KR20040026910A - Fast fourier transform apparatus and method thereof - Google Patents

Abstract

PURPOSE: An FFT(Fast Fourier Transform) device and a method thereof are provided to facilitate realization while minimizing a complex number multiplication operation process by using the flexible split Radix-2/4/8 FFT modified in order to fit to all modes. CONSTITUTION: An FFT format operator(230) outputs the setting information by setting a number and a combination of the used FFT according to the FFT symbol data. An FFT controller(220) outputs a control signal according to the setting information. The flexible split Radix-2/4/8 FFT butterfly operators(210-1¯210-n) perform the FFT according to the control signal. A twiddle factor table(200) outputs a twiddle factor according to the control signal. A multiplier multiplies an output signal of the flexible split Radix-2/4/8 FFT butterfly operator by the twiddle factor.

Description

Fast Fourier transformer and its method {FAST FOURIER TRANSFORM APPARATUS AND METHOD THEREOF}

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to fast Fourier transforms (FFTs, hereinafter referred to as FFTs), and in particular, orthogonal frequency division multiplexing (OFDM) schemes for wireless communications, variable division-FFTs. The present invention relates to a fast Fourier transform device and a method suitable for reducing the number of complex multiplication operations through a (Flexible Split-FFT) method.

As various wireless communication floods, existing frequencies are reaching saturation. Among them, the FM band is gradually falling behind due to the deterioration of the radio wave environment with the saturation of the broadcast channel.

Active research is being conducted to prevent the fall of these FM bands and provide high-quality audio services. The most active of these studies is the European Digital Audio Broadcasting (DAB), which is called the Eureka-147 project. Hereinafter referred to as DAB).

Eureka-147 uses an OFDM modulation scheme using multiple carriers orthogonal to each other to improve the quality of mobile reception and reduce the effects of selective fading. In OFDM modulation and demodulation, a common FFT is used, which is intended to speed up the Discrete Fourier Transform. It should be noted that the Eureka-147 is a means for describing a conventional OFDM modulation scheme.

Given N discrete signals X (n) (n = 0,1, ..., N-1), the discrete Fourier transform of x (n) is defined as in Equation 1 below.

A rotation factor W _N , which means a point moving the circumference of the unit circle on the complex plane by 1 / N circumference, is defined as in Equation 2.

Since the rotation factor W _N defined above is easily used in the FFT, the equation of the basic FFT obtained by substituting Equation 2 into Equation 1 is shown in Equation 3. The following description uses equation (3).

From the definition of Equation 3, the structure of the FFT implemented according to the setting of the input range n is changed. In order to efficiently calculate the DFT, dividing it into smaller DFTs is the principle of the FFT, so the Radix-2 and Radix-4 structures are the basis. For example, in the case of using the Reddix-2 structure, a complex multiplication process of (N / 2) log ₂ ^N is required to implement an N point FFT.

FIG. 1 is a flowchart of a Redix-2 FFT when N = 8 and shows 12 complex multiplications. The Redix-2 FFT processes two inputs simultaneously and requires many rotation factors, so 12 adders, 12 subtractors, and 12 complex multipliers were used to process them. A complex multiplier takes up a lot of space and takes time to compute. Therefore, the Redix-2 FFT requires a large hardware area and requires a lot of processing time, thereby consuming high power. In addition, the size of the memory to store the rotation factor required for each stage is also large.

According to Eureka-147, the 2048 point FFT must be completed for 246 ms, and the 512 point FFT is sensitive to computation time because the operation must be completed for 62 ms. Thus, to further reduce the number of multipliers, we use Redix-4 FFT, which processes four input values simultaneously.

Using Redix-4 FFT requires only Nlog ₂ ^N complex adders and (3/8) N (log ₂ ^N -2) complex multipliers smaller than the Redix- ₂ FFT.

FIG. 2 is a basic signal flow diagram of a Redix-4 FFT, which simultaneously processes four-point signals as shown. The flowchart on the left side is simply displayed as shown on the right side. Since this operation has the shape of a butterfly as shown in the figure, such an operation is called a butterfly operation.

