# The Wimax Transmitter Model Technology Essay

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All the mandatory blocks of WIMAX transmitter are described in this chapter. The block diagram of WIMAX transmitter is shown in the below figure 2.1. At first the input data in the transmitter is passes through the randomizer section then this section will randomize the data. Then by using channel encoder randomized data is coded, this channel encoder contains Reed Solomon, convolution encoder and puncture blocks. By using interleave the coded data is interleaved and mapped in to QAM symbol. Once the interleaved section is completed the data passes through OFDM symbol model which contains OFDM frames and 256 IFFT and CF(cyclic prefix) insertion. Finally the data passes through AWGN channel if we implement only wimax end to end model without channel estimation otherwise we have to use Rayleigh fading channel with Additive white Gaussian noise (AWGN). Now let us see block to block explanation of WIMAX transmitter. This chapter explains wimax simulink subsystem at the same time.

2.1 The block of WIMAX TRANSMITTER

2.1.Transmitter Data input block:

In Data block subsystem we are sending input data of 35 frames . We can send n frames of data but here we are using only 35 frames of data. Actually this data is in bits we need to convert them in to bits so we are using integer to bit converter block.

The sub system block using matlab simulink of data input is shown in below fig 2.2

Fig 2.2 Transmitter data input block

2.2 Randomizer:

The randomizer block bits need to be randomized before the transmission. The function of randomizer is it performs randomization of input data on each burst on each allocation to prevent a long sequence of 1's and 0's. The subsystem block of randomizer is shown in below fig 2.3.

Fig 2.3 Randomizer subsystem block[4]

The block PN Sequence generator which is nothing but Pseudo Random Binary Sequence (PRBS) generator, which is made of a 15 bits shift register and two XOR gates explanation as shown in below figure 2.4[1].

Fig. 2.4: Point PRBS for data randomization. [1]

In the downlink burst the initial vector for the shift register (Linear-Feedback Shift Register (LFSR) possessing characteristic polynomial (1 + x14+x15 ) is 100101010000000 and the scrambler should be reset at the start of each burst. At the start of subsequent bursts each vector should be placed which is shown in below figure 2.3.The downlink burst is utilize the frame numbers for referring the frame.[1]

Fig. 2.5: OFDM randomizer downlink initialization vector for burst #2...N. [1]

Zero padding block description:

The Pad block is used for expanding or reducing the dimensions of the input by padding along its columns and rows, or any specified dimension(s). Truncation occurs when input dimensions are longer than the output dimensions.The block will a pass-through if input and output dimensions are same.[4] .

## 2.3 Encoder:

The next three blocks contains encoder scheme which performs FEC (Forward error correction scheme)contains RS code , puncturing and interleaving .At first randomized data passes through RS encoder and then passes to Convolution encoder. After this, the encoded data is punctured and interleaved.

## 2.3.1 Reed Solomon Encoder:

## The subsystem block for reed Solomon encoder is shown in fig 2.6.

## Fig 2.7 subsystem block for RS Encoder

In this section at bits need to be converted in to integers and by using the zero pad which is discussed in above has to be performed then data will pass through RS encoder.

The RS code is a linear block codes, it's function is correcting the burst errors.

During transmission time Rs encoder add redundancy to the data sequence in order to correct the errors. RS code is derived from a systematic RS ( 255,= 239, = 8) code using a Galois field specified as (28 ), which means

255=Number of bytes after encoding,

239= Number of data bytes before encoding and is

8=Number ofdata byte that can be corrected.

