BER Performance of PUCCH Format 0
PUCCH Format 0 in 5G is used to transfer 1 or 2 HARQ acknowledgements and/or a Scheduling Request (SR). It occupies 1 Resource Block in the frequency domain and either 1 or 2 symbols in the time domain. These codes are - locally testable, - locally decodable
In this tutorial, we will analyze the bit error rate performance of PUCCH Format 0 for different link conditions characterized by signal to noise ratio(SNR). The content of the tutorial is as follows:
Table of Contents
Import Libraries
Python Libraries
%matplotlib widget
import matplotlib.pyplot as plt
import matplotlib as mpl
import os
os.environ["CUDA_VISIBLE_DEVICES"] = "-1"
import numpy as np
5G ToolKit Libraries
##
import sys
sys.path.append("../../")
from toolkit5G.SequenceGeneration import CyclicShiftHopping
from toolkit5G.Utils import VectorToBinaryArray
from toolkit5G.PhysicalChannels import PUCCHFormat0
from toolkit5G.PhysicalChannels import PUCCHFormat0Decoder
from toolkit5G.PhysicalChannels import MCSEstimation
Simulation Parameters
The simulation parameters are:
nIDdefines the hopping IDm_CSdefines the cyclic shift offset based on the control information carriedmaxPRBsdefines the maximum number of resource blocksnumBatchesdefines Number of BatchesindexPUCCHdefines the resource index if common resource is configuredslotNumberdefines the slot numberstartingPRBdefines the index of first Physical Resource Block prior to frequency hopping or for no frequency hoppingcontrolInfodefines the control information carried on PUCCH Format0secondHopPRBdefines the index of the first Physical Resource Block after frequency hoppingnumofSymbolsdefines the number of symbolsnumOfInterlacesdefines the number of interlaces, if interlaced transmission is enabled for Dedicated resource configurationinitialCycShiftdefines the initial cyclic shiftinterlaceIndex_0defines the index of a first interlace, if interlaced transmission is enabled for Dedicated resource configurationinterlaceIndex_1defines the index of a second interlace, if interlaced transmission is enabled for Dedicated resource configuration andnumOfInterlacesis twonumInterlacedRBsdefines the number of interlaced resource blocks, if interlaced transmission is enabledsymbolIndex_startdefines the starting symbol indexpucch_GroupHoppingdefines if group and/or sequence hopping is enabled/disabledpucch_ResourceCommondefines if common resource/dedicated resource configuration is usedintraSlotFreqHoppingdefines if intraslot frequency hopping is enabled/disabledinterlacedTransmissiondefines if interlaced transmission is enabled/disabled
numBatches = np.random.randint(1, 1000)