FIG. 3 is a flowchart illustrating a case where N = 16 using the Redix-4 FFT having the basic flowchart of FIG. 2 as described above.

As shown, using Redix-4 FFT, the same processing can be performed with much less computation time than using Redix-2 FFT, but the actual operation structure will be quite complicated. However, because the number of complex multipliers in the hardware configuration is small, the hardware space requirements are less than that of the Redix-2 FFT. Capable of processing eight inputs at the same time, the Redix-8 FFT can further increase processing speed. In other words, the hardware space requirements of the Reddix-8 FFT and the number of complex multipliers will be less than the Reddix-2 FFT or Reddix-4 FFT. However, Redix-8 FFTs are rarely used in Eureka-147 because of their complexity.

As described above, in order to simplify the hardware configuration while calculating the FFT during the allowable processing time of the Eureka-147, the OFDM modulation and demodulation FFT of the Eureka-147 employs a method of applying the Reddix-2 and Redix-4 FFTs.

The N-point FFT used in the European DAB is used in four modes, and N = 2048, 512, 256, and 1024 are regarded as mode 4 in mode 1, respectively. Here, the Redix-4 FFT cannot be used in modes 1 and 2 because it can be implemented only when N = 4 ⁿ . However, Redix-2 FFT can be used in all modes because N = 2 ⁿ can be implemented.

Reddix-2 FFT is available in all modes, but uses a mixed-Radix FFT structure that combines Reddix-2 FFT and Reddix-4 FFT because it requires too many complex multiplication processes. .

Before looking at the mixed-reddix FFT structure, let's look at the hardware block diagram that makes up the Reddix-2 FFT. This will show the simplicity of the mixed-reddix FFT structure and will help in understanding the present invention.

4 is a Redox-2 FFT block diagram, in which all modes 1, 2, 3, and 4 are supported. In other words, it is necessary to perform a maximum of 2048 points Redix-2 FFT, so it consists of 11 stages to execute 11 times.

Thereafter, a plurality of similar functional blocks are represented by a representative code. For example, the Reddick-2 butterfly operators 10a to 10k will be described as the Reddick-2 butterfly operator 10.

What constitutes each stage is composed of a red Dix-2 butterfly operation unit 10 performing an FFT and a rotation printing unit 20 provided to the butterfly operation. Eleven such stages are connected in series, and the three muxes 25a, 25b, and 25c are used to change the starting point of operation depending on the mode. That is, according to the three mux, the operation of the modes 1 to 4 are all possible through the structure. These functional blocks are controlled by the controller 30.

Therefore, if the FFT supporting the DAB is configured using only the Redix-2 FFT, the complex structure is increased even though the calculation structure is simple, thereby increasing the hardware size and the amount of calculation. However, when the Reddix-2 FFT and the Reddix-4 FFT are mixed, the size and the amount of calculation are greatly reduced. Such a mixed-Redix FFT structure is illustrated in FIG. 5.

5 consists of six stages as shown. As shown in the figure, one of the Red Dix-2 butterfly operation unit 40 or Red Dix-4 butterfly operation unit 50 performing the butterfly operation, and the rotation factor unit 45, 60 which provides a rotation factor to the butterfly operation. Stage is configured. That is, five Reddicks-4 FFT stages and one Reddix-2 FFT stage, basically one redundancy that can optionally start with four Reddix-4 FFT stages (4 ⁴ = 256) 2 x 4 ⁵ = 2048 with all stages, 4 ⁵ = 1024 with only 5 Reddix-4 FFT stages, 1 Reddyx-2 2 x 4 ⁴ = 512 using the FFT stage and 4 Reddix-4 FFT stages, and 4 ⁴ = 256 using only the 4 Reddix-4 FFT stages, so 6 stages are used to accommodate all modes of FFT. Can be. That is, a smaller number of complex calculations are required than in the case of using the Redix-2 FFT alone, and the power consumption and delay time are reduced accordingly.

The FFT for OFDM modulation and demodulation used in the proposed Eureka-147 uses the mixed-reddix FFT structure described above.