The following polynomials are used for the systematic code[1]:

## Fig. 2.8: The Reed Solomon code.

In WiMAX the error-correction capability is obtained shortening RS code and punctured to enable variable block sizes and variable. This can be obtain by shortened block of bytes by adding 239 -k zero bytes before the data block, these 239 âˆ’k zero bytes are removed after encoding. RS code can correct up to T symbols, where can be expressed as = ( Nâˆ’K )/2. When a codeword is punctured to permit T bytes to be corrected. Only the first 2 Tâ€² of the total 16 parity bytes shall be employed as shown in figure 2.5. For instance, QPSK with (5â„6) CC code rate, the RS code is (( N= 40), ( K= 36), (T = 2)) as shown in table 2.1. bit/byte. [1].Look in the below figure how shortening and puncturing process has performed.[4]

## Fig. 2.9: Shortening and puncturing process of the RS code.

After performing the RS encoder selector subsystem block has to be used to gain the data and this data is in integer again we need to convert then to bits.

## 2.3.2 Convolutional Encoder:

The convolutional subsystem block using matlab simulink is shown in below fig

Fig 2.11 shows convolutional encoder with puncture.

For converting binary input vector to binary output vector convolutional encoder is used. The convolutional block can process multiple symbols at a time.

If the input bit stream is k for encoder (that is, can receive 2k possible input symbols), for some positive integer L the block's input vector length is L*k. Similarly, if the encoder produces n output bit streams (that is, can produce 2n possible output symbols), this block's output vector length is L*n.The input can be a sample-based vector with L = 1, or a frame-based column vector with any positive integer for L.

During the transmission the randomly occurred errors over channel can be corrected by using convolution encoder. Convolution encoder is not a memoryless device like block encoder. The RS encoded bits are encoded by the binary convolution encoder, which has native rate of 1/2, a constraint length equal to 7 and a polynomial description[171 133] as shown in equation (2.3), (2.4) to produce its two code bits. The generator is shown in figure 2.6. [1]

Now let us see the function of convolution encoder rate ½ using block diagram in below figure 2.6

Fig. 2.6: Convolutional encoder of rate 1/2. [1]

In WIMAX after RS encoder is encoded the the data bits will pass through the convolutional encoder. For different Modulation types the block size and code rate are shown below:

Table 2.1: channel coding per modulation. [1]

## 2.3.3 Puncturing:

Puncturing technique is performed after the convolutional encoder block. For creating output vector , preserving other vectors and removing input vectors puncturing block is used.The puncturing performs the encoding and decoding of higher code rates using standard rate 1/2 encoders and decoders. puncturing mainly used to achieve variable code rate. Which can be achieved by removing bits from the output stream of a low rate encoder. The bits are removed according to the table shown below2.2 .In the below table, "1" means a transmitted bit and "0" means removed bit, [1].

If Puncture vector(k) = 0, then the kth element of the input vector does not become part of the output vector.

If Puncture vector(k) = 1, then the kth element of the input vector is preserved in the output vector.

Here k is between 1 and k the preserved element output becomes same as input.

Table 2.2: Convolutional code with puncturing configuration. [4]

## 2.4 Interleaver:

The interleaver is the last block in channel encoder section used to randomize the coded bits in order to make the possible errors at the receiver uncorrelated.The function of interleaver is it interleaved all encoded bits coming from RS-CC block size, which depends on the number of coded bits per allocated subchannels per OFDM symbol . The number of coded bits depend on modulation scheme as shown in table 2.3. The interleaver in WiMAX is defined by a two step permutation. The first permutation make sure that adjacent coded bits are mapped onto non adjacent carriers and is defined by equation shown below:[4]

The second permutation performs adjacent coded bits are mapped alternately onto less or more significant bits of the constellation and is defined by Equation (2.6): [1] [2]

With , and is the number of coded bit per carrier, is number

of coded bits per OFDM symbol, k is index of coded bits before first permutation, mk is index of coded bits after first permutation and before the second permutation and jk is index of coded bits after second permutation .

Table 2.3: Block sizes of the bit interleaver. [4]

## 2.5 Modulation:

## The subsystem block for interleaver is shown in below fig2.12

In this section first bits need to convert to interger for processing the modulation.

