Channel Timing

This notebook shows the timing characteristics of a CDL channel model when applied to input signals over a duration of 100 slots.

import numpy as np
import scipy.io
import time
import matplotlib.pyplot as plt

from neoradium import Carrier, Modem, CdlChannel, AntennaPanel, Grid, Waveform, random
from neoradium.utils import getNmse, getMse

# Create a random grid and the corresponding transmit (TX) waveform
carrierFreq=4e9 # 4 GHz

carrier = Carrier(startRb=0, numRbs=24, spacing=30)     # Try other subcarrier spacing values
bwp = carrier.curBwp
print(bwp)

txGrid = bwp.createGrid(numPorts=8)                     # Create an empty resource grid (8 antenna ports)

stats = txGrid.getStats()                               # Get grid statistics
modem = Modem("16QAM")                                  # Create a Modulator/Demodulator object
numRandomBits = stats['UNASSIGNED']*modem.qm            # Calculate total number of bits available in the grid

bits = random.bits(numRandomBits)                       # Create random bits
symbols = modem.modulate(bits)                          # Modulate the bits to complex symbols

indexes = txGrid.getReIndexes("UNASSIGNED")             # Get indexes of "UNASSIGNED" REs in the grid
txGrid[indexes] = symbols                               # Set them to symbols

txWaveform = txGrid.ofdmModulate(carrierFreq)           # OFDM modulation: Grid -> Waveform
print("Shape of transmitted signal in time domain:",txWaveform.shape)

Bandwidth Part Properties:
  Resource Blocks:    24 RBs starting at 0 (288 subcarriers)
  Subcarrier Spacing: 30 kHz
  CP Type:            normal
  Interleaving:       No
  Bandwidth:          8.64 MHz
  symbolsPerSlot:     14
  slotsPerSubFrame:   2
  nFFT:               1024
  frameNo:            0
  slotNo:             0

Shape of transmitted signal in time domain: (8, 15360)

# Baseline performance (no channel, no noise): ofdmModulate → ofdmDemodulate
rxGridTD = txWaveform.ofdmDemodulate(bwp, f0=carrierFreq)
print(f"NMSE: {getNmse(txGrid.grid,rxGridTD.grid)}")
print(f"MAE: {np.abs(txGrid.grid-rxGridTD.grid).max()}")

NMSE: 3.952488193394566e-32
MAE: 7.108895957933346e-16

# Create a CDL-D channel model
channel = CdlChannel(bwp, 'D', delaySpread=300, carrierFreq=4e9, dopplerShift=15,
                     txAntenna = AntennaPanel([2,4], polarization="|"),  # 8 TX antenna
                     rxAntenna = AntennaPanel([1,2], polarization="|"),  # 2 RX antenna
                     seed = 1234)
channel

CDL-D Channel Properties:
  carrierFreq:              4 GHz
  normalizeGains:           True
  normalizeOutput:          True
  txDir:                    Downlink
  filterLen:                16 samples
  delayQuantSize:           64
  stopBandAtten:            80 dB
  dopplerShift:             15 Hz
  coherenceTime:            28.209 milliseconds
  delaySpread:              300 ns
  ueDirAZ:                  0°, 90°
  xPolPower:                11.00 dB
  angleSpreads:             5° 8° 3° 3°
  TX Antenna:
    Total Elements:         8
    spacing:                0.5𝜆, 0.5𝜆
    shape:                  2 rows x 4 columns
    polarization:           |
  RX Antenna:
    Total Elements:         2
    spacing:                0.5𝜆, 0.5𝜆
    shape:                  1 rows x 2 columns
    polarization:           |
    Orientation (𝛼,𝛃,𝛄):     180° 0° 0°
  hasLOS:                   True
  LOS Path:
    Delay (ns):             0.00000
    Power (dB):             -0.20000
    AOD (Deg):              0.0
    AOA (Deg):              -180.0
    ZOD (Deg):              98.0
    ZOA (Deg):              82.0
  NLOS Paths (13):
    Delays (ns):            0.000 10.50 183.6 408.9 421.5 541.2 778.8 532.5 1212. 2381. 2827. 2912. 3757.
    Powers (dB):            -13.5 -18.8 -21.0 -22.8 -17.9 -20.1 -21.9 -22.9 -27.8 -23.6 -24.8 -30.0 -27.7
    AODs (Deg):             0    89   89   89   13   13   13   35   -64  -33  53   -132 77
    AOAs (Deg):             -180 89   89   89   163  163  163  -137 74   128  -120 -9   -84
    ZODs (Deg):             98   86   86   86   98   98   98   98   88   91   104  80   86
    ZOAs (Deg):             82   87   87   87   79   79   79   78   74   78   87   71   73

# Apply the channel in the time domain
maxDelay = channel.getMaxDelay()                         # Get maximum channel delay
paddedTxWaveform = txWaveform.pad(maxDelay)              # Pad the waveform with zeros
rxWaveform = channel.applyToSignal(paddedTxWaveform)     # Apply the channel to the waveform

syncedWaveform = rxWaveform.sync(channel.chanOffset)     # Synchronization
rxGridTd = syncedWaveform.ofdmDemodulate(bwp, f0=carrierFreq)

# Apply the channel in the frequency domain
chanMat = channel.getChannelMatrix()
rxGridFd = txGrid.applyChannel(chanMat)

# Compare time-domain vs. frequency-domain results
print(f"NMSE: {getNmse(rxGridFd.grid,rxGridTd.grid)}")

NMSE: 8.292828250427552e-06

# Apply the channel to 100 slots of the input signal
chanMats = []
for s in range(100):
    # Move to the next slot
    channel.goNext()

    txGrid = bwp.createGrid(numPorts=8)

    stats = txGrid.getStats()
    numRandomBits = stats['UNASSIGNED']*modem.qm
    bits = random.bits(numRandomBits)
    symbols = modem.modulate(bits)
    indexes = txGrid.getReIndexes("UNASSIGNED")
    txGrid[indexes] = symbols

    txWaveform = txGrid.ofdmModulate(carrierFreq)

    # Apply the channel in the time domain:
    maxDelay = channel.getMaxDelay()                            # Get maximum channel delay
    paddedTxWaveform = txWaveform.pad(maxDelay)                 # Pad the waveform with zeros
    rxWaveform = channel.applyToSignal(paddedTxWaveform)        # Apply the channel to the waveform

    syncedWaveform = rxWaveform.sync(channel.chanOffset)        # Synchronization
    rxGridTd = syncedWaveform.ofdmDemodulate(bwp, f0=carrierFreq)

    # Apply the channel in the frequency domain and compare results
    chanMat = channel.getChannelMatrix()
    rxGridFd = txGrid.applyChannel(chanMat)
    assert getNmse(rxGridFd.grid,rxGridTd.grid)<1e-3
    chanMats += [chanMat]

gs = np.concatenate([chanMat[:,0,0,0] for chanMat in chanMats])
plt.plot(np.abs(gs))
plt.title("The channel gains for the first pair of RX/TX antenna \n"+
          "and first subcarrier during 100 slots")
plt.grid()