interlacedTransmission = np.random.choice([True, False])
pucch_ResourceCommon = np.random.choice([True, False])
print("Number of Batches : "+str(numBatches))
print("Interlaced Transmission : "+str(interlacedTransmission) )
print("Common Resource Status : "+str(pucch_ResourceCommon))
if pucch_ResourceCommon == False:
indexPUCCH = None
initialCycShift = np.random.randint(0, 12)
symbolIndex_start = np.random.randint(0, 14)
if symbolIndex_start == 13:
numofSymbols = 1
else:
numofSymbols = np.random.choice([1, 2])
print("numofSymbols : "+str(numofSymbols))
print("symbolIndex_start : "+str(symbolIndex_start))
print("initialCS : "+str(initialCycShift))
else:
indexPUCCH = np.random.randint(0, 3)
print("PUCCH Index - Common : "+str(indexPUCCH))
initialCycShift = None
symbolIndex_start = None
numofSymbols = None
if interlacedTransmission == True or numofSymbols == 1:
intraSlotFreqHopping = False
elif pucch_ResourceCommon == True:
intraSlotFreqHopping = True
else:
intraSlotFreqHopping = np.random.choice([True, False])
print("Hopping Status : "+str(intraSlotFreqHopping))
slotNumber = np.random.randint(0, 11)
nID = np.random.randint(0, 1024)
validHoppingInfo = np.array(['neither', 'Neither', 'enable' , 'Enable' , 'disable', 'Disable'])
pucch_GroupHopping = np.random.choice(validHoppingInfo)
controlInfo = np.random.choice(["1-HARQ", "2-HARQ", "SR", "HARQ+SR"])
print("Control Info : "+str(controlInfo))
if controlInfo == "1-HARQ":
m_CS = np.random.choice([0, 6], size = numBatches)
elif controlInfo == "2-HARQ":
m_CS = np.random.choice([0, 3, 6, 9], size = numBatches)
elif controlInfo == "SR":
m_CS = np.random.choice([0], size = numBatches)
elif controlInfo == "HARQ+SR":
m_CS = np.random.choice([0, 3, 6, 9], size = numBatches)
print("slotNumber : "+str(slotNumber))
print("nID : "+str(nID))
print("pucch_GroupHopping Info : "+str(pucch_GroupHopping))
print("slotNumber : "+str(slotNumber))
print("m_CS : "+str(m_CS))
if interlacedTransmission == True:
numInterlacedRBs = 10 if pucch_ResourceCommon == True else np.random.choice([10, 11])
print("Number of InterlacedRBs : "+str(numInterlacedRBs))
else:
numInterlacedRBs = None
if pucch_ResourceCommon == False:
refNum = np.random.choice([0, 1])
maxPRBs = 275
startingPRB = int(np.floor(maxPRBs/2) * refNum + np.random.randint(0, np.ceil(maxPRBs/2)))
print("Starting PRB : "+str(startingPRB))
secondHopPRB = None
if intraSlotFreqHopping == True:
secondHopPRB = int(np.floor(maxPRBs/2) * int(not(refNum)) + np.random.randint(0, np.ceil(maxPRBs/2)))
print("Second Hop PRB : "+str(secondHopPRB))
else:
startingPRB = None
secondHopPRB = None
if interlacedTransmission == True:
numOfInterlaces = 1 if pucch_ResourceCommon == True else np.random.choice([1, 2])
print("Number of interlaces : "+str(numOfInterlaces))
print("Number Of Interlaced RBs : "+str(numInterlacedRBs))
if pucch_ResourceCommon == False:
interlaceIndex_0 = np.random.randint(0, 10)
print("interlaceIndex_0 : "+str(interlaceIndex_0))
interlaceIndex_1 = None
if numOfInterlaces == 2:
interlaceIndex_1 = np.mod(interlaceIndex_0+2, 9)
print("interlaceIndex_1 : "+str(interlaceIndex_1))
else:
interlaceIndex_0 = None
interlaceIndex_1 = None
else:
numOfInterlaces = None
interlaceIndex_0 = None
interlaceIndex_1 = None
Number of Batches : 853
Interlaced Transmission : False
Common Resource Status : False
numofSymbols : 1
symbolIndex_start : 0
initialCS : 8
Hopping Status : False
Control Info : 2-HARQ
slotNumber : 7
nID : 779
pucch_GroupHopping Info : disable
slotNumber : 7
m_CS : [0 0 6 0 9 6 6 0 3 3 6 0 0 0 0 9 9 9 3 0 0 9 0 9 9 9 0 9 6 0 6 6 3 9 6 9 9
0 6 3 6 3 3 9 6 3 6 3 0 3 3 3 0 9 6 3 6 6 6 0 6 6 3 9 0 6 3 6 0 6 9 0 9 3
9 0 9 6 0 0 3 0 9 3 0 6 6 3 3 9 0 9 9 0 0 9 9 3 0 6 0 9 6 6 3 6 9 3 0 9 9
0 0 0 0 9 3 3 6 3 9 0 9 9 3 9 3 3 0 3 6 0 0 6 0 9 6 6 0 6 0 6 9 3 6 0 3 3
9 0 9 0 3 6 6 0 3 3 9 9 3 3 3 9 6 6 9 0 3 3 6 3 6 3 6 0 9 3 9 9 0 3 9 9 9
6 6 6 0 0 6 0 0 3 6 3 9 3 0 6 0 9 9 0 9 0 9 3 9 9 3 9 9 6 9 6 0 0 0 6 3 6
9 0 0 0 3 6 9 6 6 0 0 9 3 3 3 0 3 9 3 3 9 9 3 6 9 6 3 9 6 9 3 0 3 9 6 3 0
0 0 3 3 0 6 9 3 9 0 9 0 6 0 9 3 3 9 0 9 9 6 3 3 9 9 6 0 3 0 6 9 9 0 3 6 9
3 3 6 6 9 6 9 3 0 9 9 6 0 3 9 9 3 9 9 0 3 0 3 6 9 3 3 0 0 6 3 6 9 9 9 0 0
3 9 6 9 3 3 9 9 9 0 6 9 3 0 9 0 0 0 9 9 0 9 9 6 6 0 6 0 9 0 0 3 9 6 6 0 3
3 3 9 3 3 3 0 3 9 9 3 6 9 6 3 3 0 9 9 0 3 0 0 3 3 0 6 6 9 6 9 6 6 0 9 0 0
6 6 6 9 9 3 3 9 9 6 9 9 3 6 3 9 9 3 6 6 3 0 9 6 3 9 3 0 3 0 6 6 3 9 9 3 3
3 0 3 0 6 6 6 3 9 0 3 6 6 9 9 0 6 3 0 3 9 3 9 9 9 0 3 0 3 3 3 0 0 3 6 6 0
6 9 9 3 3 0 6 6 0 6 9 9 0 3 6 6 3 9 9 0 6 3 6 6 3 6 0 9 3 9 6 0 0 6 6 0 9
3 6 9 0 9 3 6 9 6 6 6 9 9 0 3 9 6 9 0 6 3 9 3 6 9 3 3 3 0 9 3 3 6 3 3 6 3
0 6 6 6 3 3 0 0 6 6 3 0 3 6 6 6 6 3 0 3 3 9 6 0 9 3 0 9 6 0 9 3 6 9 9 6 6
9 9 0 6 3 3 6 0 0 3 3 9 0 9 0 0 0 9 0 0 0 3 3 0 9 6 0 0 3 0 3 3 0 3 0 6 9
3 0 6 0 6 9 3 0 9 6 3 0 0 3 3 0 3 9 0 0 9 9 6 9 6 9 6 0 6 3 0 6 9 9 0 6 3
6 9 3 6 0 0 3 3 6 0 9 3 3 6 0 9 9 9 0 3 6 3 6 3 0 9 6 0 9 6 9 9 6 6 3 6 0
9 0 0 0 0 3 0 3 0 9 6 3 3 0 0 6 9 3 3 0 6 0 9 3 9 3 6 0 9 6 9 3 0 0 0 3 3
6 6 3 6 0 9 0 9 9 6 3 9 9 6 9 6 3 3 6 3 0 6 9 9 9 9 6 9 9 6 9 3 0 3 6 6 6
6 9 3 0 6 6 3 3 0 3 3 3 3 9 3 0 3 6 3 0 3 9 3 3 9 0 3 6 6 3 9 3 3 0 3 6 3
6 6 6 9 9 6 3 3 6 3 0 6 3 3 9 9 9 9 9 9 9 6 3 0 3 6 6 0 0 3 9 6 9 9 6 9 9
9 3]
Starting PRB : 168
Format 0
This method generates the sequence and maps it onto the resources allocated.