The modulation constellation used in WiMAX is two types of phase shift keying (PSK) modulation (binary (BPSK) and quadrature (QPSK)) and two types of quadrature amplitude (QAM) modulation (16QAM and 64QAM). The complex constellation value is scaled by factor (Normalization constant), such that the average transmitted power is unity, c equals 1â„âˆš2 for QPSK, 1â„âˆš10 for 16-QAM, 1â„âˆš42 for 64-QAM .

Fig. 2.13: constellations of BPSK, QPSK, 16-QAM and 64-QAM. [4]

2.6 OFDM SYMBOL:

In WiMAX, each OFDM symbol consists of 256 subcarriers as shown in figure 2.8. They canbe divided into.

1. 192 data subcarriers that are used for conveying data.

2. 8 pilot subcarriers that are used for conveying pilot symbols.

3. 56 null subcarriers that have no power allocated to them, including the DC subcarrierand the guard subcarriers toward the edge.

Fig. 2.14: Frequency domain representation of OFDM symbol. [1]

The rearranging of carrier is required to construct OFDM symbol. So assembler block is inserted to perform this process. The operation process is divided in to two types they are first pilot tones need to be inserted and then with the process of vertical concatenation zero DC has to be inserted. The training symbols in this procees has to be send in horizontal way which is shown in below fig 2.15. The fig represents that in first step concatenation occurs in frequency domain and second step occurs in time domain.

Fig 2.15 OFDM burst structure

Shift on the index value is needed in the simulator because matlab allows only positive indices. So the offset indices of 13, 38, 63, 88, 114, 139, 164, and 189 frequency pilot subcarriers are inserted. Same process will occurs even for zero DC subcarriers. At the beginning of the each burst the training symbols are appended.

The subsystem block for OFDM symbol with IFFT and CP using matlab simulink is shown in below fig 2.16

## 2.6.1 Pilot modulation:

The pilots has to be modified before inserting in a specified position which is shown in figure 2.8. By using Pseudo Random Binary Sequence (PRBS) generator pilots can be generated as shown in figure 2.9.

Fig. 2.10: PRBS for pilot modulation. [1]

PRBS generator polynomial is:

Which can be used for various channel estimation purposes.

## 2.6.2 Inverse Fast Fourier Transform (IFFT):

To convert frequency domain into time domain, and to assign all allocated subcarriers the IFFT block function is used. We can calculate time duration of the IFFT time signal by multiply the number of FFT by using sample period. Zeros are added at the end and beginning of OFDM symbol. These zero carriers are used as guard band to prevent inter channel interference (ICI).

Besides ensuring the orthogonality of the OFDM subcarriers, the IFFT represents also a rapid way for modulating these subcarriers in parallel, and thus, the use of multiple modulators and demodulators, which spend a lot of time and resources to

perform this operation, is avoided.

The subcarriers are rearranged before doing the IFFT operation in the simulator. Figure 2.17 shows the subcarrier structure that enters the IFFT block after performing the cited rearrangement. Zero subcarriers are kept in the center of the structure which can be viewed in the below fig.

Fig 2.17 before performing IFFT operation rearrangement is performed.

To facilitate the realization of the algorithm or IFFT should be of length 2r.So finally the FFT length is given by

## 2.6.3 Cyclic Prefix insertion (CP):

The cyclic prefix is used to avoid inter symbol interference (ISI) before each transmitted symbol. This can be achieved by copying the last part of an OFDM symbol to the beginning which is shown in below fig 2.11 . WiMAX supports four different duration of cyclic prefix (i.e. assuming is the ratio of guard time to OFDM symbol time, this ratio is equal to 1/32, 1/6, 1/8 an 1/4).

Fig 2.18 cyclic prefix

Copying the end of a symbol and joining to the start results in a longer symbol time. Thus, the total length of the symbol is

.............2.2

where:

â€¢ Tsym is the OFDM symbol time,

â€¢ Tb is the useful symbol time, and

â€¢ Tg represents the CP time.

The ratio of CP length is G which uses symbol time. The CP should be longer than the dispersion of channel when eliminating ISI . For this reason G is usually less than ¼.

................2.3