Pseudocode
Pseudocode for Generating Digital Signal from Gaussi an
Random Values
Start
Set the number of bits to generate (e.g., 1000)
Generate a vector of random values using Gaussian (normal) distribution
→ Each value is from a standard normal distribution (mean = 0, std = 1)
Convert random values into binary bits:
→ If value > 0, set bit to 1
→ Else, set bit to 0
Plot the resulting bit sequence:
- Use circles connected by lines for visualization
- Set title: "Generated Signal"
- Label x-axis as "Bit Index"
- Label y-axis as "Value"
- Limit y-axis to slightly below 0 and above 1 for clarity
- Enable grid for better readability
End
Pseudocode for Generating and Plotting BPSK Signal
Start
Set the number of bits to generate (e.g., 1000)
Step 1: Generate random values
- Generate 1000 random values from a standard normal (Gaussian) distribution
Step 2: Convert random values to bits
- If a value > 0 → bit = 1
- If a value <= 0 → bit = 0
Step 3: Map bits to BPSK symbols
- If bit = 1 → symbol = +1
- If bit = 0 → symbol = -1
- This is done using: BPSK_symbol = 2 * bit - 1
Step 4: Plot the BPSK signal
- Use circle markers connected with lines to show transitions
- Add title: "BPSK Signal After Modulation"
- Label x-axis as "Sample Index"
- Label y-axis as "+1 or -1"
- Enable grid for visual clarity
End
Pseudocode for Generating and Plotting QPSK Signal
Start
Set number of bits to generate (e.g., 1000)
Step 1: Generate Gaussian random values
- Generate 1000 random values from a standard normal distribution
Step 2: Convert random values to bits (0 or 1)
- For each value:
If value > 0, bit = 1
Else, bit = 0
Step 3: Group bits into pairs (because QPSK uses 2 bits per symbol)
- Reshape the bit vector into 2 rows and N/2 columns
Step 4: Map each bit pair to a QPSK phase angle:
- Convert the 2-bit pair into a decimal number (0 to 3)
Example:
00 → 0
01 → 1
10 → 2
11 → 3
- Map these numbers to phase angles according to:
00 → -π/2
01 → +π/2
10 → +3π/4
11 → -3π/4
Step 5: Calculate constellation points:
- For each phase angle θ:
Compute (cos(θ), sin(θ))
Step 6: Plot constellation points:
- Use circles connected with lines for visualization
- Set title: "QPSK Signal After Modulation"
- Label x-axis as "In-phase component"
- Label y-axis as "Quadrature component"
- Enable grid
- Use equal axis scaling for accurate constellation shape
End
Pseudocode for Generating and Plotting 16QAM Signal
Start
Set initial number of bits to generate (e.g., 1000)
Check if the number of bits is a multiple of 4 (because 16 -QAM uses 4 bits
per symbol)
o If not multiple of 4:
Increase numBits to the next multiple of 4
Generate random Gaussian values of length numBits
Convert random values to bits (0 or 1):
o For each value:
If value > 0 → bit = 1
Else → bit = 0
Group bits into sets of 4 (reshape into 4 rows, each column is one 16 -QAM
symbol)
Map each group of 4 bits into a decimal number:
o symbol_value = 2*bit1 + 2*bit2 + 4*bit3 + 8*bit4
Shift symbols to be centered around zero:
o symbol_value = symbol_value - 8
Plot constellation diagram for 16 -QAM:
o Plot each symbol’s real part on the x -axis
o Plot each symbol’s imaginary part on the y -axis
o Use scatter plot with circle markers
o Add title: "16-QAM Signal After Modulation"
o Label x-axis: "In-phase component"
o Label y-axis: "Quadrature component"
o Enable grid
o Use equal axis scaling to preserve the constellation shape
End
Pseudocode for Generating and Plotting 64QAM Signal
Start
Set initial number of bits to generate (e.g., 1000)
Check if the number of bits is a multiple of 6 (because 64-QAM uses 6 bits per symbol)
o If not a multiple of 6:
Increase numBits to the next multiple of 6
Generate random Gaussian values of length numBits
Convert random values to bits (0 or 1):
o For each value:
If value > 0, bit = 1
Else, bit = 0
Group bits into sets of 6 (reshape into 6 rows, each column represents one QAM
symbol)
Map each group of 6 bits into a decimal number:
o symbol_value = 32*bit1 + 16*bit2 + 8*bit3 + 4*bit4 + 2*bit5 + bit6