pucchFormat0Obj = PUCCHFormat0(numBatches, m_CS, controlInfo, nID, slotNumber, pucch_GroupHopping, initialCycShift, numofSymbols, symbolIndex_start)
pucchFormat0Grid = pucchFormat0Obj(intraSlotFreqHopping, interlacedTransmission, pucch_ResourceCommon, indexPUCCH, numInterlacedRBs, startingPRB, secondHopPRB, numOfInterlaces, interlaceIndex_0, interlaceIndex_1)
intraSlotFreqHopping : False interlacedTransmission : False pucch_ResourceCommon : False numBatches : 853 m_CS : [0 0 6 0 9 6 6 0 3 3 6 0 0 0 0 9 9 9 3 0 0 9 0 9 9 9 0 9 6 0 6 6 3 9 6 9 9 0 6 3 6 3 3 9 6 3 6 3 0 3 3 3 0 9 6 3 6 6 6 0 6 6 3 9 0 6 3 6 0 6 9 0 9 3 9 0 9 6 0 0 3 0 9 3 0 6 6 3 3 9 0 9 9 0 0 9 9 3 0 6 0 9 6 6 3 6 9 3 0 9 9 0 0 0 0 9 3 3 6 3 9 0 9 9 3 9 3 3 0 3 6 0 0 6 0 9 6 6 0 6 0 6 9 3 6 0 3 3 9 0 9 0 3 6 6 0 3 3 9 9 3 3 3 9 6 6 9 0 3 3 6 3 6 3 6 0 9 3 9 9 0 3 9 9 9 6 6 6 0 0 6 0 0 3 6 3 9 3 0 6 0 9 9 0 9 0 9 3 9 9 3 9 9 6 9 6 0 0 0 6 3 6 9 0 0 0 3 6 9 6 6 0 0 9 3 3 3 0 3 9 3 3 9 9 3 6 9 6 3 9 6 9 3 0 3 9 6 3 0 0 0 3 3 0 6 9 3 9 0 9 0 6 0 9 3 3 9 0 9 9 6 3 3 9 9 6 0 3 0 6 9 9 0 3 6 9 3 3 6 6 9 6 9 3 0 9 9 6 0 3 9 9 3 9 9 0 3 0 3 6 9 3 3 0 0 6 3 6 9 9 9 0 0 3 9 6 9 3 3 9 9 9 0 6 9 3 0 9 0 0 0 9 9 0 9 9 6 6 0 6 0 9 0 0 3 9 6 6 0 3 3 3 9 3 3 3 0 3 9 9 3 6 9 6 3 3 0 9 9 0 3 0 0 3 3 0 6 6 9 6 9 6 6 0 9 0 0 6 6 6 9 9 3 3 9 9 6 9 9 3 6 3 9 9 3 6 6 3 0 9 6 3 9 3 0 3 0 6 6 3 9 9 3 3 3 0 3 0 6 6 6 3 9 0 3 6 6 9 9 0 6 3 0 3 9 3 9 9 9 0 3 0 3 3 3 0 0 3 6 6 0 6 9 9 3 3 0 6 6 0 6 9 9 0 3 6 6 3 9 9 0 6 3 6 6 3 6 0 9 3 9 6 0 0 6 6 0 9 3 6 9 0 9 3 6 9 6 6 6 9 9 0 3 9 6 9 0 6 3 9 3 6 9 3 3 3 0 9 3 3 6 3 3 6 3 0 6 6 6 3 3 0 0 6 6 3 0 3 6 6 6 6 3 0 3 3 9 6 0 9 3 0 9 6 0 9 3 6 9 9 6 6 9 9 0 6 3 3 6 0 0 3 3 9 0 9 0 0 0 9 0 0 0 3 3 0 9 6 0 0 3 0 3 3 0 3 0 6 9 3 0 6 0 6 9 3 0 9 6 3 0 0 3 3 0 3 9 0 0 9 9 6 9 6 9 6 0 6 3 0 6 9 9 0 6 3 6 9 3 6 0 0 3 3 6 0 9 3 3 6 0 9 9 9 0 3 6 3 6 3 0 9 6 0 9 6 9 9 6 6 3 6 0 9 0 0 0 0 3 0 3 0 9 6 3 3 0 0 6 9 3 3 0 6 0 9 3 9 3 6 0 9 6 9 3 0 0 0 3 3 6 6 3 6 0 9 0 9 9 6 3 9 9 6 9 6 3 3 6 3 0 6 9 9 9 9 6 9 9 6 9 3 0 3 6 6 6 6 9 3 0 6 6 3 3 0 3 3 3 3 9 3 0 3 6 3 0 3 9 3 3 9 0 3 6 6 3 9 3 3 0 3 6 3 6 6 6 9 9 6 3 3 6 3 0 6 3 3 9 9 9 9 9 9 9 6 3 0 3 6 6 0 0 3 9 6 9 9 6 9 9 9 3] controlInfo : 2-HARQ nID : 779 slotNumber : 7 pucch_GroupHopping : disable initialCyclicShift : 8 numOfSymbols : 1 symbolIndexStart : 0 ********************Sequence Generation************************ PUCCH Format0 Sequence : (853, 1, 12) startingPRB : 168 numOfInterlaces : None ********************Resource Mapping************************ OFDM Grid : (853, 3300, 14)
Format 0 Decoder
This method decodes the sequences mapped on the OFDM Grid.
