizing U, if the set is G = { g ( i , t )| i =1, 2, ..... n }, then g ( i , t ) in G must be The linear combination of u ( i , t ), namely:

Where α( i , j ) are constants, i =1, 2,..... n ; j i .

α( i , j ) can be obtained one by one by using the orthogonal conditions required by the formula (2).

However, in actual implementation, we found that the larger g is , the smaller g ( n , t ) will be in the orthogonal interval [0, T], even as small as 10 ^{- 2} times below g (1, t ). At this time, if the g ( n , t ) function is used to carry data, it will be susceptible to interference.

In view of the shortcomings of the above-mentioned prior art, the author has been inspired to conduct the research of the present invention.

First, "this set of orthogonal" and "other set orthogonal" will be explained.

The so-called "his set of orthogonal" is the author's tentative. Explain that this set must be explained before the orthogonality is also the author's tentative "orthogonal orthogonal". It is stated that the definition of these two orthogonals is as follows:

(1) This set of orthogonals: a set of functions G = { g ( i , t ) | i =1, 2, ... n } (t is the time variable of the function), if G is at t When [a,b] has the following relationship, then we call g(i,t) in G orthogonal to the mutual cost set between [a,b]:

(3) is actually the orthogonal relationship of orthogonal family functions that is currently familiar.

(2) He sets orthogonal:

It is provided with a set of two functions G = { g ( i , t )| i =1, 2, ... n } and H = { h ( i , t )| i =1, 2, .... .. m }, if n=m and G and H are at t When [ a , b ] has the following relationship, then we say that g(i,t) and h(i,t) in G and H are orthogonal to each other in [a,b]:

The preconditions for the above equations (3) and (4) can be established: g(i,t) in G and h(i,t) in H are at t [ a , b ] must be linearly independent of each other.

The mathematical formula of the set orthogonal is derived underneath, and the derivation process is carried out in the following nine points:

(A) Select a function set G = { g ( i , t )| i =1, 2,..... n }, where t is a time variable, if the communication period of a transmitted data is [a, b ], then we choose G, so that when t When [ a , b ], g ( i , t ) in G is linearly independent of each other.

(B) Select n ² real numbers a ( i , j ), and make the n-order determinant A _n [ a ( i , j )] ≠ 0 formed by these real numbers, namely:

(C) Order:

Since A _n [ a ( i , j )] ≠ 0, a ( i , 1), a ( i , 2)... a ( i , n ) must not be all zero (otherwise A _n [ a ( i , j ) )] = 0, which does not match the assumption); and because the function g ( i , t ) in G is at t [ a , b ] is linearly independent of each other, so h ( i , t ) is never more than zero ( i =1, 2, ..... n ).

That is to say, if g ( i , t ) is regarded as the unknown number to be solved, then (6)-1~(6)-n is a set of simultaneous equations with a unique solution, and the solution is:

(D) Order:

then;

(E) Change the formula (9) to the traditional simultaneous equations, then write:

(F) According to the requirements of the orthogonal conditions of the set, that is, the conditional requirements shown in the formula (4), we first multiply g(j, t) on both sides of the (10)-i type, and then [a, b ] Interval pair t scores are available:

On the right side of the above formula, except for the point of u=j In addition, the points for other items are zero, so:

Change the above-mentioned integral dummy variable to x, which means:

Where i, j=1, 2, . . . n.

(G) returns to the formula (6)-1~(6)-n. On both sides of (6)-i, multiply each by g(1,t), g(2,t),...,g(n,t), and then integrate t in the [a,b] interval. And substituting (11) for the following simultaneous equations with n independent equations:

In the above formula, except that the right side of the formula (12)-i-i is 1, the remainder is zero, which is obtained by the orthogonal condition of the set of (4).

Also, because i=1, 2, ..., n in the formula (12)-i-1~(12)-i-n, there are a total of n groups of such simultaneous equations.

(H) If order:

The above Y _n ( i , j ) is a sub-determination of Z _n after deleting the i- row j -row.

Then the solution of (12)-i-1~(12)-in is:

Where i, j=1, 2, .....n.

(I) to (15) Substituting back (6) -1 ~ (6) -n wherein the resulting set of functions H = {h (i, t ) | i = 1,2, ..... n } and G = { g ( i , t ) | i =1, 2, ..... n } into his set of orthogonal relations, and this relationship is as shown in (4).

He has set up orthogonal mathematics, and all of them have been deduced.

The implementation method is divided into two points: the following senders and receivers:

(1) The sender:

Assuming that there are n data D ₁ , D ₂ , ..., D _n will be transmitted in the [a, b] time period, the sender can select a linear independent function between [a, b] in advance. Set G = { g ( i , t )| i =1, 2, ..... n } (t is a time variable) and let:

The actual transmitted signal is SM(t). From (16), we can carry the data D _i to be transmitted on the bearer function g(i, t).

(2) Receiver:

The receiver finds the set of functions H ={ h in advance based on the function set G ={ g ( i , t )| i =1,2,..... n } selected by the sender. ( i , t )| i =1,2,..... n } and parameterize it. After receiving the SM(t) signal, do the following calculations:

Where i=1,2,....n.

In this way, the data D _i will be released!

The above embodiment shows that we can understand more clearly by means of Figures 1 and 2.

As for the various calculation circuits required for its implementation, as it is a well-known technology, the author will not repeat them.

1‧‧‧D _i register

2‧‧‧g(i,t) memory

3‧‧‧Plus calculator

4‧‧‧D/A converter

5‧‧‧A/D converter

6-1~6-n‧‧‧ is h(1,x)~h(n,x) memory

7-1~7-n‧‧·point calculator

Figure 1: Circuit block diagram of the sender.

Figure 2: Block diagram of the receiver's circuit.

1‧‧‧D _i register

2‧‧‧g(i,t) memory

3‧‧‧Plus calculator

4‧‧‧D/A converter

5‧‧‧A/D converter

6-1~6-n‧‧‧ is h(1,x)~h(n,x) memory

7-1~7-n‧‧·point calculator

Claims (3)

One in the communication interval [a, b] (ie t [a, b], t is a time variable of communication) a demodulation method for demodulating the data D _i contained in the transmission signal SM(t) described in the first application of the patent scope, the method is: t Find a family of demodulation functions {h(i,t)|i=1,2,...n} between [a,b], so that the family of demodulation functions and the family of bearer functions {g(i,t)| i=1,2,...n} at t [a,b] is the following relationship: ,among them: Z _n is an n-order determinant composed of b ( i , j )( i , j =1,2,... n ), and Y _n ( i , j ) is Z _n in deleting i column j row Sub-column after. An executable in the communication interval [a, b] (ie t [a, b], t is the time variable of communication), as a device for generating a signal SM(t), the device includes: a set of storage function families {g(i,t)| Memory for i=1, 2,...n}; a set of registers that can be used as pre-stored data sets {D _i |i=1,2,...n} to be transmitted; n Can be used as a calculation D _i . a multiplier for g(i,t){i=1,2,...n}; and one can be used as a calculation Use the adder. A device for _performing demodulation of data D _i contained in a transmission signal SM(t) in a technical method according to the first aspect of the patent application, the device comprising: a set of storage capable of storing a preselected load Function family {h(i,t)|i=1,2,...n} memory; one can be used as calculation Integral calculator used; And a receiver for receiving SM ( t ) transmitted from the sender.