Shift symbol values to be centered around zero:
o symbol_value = symbol_value - 32
Plot the constellation diagram for 64-QAM:
o Plot each symbol as a complex number (usually QAM symbols have both real (I)
and imaginary (Q) parts)
o Note: Current symbols are real numbers only; typically, QAM symbols should be
processed as complex numbers with I and Q components
o Use scatter plot
o Add title: "64-QAM Signal After Modulation"
o Label x-axis: "In-phase component"
o Label y-axis: "Quadrature component"
o Enable grid
o Set axis scaling to equal for proper display
End
Pseudocode for Visualizing OFDM Subcarriers in Time and
Frequency Domains
Start
Clear all variables and figures
Define different values of N (number of subcarriers)
Set number of OFDM symbols to 1
Set oversampling factor
Set sampling frequency (fs)
Set FFT size (Nfft)
For each N in N_values:
Compute sampling time Ts
Create a time vector 't' using oversampling
Generate QPSK symbols:
Generate complex Gaussian random numbers
Convert to QPSK by taking sign of real and imaginary parts
Normalize power
Generate OFDM signal in time domain using IFFT
Apply oversampling (interpolation) to the OFDM waveform
For each subcarrier from 1 to N:
Set only that subcarrier with data, others to zero
Apply IFFT to get its individual time-domain waveform
Interpolate the waveform for smooth plotting
Store each subcarrier waveform in a matrix
Generate distinguishable colors for plotting
Plot time-domain waveforms:
For each subcarrier:
Plot waveform vs time using assigned color
Add labels, grid, title, and legend
Plot frequency-domain spectrum:
Define frequency axis using FFT size
For each subcarrier:
Compute FFT and shift it to center
Plot the power spectrum in dB using assigned color
Add labels, grid, title, and legend
Zoom in on useful frequency range
Adjust y-axis to enhance visibility
End loop
Define helper function to generate distinguishable colors:
Use HSV color map and pick evenly spaced entries
Return color array
End
Pseudo Code for PAPR Reduction Techniques Simulation
Initialize parameters:
N = number of subcarriers (e.g., 64)
M = modulation order (e.g., 4 for QPSK)
numSymbols = number of OFDM symbols to simulate
SNRdB = range of SNR values (e.g., 0:5:30)
L = number of phase sequences for SLM
PTS_blocks = number of sub-blocks for PTS
clipRatio = clipping threshold for Clipping method
Initialize storage for results:
BER array for each SNR and technique
PAPR array for each technique
For each technique in [Clipping, SLM, PTS, TI, TR, LBC]:
For each SNR value in SNRdB:
Initialize totalErrors = 0, totalBits = 0
For each OFDM symbol from 1 to numSymbols:
Generate random bits of length 2*N (for QPSK)
Map bits to QPSK symbols using modulation
Apply the PAPR reduction technique:
If Clipping:
Perform IFFT on symbols to get time-domain signal
Clip signal amplitudes between -clipRatio and +clipRatio
Calculate PAPR
If SLM:
Generate L random phase sequences
Multiply symbols by each phase sequence
Perform IFFT and calculate PAPR for each
Choose sequence with minimum PAPR
If PTS:
Divide symbols into PTS_blocks sub-blocks
Search phase rotations from set {1, -1, j, -j}
Combine sub-blocks with phase rotations
Perform IFFT and select minimum PAPR combination
If TI:
Add small random perturbation to symbols
Perform IFFT and calculate PAPR
If TR:
Add tone reservation vector to symbols
Perform IFFT and calculate PAPR
If LBC:
Add parity bits for error correction
Modulate updated bits
Perform IFFT and calculate PAPR
Transmit signal over AWGN channel with current SNR
Receive and perform FFT to get frequency-domain signal
If technique is SLM or PTS:
Compensate received symbols by conjugate of chosen phase
Demodulate received symbols back to bits
Compare received bits to transmitted bits to count errors
Update totalErrors and totalBits
Calculate BER for current SNR and technique
Store PAPR results for current technique
Plot BER vs SNR for all techniques
Plot CCDF of PAPR for all techniques
Display average PAPR per technique