pucchFormat0DecoderObj = PUCCHFormat0Decoder(numofSymbols, symbolIndex_start)
pucchFormat0DecoderOp = pucchFormat0DecoderObj(pucchFormat0Grid, intraSlotFreqHopping, interlacedTransmission, pucch_ResourceCommon, indexPUCCH, numInterlacedRBs, startingPRB, secondHopPRB, numOfInterlaces, interlaceIndex_0, interlaceIndex_1)
M_CS Estimation
This method estimates the cyclic shift offset, thereby estimating the information bits
hardOut = np.random.choice([True, False])
hardOut
False
Obj_mcs = MCSEstimation(interlacedTransmission, pucch_ResourceCommon, hardOut)
estimatem_CS = Obj_mcs(pucchFormat0DecoderOp, controlInfo, indexPUCCH, nID, slotNumber, symbolIndex_start, numofSymbols, initialCycShift, numInterlacedRBs)
estimatem_CS[0], estimatem_CS[1], m_CS, Obj_mcs.controlInfo
(array([0, 0, 6, 0, 9, 6, 6, 0, 3, 3, 6, 0, 0, 0, 0, 9, 9, 9, 3, 0, 0, 9,
0, 9, 9, 9, 0, 9, 6, 0, 6, 6, 3, 9, 6, 9, 9, 0, 6, 3, 6, 3, 3, 9,
6, 3, 6, 3, 0, 3, 3, 3, 0, 9, 6, 3, 6, 6, 6, 0, 6, 6, 3, 9, 0, 6,
3, 6, 0, 6, 9, 0, 9, 3, 9, 0, 9, 6, 0, 0, 3, 0, 9, 3, 0, 6, 6, 3,
3, 9, 0, 9, 9, 0, 0, 9, 9, 3, 0, 6, 0, 9, 6, 6, 3, 6, 9, 3, 0, 9,
9, 0, 0, 0, 0, 9, 3, 3, 6, 3, 9, 0, 9, 9, 3, 9, 3, 3, 0, 3, 6, 0,
0, 6, 0, 9, 6, 6, 0, 6, 0, 6, 9, 3, 6, 0, 3, 3, 9, 0, 9, 0, 3, 6,
6, 0, 3, 3, 9, 9, 3, 3, 3, 9, 6, 6, 9, 0, 3, 3, 6, 3, 6, 3, 6, 0,
9, 3, 9, 9, 0, 3, 9, 9, 9, 6, 6, 6, 0, 0, 6, 0, 0, 3, 6, 3, 9, 3,
0, 6, 0, 9, 9, 0, 9, 0, 9, 3, 9, 9, 3, 9, 9, 6, 9, 6, 0, 0, 0, 6,
3, 6, 9, 0, 0, 0, 3, 6, 9, 6, 6, 0, 0, 9, 3, 3, 3, 0, 3, 9, 3, 3,
9, 9, 3, 6, 9, 6, 3, 9, 6, 9, 3, 0, 3, 9, 6, 3, 0, 0, 0, 3, 3, 0,
6, 9, 3, 9, 0, 9, 0, 6, 0, 9, 3, 3, 9, 0, 9, 9, 6, 3, 3, 9, 9, 6,
0, 3, 0, 6, 9, 9, 0, 3, 6, 9, 3, 3, 6, 6, 9, 6, 9, 3, 0, 9, 9, 6,
0, 3, 9, 9, 3, 9, 9, 0, 3, 0, 3, 6, 9, 3, 3, 0, 0, 6, 3, 6, 9, 9,
9, 0, 0, 3, 9, 6, 9, 3, 3, 9, 9, 9, 0, 6, 9, 3, 0, 9, 0, 0, 0, 9,
9, 0, 9, 9, 6, 6, 0, 6, 0, 9, 0, 0, 3, 9, 6, 6, 0, 3, 3, 3, 9, 3,
3, 3, 0, 3, 9, 9, 3, 6, 9, 6, 3, 3, 0, 9, 9, 0, 3, 0, 0, 3, 3, 0,
