Table of contents
1. Theoretical basis
The transmission technology of 802.11a is a multi-carrier modulation technology. The 802.11a standard is the follow-up standard of the 802.11b wireless networking standard that has been widely used in offices, homes, hotels, airports and many other occasions. It works in the 5GHzU-NII frequency band, the physical layer speed can reach 54Mb/s, and the transmission layer can reach 25Mbps. It can provide 25Mbps wireless ATM interface, 10Mbps Ethernet wireless frame structure interface, and TDD/TDMA air interface; support voice, data, image services; one sector can access multiple users, and each user can carry multiple user terminal. IEEE wireless networking standard specifying a maximum data transfer rate of 54Mbps and an operating frequency band of 5GHz.
The 802.11a standard adopts the same core protocol as the original standard, the operating frequency is 5GHz, and 52 OFDM subcarriers are used. The maximum original data transmission rate is 54Mb/s, which reaches the medium throughput of the actual network. (20Mb/s) requirement. Data rates can be reduced to 48, 36, 24, 18, 12, 9 or 6Mb/s if desired. 802.11a has 12 non-overlapping channels, 8 for indoor use and 4 for point-to-point transmission. It cannot interoperate with IEEE 802.11b unless equipment that adopts both standards is used.
OFDM (Orthogonal Frequency Division Multiplexing) is Orthogonal Frequency Division Multiplexing technology. In fact, OFDM is MCM (Multi Carrier Modulation), a type of multi-carrier modulation. The parallel transmission of high-speed serial data is realized through frequency division multiplexing, it has better anti-multipath fading ability, and can support multi-user access. OFDM technology is developed from MCM (Multi-Carrier Modulation, multi-carrier modulation). OFDM technology is one of the implementation methods of multi-carrier transmission schemes. Its modulation and demodulation are realized based on IFFT and FFT respectively. It is a multi-carrier transmission scheme with the lowest implementation complexity and the most widely used.
The main idea of OFDM is: divide the channel into several orthogonal sub-channels, convert high-speed data signals into parallel low-speed sub-data streams, and modulate them for transmission on each sub-channel. Orthogonal signals can be separated by using correlation techniques at the receiver, which can reduce the mutual interference (ISI) between subchannels. The signal bandwidth on each sub-channel is smaller than the relevant bandwidth of the channel, so each sub-channel can be regarded as flat fading, which can eliminate intersymbol interference, and because the bandwidth of each sub-channel is only a small part of the original channel bandwidth, the channel Equilibrium becomes relatively easy.
OFDM is a special multi-carrier transmission scheme. OFDM uses DFT and its inverse transformation IDFT method to solve the problem of generating multiple mutually orthogonal subcarriers and recovering the original signal from the subcarriers. This solves the problem of sending and transmitting in a multi-carrier transmission system. The application of fast Fourier transform makes the complexity of the multi-carrier transmission system greatly reduced. From then on, OFDM technology began to be practical. However, the application of the OFDM system still requires a large number of complex digital signal processing processes, and at that time there was a lack of components with powerful digital processing functions, so the OFDM technology has not been developed rapidly.
OFDM system implemented based on IFFT/FFT:
OFDM uses BPSK, QPSK, 16QAM, 64QAM four kinds of modulation methods. According to the constellation diagram, the data on each sub-channel is mapped to the complex number representation of the constellation diagram points, and converted into an in-phase Ich and a quadrature component Qch.
In fact, this is a table lookup method. Taking the 16QAM constellation as an example, bits_per_symbol=4, there are 4 binary numbers {d1, d2, d3, d4} on each sub-channel of each OFDM symbol, and there are 16 values in total. , corresponding to 16 points on the constellation diagram, and the real part of each point is recorded as Qch. In order for all mapping points to have the same high average power, the output must be normalized, so corresponding to BPSK, PQSK, 16QAM, 64QAM, respectively multiplied by the normalization coefficient coefficient 1, , , . The output complex sequence is the mapped modulation result.
Perform IFFT operation on the same component and orthogonal component obtained in the previous step according to (Ich+Qch*i). And the real part of the obtained complex number is used as a new Ich, and the imaginary part is used as a new Qch.
Synchronization technology is very critical for various digital transmission technologies, especially for OFDM systems. Because OFDM is very sensitive to synchronization errors, the quality of synchronization performance directly affects the performance of reception. Once the synchronization performance is not good, the overall performance of OFDM will seriously decline.
In practical application, the generation and demodulation of the signal are realized by the method of digital signal processing. At this time, the signal should be sampled to form a discrete-time signal. Since the bandwidth of the OFDM signal is B=N·Δf, the signal must be sampled at a time interval of Δt=1/B=1/(N·Δf). The sampled signal is represented by sn,i
The time interval of t=1/B=1/(N·Δf) is sampled. The sampled signal is represented by sn,i, i = 0, 1, …, N-1, then there is
It can be seen from this formula that it is a strict expression of the discrete inverse Fourier transform (IDFT). IDFT can be implemented using Fast Inverse Fourier Transform (IFFT)
The in-phase component and quadrature component of each symbol after the IFFT operation are respectively converted into serial data, and the data of G length at the end of the symbol is added to the head to form a cyclic prefix. If an empty interval is added, under the influence of multipath propagation, it will cause inter-carrier interference ICI. The length G of the protection section should be greater than the maximum value of the expansion during multipath.
2. Core program
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for snr = 5
%======================
% Channel
%======================
temp_channel = channel_response(:,nframe+1).'; % Channel response at the current frame
ry = channel_multipath(tx,temp_channel); % Multi-path channel
ry = awgn(ry,snr); % Add addictive white gaussian noise
%======================
% Receiver
%======================
[RY,R_pilot] = ry_time_to_fre(ry,N_SPF,temp_channel); % Recover the time signal to frequency symbols of each subcarrier and Channel Equalization
figure(2)
a=real(RY);
b=imag(RY);
plot(a,b,'bx')
axis([-2 2 -2 2]);
hold on
Rcode_bits = ry_16qam_demod(RY); % Demodulate the received symbols
dec_bits = ry_sovadec(Rcode_bits, trl, N_DBPF,N_DBPF); % Soft output viterbi decoding, out = ln( p(info_bits(i)=1)/p(info_bits(i)=0));
%======================
% Error detection
%======================
for i = 1:N_DBPF
if dec_bits(i) >= 0
hard_det(i) = 1; % hard_det refers to the hard decision
else
hard_det(i) = 0;
end
if hard_det(i) ~= info_bits(i)
nerror = nerror+1;
end
end
nframe = nframe + 1;
end
BER = nerror/(frame_num * N_DBPF);
fprintf('\nSNR is %1.2f dB, BER is %e\n ',snr,BER);
end
UP1533. Simulation conclusion
SNR=5
SNR=10
SNR=15
SNR=20
SNR=25
