ofdm实现文档.docx

1、ofdm实现文档Design overviewThe OFDM technique (Orthogonal Frequency Division Multiplexing) has been used in the last years in applications that require a huge transmission rate like ADSL modem, wireless network (Wi-Fi 802.11), DVB (Digital Video Broadcasting) and DAB (Digital Audio Broadcasting). In all

2、 these cases, one needs to implement an integrated circuit (IC) that performs the necessary chip functions. For prototyping circuits FPGA is better choice than using ASIC (application Specific Integrated Circuit), CUSTOM or SEMICUSTOM. FPGA implementations because avoid the: Initial costs; Great dev

3、elopment time and the inherent risks of conventional ASIC. So, in this way, the development of high advanced techniques of digital data transmission and the actual FPGA stage of integration make possible the building all the circuits that compounds a digital communication systems in an unique chip.

4、To make use of this modern technologies of data transmission, it is necessary the development efficient techniques of digital modulation. The OFDM is the biggest utilized recently, principally, because of it use the efficient FFT to do the modulation.This work describes how implement an OFDM modem o

5、n FPGA using VHDL for a 31 subcarrier (channels) OFDM system using 64 points radix-4 FFT time decimation, a CORDIC implementation to perform the butterfly calculus, and each channel modulation will use a 4-QAM constellation. The system is divided in a transmission section and a reception section. Bl

6、ock diagramDetailed descriptionIntroductionBasically, OFDM technique consists of dividing the flow of entrance data over orthogonal channels. In this way, and based on the orthogonality principle, the interference between each transmission channel is minimal. Another advantage that comes from this a

7、pproach is related to the assumptions about the noise in each channel. Over a large and unique passband channel it is difficult (impossible in fact, in many situations) to assume that the model noise is AWGN (Additive Noise Gaussian Noise). That is important because if the model is know, and it is c

8、orrect, one can select the best way of frequency equalization. But, in large passband channels (tenths of Mhz) the noise model is unknown and unpredictable. The solution of dividing a unique channel in subchannels simplifies the assumptions of the noise over each subchannel and, of course, one can s

9、uppose it approximately AWGN. In each one of these subchannels, a digital modulation is made, each one with a subcarrier that presents different frequency, in a such form that a channel does not intervene with another one, thus keeping the orthogonallity.The way of implementation and the orthogonall

10、ity property of a system of this type can vary sufficiently: since band pass filters each frequency until sophisticated techniques as the use of the FFT with guard interval, which is the used one for the OFDM.In literature, this technique has been called for some designations as orthogonally multipl

11、exed QAM (O-QAM), parallel quadrature AM, and so one. However, OFDM for wireless and DMT for systems wired (like DSL) are the most common designations that one can find in literature. As all the above techniques basically use the same principle, it is common to refer to them by means of a generic na

12、me: MCM (to Multi-Carrier Modulation). In that way, MCM is the technique in the general direction, and OFDM is related to the implementation of technique MCM using the FFT.ImplementationMapping the constellationThe encoder of the constellation maps the m bits of the channel in a point a + jb in the

13、constellation of the modulator. Decoding receives that point and the remap as the m transmitted bits.Encoder of the constellationIt is important to notice that in that mapping it is just made a conversion of bits for the fasor that acts, however it is not made any modulation, as in the case of QAM,

14、because that as shown, it is done by IFFT.It is necessary to specify how the constellation will be to be mapped, to implement that block. However, independently of the format of the constellation, the block encoder can be made through a consultation at a conversion table, implemented by LUT that exi

15、sts in LCs of FPGAs.For instance, for a 4-QAM constellation in such a way that a and b are binary numbers of 3 bits, and are converted to complement two.Attempt that the entrance of the encoder a binary number of m bits, and that the exit generates two binary numbers, one in phase, the, and other in

16、 quadrature, b, whose size is defined by IFFT.Decoder of the constellationIn the receiver, the point of the constellation transmitted it can have changed due to the noises of the transmission channel, mistake in the time of sampling of the receiver and several other causes.Therefore it is necessary

17、to define a threshold so that it can be made the decision on which point in the constellation the received sign is acting. That is the function of the decoder.For the system exemplified above the bit 0 is converted for 010b and the bit 1 for 110b. In that case, the decoder is implemented in a simple