Split-Radix, which satisfies Reddix-2 / 4 FFT or Reddix-2 / 8 FFT, which requires only smaller complex operations, is emerging as a new algorithm, but FFT symbol data (N: As the operation changes considerably as the value changes, the complexity of the implementation is so high that it cannot be practically applied to Eureka-147 using four input modes.

As described above, OFDM modulation and demodulation is conventionally handled by mixing Redix-2 FFT or Redix-2 FFT and Redix-4 FFT, which requires complex number multiplication of more than a certain number, resulting in complicated design and high computation time and power consumption. There is a big problem, and the split-reddix FFT method using Reddix-2 / 4 FFT or Reddix-2 / 8 FFT has a problem in that the implementation becomes complicated because the operation varies according to the change of the mode.

In view of the above problems, the present invention provides a fast Fourier transform apparatus and method for simplifying implementation while minimizing complex multiplication operations by using a variable division reddix-2 / 4/8 FFT modified for all modes. The purpose is to provide.

1 is a signal flow diagram of an eight-point Redix-2 fast Fourier Trasnform (FFT).

2 is a basic signal flow diagram of a Redix-4 FFT.

3 is a signal flow diagram of a 16 point Redix-4 FFT.

4 is a block diagram of a Redix-2 FFT.

FIG. 5 is a block diagram of a Reddicks-4 FFT for Eureka-147 digital audio broadcasting.

6 is a basic signal flow diagram of a Redix-2 / 4/8 FFT.

7 is a block diagram of a variable division reddicks-2 / 4/8 FFT butterfly operator used in the present invention.

8 is a block diagram of the present invention's variable division reddix-2 / 4/8 FFT.

*** Explanation of symbols for main parts of drawing ***

200: rotation factor table 210-1 to n: variable division reddick-2 / 4/8 FFT butterfly operation unit

215a to b: multiplier 220: FFT control unit

230: FFT format operator

The present invention for achieving the above object is an FFT format calculator for setting the number and combination of the FFT used in accordance with the FFT symbol data to output the setting information; An FFT controller for outputting a control signal according to the setting information; A variable division reddix 2/4/8 FFT butterfly operator for performing FFT according to the control signal; A rotation factor table for outputting a rotation factor in accordance with the control signal; And a multiplier multiplying the output signal by the variable division reddix 2/4/8 FFT butterfly operator and the rotation factor.

The number of the variable division reddicks-2 / 4/8 FFT butterfly operations is the same as the required number of stages.

The FFT format operator repeats dividing the input FFT symbol data value by a divisor 8 and finishes the operation if the quotient is one of 1, 2, and 4, and sets the number and combination of FFT processing units to be used through the quotient and division number. It is characterized by providing setting information by setting.

The FFT format operator stores the number and combination of FFT processing units according to a predetermined FFT symbol data value and sets the number and combination of FFT processing units to be used according to the provided FFT symbol data value to provide setting information. It is done.

The method may further include generating setting information by setting a number and a combination of FFT processing units to be used through FFT symbol data values; By using the setting information set through the above steps, the control of the operations of the FFT processing units belonging to the plurality of variable partitioned Redix-2 / 4/8 FFT butterfly operations is individually controlled, and the appropriate rotation factor values are changed. And / 8 multiply the output of the FFT butterfly operation unit.

Generating setting information by setting the number and combination of the FFT processing units may be performed by repeatedly dividing the FFT symbol data value by a divisor of 8 and ending the operation if the quotient is one of 1, 2, and 4, and the number of quotients and divisions. The method may further include generating setting information by setting the number and the combination of the FFT processing units to be used.

Generating setting information by setting the number and combination of the FFT processing units may include storing the number and the combination of the FFT processing units according to a predetermined FFT symbol data value and then using the FFT symbol data values. And setting the number and combination to generate setting information.

Reference will be made to FIGS. 6 to 8 to describe the present invention as described above in detail.

First, Figure 6 is a basic signal flow diagram of the Redix-2 / 4/8 FFT, which has now emerged as a new algorithm. However, as shown, it consists of an L-shaped (dotted line) Reddix-2 / 8 FFT, Reddix-2 / 4 FFT, and Reddix-2 FFT, so the input FFT processing is reduced even though the number of complex multiplications is reduced. It should have a fixed configuration depending on the number N of units.

As shown in the figure, the structure of Redix-2 / 4/8 FFT may be represented by the structures of L-type composite FFT, and may be thought of as stages such as PE1, PE2, and PE3.

First, in the method of deriving the Reddick-2 / 4/8 FFT structure, after applying the Reddix-2 FFT algorithm to Equation 3 and arranging the even area, the odd area to which the Reddix-8 FFT algorithm is applied To sum up, we can implement Reddix-2 / 8 FFT, the largest L-shaped butterfly operation structure, and apply Reddix-2 / 4 FFT algorithm to even area again. You can get it.

In general implementations, the split reddix-2 / 4 FFT and the split reddix-2 / 8 FFT are difficult to use in general because they vary in operation depending on the input change. However, the split reddix-2 / 4/8 FFT structure is only applicable when the input is 8 ⁿ but has regularity.

The OFDM modulation and demodulation used in the Eureka-147, which is an embodiment to which the present invention is applied, performs FFTs for four modes, and among these modes, the input may not be 8 ⁿ . The FFT structure cannot be applied as it is.

Therefore, in the present invention, the division reddix-2 / 4/8 FFT structure is appropriately modified to apply to all cases ^where the input becomes 2 ⁿ . Here, the OFDM modulation and demodulation of Eureka-147 used as an embodiment is for explaining a specific application example of the present invention in detail. Note that there is.

Gritty brief introduction to the heart of the present invention prior to detailed description, to change the structure to be the same when the input is 8 ⁿ of division les Dix input is 2 ⁿ -2/4/8 the FFT can be applied to a case A high speed, low power FFT device that can be used for all OFDM modulation and demodulation will be described.

Now, if the configuration of FIG. 6 is divided into FFT processing elements (PEs), the Redix-8 FFT portion is called PE1, the Redix-4 FFT portion is called PE2, and the Redix-2 FFT portion is called PE3. In the split reddix-2 / 4/8 FFT, these FFT processing parts are collectively called PE, which are not individually controlled by the lower PE1, PE2, PE3, but in the present invention, the input N corresponding to 2 ⁿ must be processed. So control them individually. This will be referred to as a variable division reddick-2 / 4/8 FFT butterfly operation unit.

Referring to FIG. 6, a block diagram of a variable division reddicks-2 / 4/8 FFT butterfly operator, which is an FFT processing unit used in the present invention of FIG. 7, will be described.

As shown in FIG. 6, the FFT processing units PE1, PE2, and PE3 of FIG. 6 are separated from each other, and the memories 130 and 140 of the respective FFT processing units 100, 110, and 120, and the respective processing units. 150, muxes 160 and 170 for selectively using the respective processing units PE1, PE2, and PE3, and a control unit connected to each of them to individually select their operations ( 180).

Accordingly, since the Reddick-8 FFT 100, the Reddick-4 FFT 110, and the Reddick-2 FFT 120 can be individually selected, the input N corresponding to 2 ⁿ can be processed.

Now, with reference to the structure of the present invention shown in Figure 8 will be described in more detail with respect to each of the variable division reddicks-2 / 4/8 FFT butterfly operation.

FIG. 8 is a block diagram of the variable division redics-2 / 4/8 FFT of the present invention used in an OFDM modulation and demodulation system, and the structure of FIG. 7 is used as the variable redics-2 / 4/8 FFT butterfly operations 210. FIG. Note that