18、 way, sticks to the most significant (that indicates the sign) bit to do the decoding, and generating a binary number of m bits again.For systems in that the constellation diagram is larger than 4-PSK it will be necessary the implementation of more advanced methods, like a neural network.The Hemetia

19、n symmetryAfter having mapped the N channels it is applied the Hermetian symmetry so that the modulation can be made by an IFFT. It is generated 2N+2 channels in symmetry.In the receiver, to the end of the processing of FFT, they are sent to the decoder only N channels, being eliminated the channels

20、 generated due to Hermetian symmetry.The Hermetian symmetry is implemented in agreement withfor k = 1, 2., N - 1, where N = N +1.For instance, to transmit N = 3 channels (d1, d2, d3) N = 4, 2N = 8 and k = 1, 2, 3. Applying in the above equation it is obtained the result shown in the following table.

21、Knowing that X0 = XN=4 = 0 + j0, is obtained in agreement with the Table 2 the result shown in the following equation:In that way, it can stay X0 and XN always in zero. While it is made XN+1 even X2n - i same to the conjugated of Xn-1.Being it conjugated of Z = a+jb the same of Z* = a- jb, then to d

22、o the operation of having conjugated he should move the sign of the imaginary part, in other words, to do a sign inversion. In hardware, the inversion of sign of a binary number in complement two.The (I)FFTThe modulation OFDM can be made through an IDFT. The fast implementation of IDFT, IFFT, can be

23、 used reducing the time of processing and the used hardware. The demodulation, in the same way, can be made by DFT, or better, by FFT, that is it efficient implementation.FFT calculates DFT with a great reduction in the amount of operations, leaving several existent redundancies in the direct calcul

24、ation of DFT. That efficiency is gotten at the cost of an additional step to reverse-order the data in order to be determined the final result. That additional step, since implemented efficiently, they wont increase in a significant way the complexity computational of the calculation. As result, FFT

25、 is an extremely efficient algorithm that provides a good implementation in hardware.For great values of N, the computational efficiency is gotten being broken DFT successively in smaller calculations. That can be made so much in the domain of the time, as in the domain of the frequency, as discusse

26、d ahead.Decimation in time and in frequencyAs mentioned, it is possible to divide the entrance of FFT successively generating small sequence in the domain of the time, for that the name decimation in the time, TD. It is also possible to become separated the sequence of exit of FFT successively, inst

27、ead of dividing the entrance. That implementation is called of decimation in the frequency, FD. The decimation can be used so much for FFT as for IFFT.It is possible to repeat the process until reaching the possible maximum level of division. In that point the basic block decimation is generated so

28、it will be used in the whole FFT (called butterfly). An example of the butterfly of the FFT radix-2 TD is in the following illustration.An example of a FFT radix-2 DT, for N = 8 are shown below. It is noticed that is necessary an alteration in the entrance of data, because he/she has to separate the

29、 equal part of the odd part.In the same way that the decimation in the time generates a butterfly, the decimation in the frequency generates a corresponding butterfly. However the alteration in the flow of data will have to be done in the exit, and no more in the entrance.Implementation of Butterfly

30、The sum used in the butterfly possesses the same algorithm, so much for FFT as for IFFT. To avoid overflow danger due to sum in complement two, it is made the extension of the sign in the binary number, repeating the most significant bit, like this to the if it adds 2 binary numbers of 10 bits, we w

31、ill have of first to do the extension of the sign, obtaining like this, two numbers of 11 bits, to do the sum, where the result will also be of 11 bits. That procedure has to be done every time that will add or to subtract a number.Already for the multiplication, the exit has to be of the size of th

32、e sum of the number of bits of the two multiplicands. In that way, to do the multiplication of two numbers of 10 bits, we will have to an exit of 20 bits. That procedure has to be done to each multiplication.If there is not impediment, it can be made a rotation for right (divisions for two) in the numbers and to reduce its size, since in the end of the procedure a corresponding multiplier is applied.The order as it will be made the butterfly is defined by the decimation of the radix. If it goes TD, first it is made multiplication and later the sum. If it goes FD, first it