In the structure shown, the FFT format operator 230 sets the number and combination of FFTs to be used according to the FFT symbol data value N (depending on the usage mode); A plurality of variable partition levels having first, second, and third FFT processing units 100, 110, and 120, and memories 130, 140, and 150, respectively, of different types and numbers that can be controlled, respectively. Dix-2 / 4/8 FFT butterfly operation unit 210; Receives a setting of the FFT used by the FFT format operator 230 and operates only the FFT processing units 100, 110, and 120 set by the variable division reddicks-2 / 4/8 FFT butterfly operators 210. An FFT controller 220; A rotation factor table 200 having a rotation factor to be provided to the output of the variable division reddicks-2 / 4/8 FFT butterfly operation unit 210 and controlled by the FFT control unit 220; Multiply the outputs of the variable division redids-2 / 4/8 FFT butterfly operator 210 by the rotation factors from the rotation factor table 200 and then multiply them by the variable division reddicks-2 / 4/8 of the next stage. It is composed of a plurality of multipliers 210 to provide as an input of the FFT butterfly operation unit 210.

The number of the variable division redics- _{2 /} 4/8 FFT butterfly operations 210 is equal to log ₂ N, i.e., the required number of stages n.

The FFT format operator 230 repeatedly divides the input FFT symbol data value (N) by a divisor 8. If the quotient is one of 1, 2, or 4, the FFT format operator 230 can obtain the divided number (k) and the quotient up to that time. have. The setting information is provided by setting the number and combination of the FFT processing units PE1, PE2, and PE3 to be used through the quotient and the number of divisions. In other words, if the quotient is 1, k split reddix-2 / 4/8 FFTs (using both PE1, PE2, and PE3) are required.If the quotient is 2, split reddix-2 / 4/8 FFTs (PE1, PE2, Use both PE3) k and 1 Reddix-2 FFT (PE3) required, with a quotient of 4 k split and Reddix-2 / 4/8 FFTs (using both PE1, PE2 and PE3) and 1 split reddix -2/4 FFT (using PE2, PE3) is required.

Here, considering that the mode applied to a general OFDM system is fixed to a predetermined number (four modes in the embodiment Eureka-147), it is necessary to perform the above operation every time through the FFT format operator 230. Disappear. That is, the internal table may be set to obtain the number and combination of FFTs to be used immediately according to the mode or to obtain the data itself to be transmitted to the FFT control unit 220. In this case, the FFT format calculator 230 may control the FFT control unit. Act as part of 220.

Number of inputs (N) Reddicks-2/4/8 Reddicks-2 / 4 Reddicks-2 n 64 2 2 128 2 One 3 256 2 One 3 512 3 3 1024 3 One 4 2048 3 One 4 4096 4 4 8192 4 One 5

If the internal table shown in Table 1 is used and used, it can be used in an FFT device that can cover all the modes of Eureka-147 as an embodiment of the application and can be applied to the inputs below and above. That is, when the configuration of the FFT according to the setting mode can be controlled by the FFT control unit 220, the FFT format operator 230 may not be used while utilizing the variable reddix-2 / 4/8 FFT.

The combination of the necessary processing units PE1, PE2, and PE3 and the number thereof are applied to the FFT controller 180, and based on the FFT controller 180, the FFT controller 180 is connected to a plurality of variable partitioned reddix-2 / 4/8. Only the necessary number of processing units PE1, PE2, and PE3 in the FFT butterfly operations 210 are activated.

Now, an operation of the processing units PE1, PE2, and PE3 existing in one variable division redics-2 / 4/8 FFT butterfly operator 210 will be described.

The first FFT processing unit (PE1) 100 bypasses the input values by the control signal of the FFT controller 180, or performs the -j operation according to the position of the intermediate values after performing the Redox-8 FFT. You can run This is evident with reference to FIG. 6, and the -j operation to perform this post-execution of such Reddix-8 FFT is known to those skilled in the art.

The second FFT processing unit (PE2) 110 bypasses input values according to the control signal of the FFT control unit 180 or rotates a factor for the Redox-8 FFT of the first FFT processing unit (PE1) 100. And selectively perform the -j operation on the Redix-4 FFT. Portions that process the rotation factors W ^{N / 8} and W ^{3N / 8} for the Reddix-8 FFT are common in a split reddix-2 / 4/8 FFT structure.

The third FFT processing unit (PE3) 120 performs only basic Redix-2 FFT according to the control signal of the FFT control unit 180 or is connected to the first FFT and second FFT processing units (PE1, PE2) and has an intermediate value. Differential Redix-2 FFT is performed according to their location. In other words, if split reddix-2 / 4/8 FFT and split reddix-2 / 4 FFT are in use, they must be processed by PE3.

As described above, the variable division reddicks-2 / 4/8 FFT butterfly operation unit 210 and the control unit 220 are configured to be used to variably set desired processing units, and at the same time, appropriate rotation factors according to the flow of signals passing through them. To be multiplied by the output of each variable division redisx-2 / 4/8 FFT butterfly operation unit 210. To this end, the output of the rotation factor table 200 having the rotation factor is controlled by the FFT control unit 220 to control the flow of signals between the variable division reddix-2 / 4/8 FFT butterfly operations 210. Provide suitable rotation factors to the multipliers 215 located. Through this, the output of the variable division reddicks-2 / 4/8 FFT butterfly operation unit 210 at the front end is multiplied by the appropriate rotation factor, and the value thereof is the variable reddix-2 / 4/8 FFT butterfly operation unit 210 at the rear end. To be input.

Through the above-described configuration and operation, the FFT for the FFT symbol data value N consisting of multiples of 2, 4, and 8 can be implemented with a minimum complex multiplier.

As described above, the present invention minimizes complex multiplication operations by using a variable division reddix-2 / 4/8 FFT modified to suit all modes used for OFDM modulation and demodulation, while simplifying the structure required for hardware. This saves space and computation time, which in turn reduces power consumption.

Claims (8)

An FFT format calculator configured to output setting information by setting the number and combination of FFTs used according to the FFT symbol data; An FFT controller for outputting a control signal according to the setting information; A variable division reddix 2/4/8 FFT butterfly operator for performing FFT according to the control signal; A rotation factor table for outputting a rotation factor in accordance with the control signal; And a multiplier multiplying an output signal of the variable division redis 2/4/8 FFT butterfly operator by the rotation factor. The method of claim 1, wherein the first FFT processing unit is composed of one Redix-8 FFT, the second FFT processing unit is one Redix-4 FFT, and the third FFT processing unit is one Reddix-2 FFT. High speed Fourier inverter. 2. The fast Fourier transform apparatus as set forth in claim 1, wherein the number of the variable partitioned Reddix-2 / 4/8 FFT butterfly operators is equal to the required number of stages. The FFT format operation according to claim 1, wherein the FFT format operator repeatedly divides the input FFT symbol data value by a divisor of 8 and completes the operation if the quotient is one of 1, 2, and 4, and uses the FFT process to be used through the quotient and the number of divisions. A high speed Fourier transform apparatus for setting information and setting the number and combination of units. The FFT format operator of claim 1, wherein the FFT format operator stores the number and combination of FFT processing units according to a predetermined FFT symbol data value by the number of modes used, and then uses the number of FFT processing units to be used according to the provided FFT symbol data value. A fast Fourier transform apparatus comprising a function unit for setting a combination to provide setting information included in the FFT control unit. Generating setting information by setting the number and combination of FFT processing units to be used through the FFT symbol data value; By using the setting information set through the above steps, the control of the operations of the FFT processing units belonging to the plurality of variable partitioned Redix-2 / 4/8 FFT butterfly operations is individually controlled, and the appropriate rotation factor values are changed. / 8 FFT multiplying the output of the butterfly operation unit, characterized in that the fast Fourier transform method. The method of claim 6, wherein the setting of the number and combination of the FFT processing units to generate the setting information comprises repeating dividing the FFT symbol data value by a divisor of 8 to complete the calculation if the quotient is one of 1, 2, and 4, And setting the number and combination of FFT processing units to be used through the quotient and the number of divisions to generate setting information. The method of claim 6, wherein the setting of the number and the combination of the FFT processing units to generate the setting information comprises storing the number and the combination of the FFT processing units according to a predetermined FFT symbol data value. And setting the number and combination of FFT processing units to be used according to the set, to generate setting information.