6, 6, 9, 6, 9, 6, 6, 0, 9, 0, 0, 6, 6, 6, 9, 9, 3, 3, 9, 9, 6, 9,
9, 3, 6, 3, 9, 9, 3, 6, 6, 3, 0, 9, 6, 3, 9, 3, 0, 3, 0, 6, 6, 3,
9, 9, 3, 3, 3, 0, 3, 0, 6, 6, 6, 3, 9, 0, 3, 6, 6, 9, 9, 0, 6, 3,
0, 3, 9, 3, 9, 9, 9, 0, 3, 0, 3, 3, 3, 0, 0, 3, 6, 6, 0, 6, 9, 9,
3, 3, 0, 6, 6, 0, 6, 9, 9, 0, 3, 6, 6, 3, 9, 9, 0, 6, 3, 6, 6, 3,
6, 0, 9, 3, 9, 6, 0, 0, 6, 6, 0, 9, 3, 6, 9, 0, 9, 3, 6, 9, 6, 6,
6, 9, 9, 0, 3, 9, 6, 9, 0, 6, 3, 9, 3, 6, 9, 3, 3, 3, 0, 9, 3, 3,
6, 3, 3, 6, 3, 0, 6, 6, 6, 3, 3, 0, 0, 6, 6, 3, 0, 3, 6, 6, 6, 6,
3, 0, 3, 3, 9, 6, 0, 9, 3, 0, 9, 6, 0, 9, 3, 6, 9, 9, 6, 6, 9, 9,
0, 6, 3, 3, 6, 0, 0, 3, 3, 9, 0, 9, 0, 0, 0, 9, 0, 0, 0, 3, 3, 0,
9, 6, 0, 0, 3, 0, 3, 3, 0, 3, 0, 6, 9, 3, 0, 6, 0, 6, 9, 3, 0, 9,
6, 3, 0, 0, 3, 3, 0, 3, 9, 0, 0, 9, 9, 6, 9, 6, 9, 6, 0, 6, 3, 0,
6, 9, 9, 0, 6, 3, 6, 9, 3, 6, 0, 0, 3, 3, 6, 0, 9, 3, 3, 6, 0, 9,
9, 9, 0, 3, 6, 3, 6, 3, 0, 9, 6, 0, 9, 6, 9, 9, 6, 6, 3, 6, 0, 9,
0, 0, 0, 0, 3, 0, 3, 0, 9, 6, 3, 3, 0, 0, 6, 9, 3, 3, 0, 6, 0, 9,
3, 9, 3, 6, 0, 9, 6, 9, 3, 0, 0, 0, 3, 3, 6, 6, 3, 6, 0, 9, 0, 9,
9, 6, 3, 9, 9, 6, 9, 6, 3, 3, 6, 3, 0, 6, 9, 9, 9, 9, 6, 9, 9, 6,
9, 3, 0, 3, 6, 6, 6, 6, 9, 3, 0, 6, 6, 3, 3, 0, 3, 3, 3, 3, 9, 3,
0, 3, 6, 3, 0, 3, 9, 3, 3, 9, 0, 3, 6, 6, 3, 9, 3, 3, 0, 3, 6, 3,
6, 6, 6, 9, 9, 6, 3, 3, 6, 3, 0, 6, 3, 3, 9, 9, 9, 9, 9, 9, 9, 6,
3, 0, 3, 6, 6, 0, 0, 3, 9, 6, 9, 9, 6, 9, 9, 9, 3]),
None,
array([0, 0, 6, 0, 9, 6, 6, 0, 3, 3, 6, 0, 0, 0, 0, 9, 9, 9, 3, 0, 0, 9,
0, 9, 9, 9, 0, 9, 6, 0, 6, 6, 3, 9, 6, 9, 9, 0, 6, 3, 6, 3, 3, 9,
6, 3, 6, 3, 0, 3, 3, 3, 0, 9, 6, 3, 6, 6, 6, 0, 6, 6, 3, 9, 0, 6,
3, 6, 0, 6, 9, 0, 9, 3, 9, 0, 9, 6, 0, 0, 3, 0, 9, 3, 0, 6, 6, 3,
3, 9, 0, 9, 9, 0, 0, 9, 9, 3, 0, 6, 0, 9, 6, 6, 3, 6, 9, 3, 0, 9,
9, 0, 0, 0, 0, 9, 3, 3, 6, 3, 9, 0, 9, 9, 3, 9, 3, 3, 0, 3, 6, 0,
0, 6, 0, 9, 6, 6, 0, 6, 0, 6, 9, 3, 6, 0, 3, 3, 9, 0, 9, 0, 3, 6,
6, 0, 3, 3, 9, 9, 3, 3, 3, 9, 6, 6, 9, 0, 3, 3, 6, 3, 6, 3, 6, 0,
9, 3, 9, 9, 0, 3, 9, 9, 9, 6, 6, 6, 0, 0, 6, 0, 0, 3, 6, 3, 9, 3,
0, 6, 0, 9, 9, 0, 9, 0, 9, 3, 9, 9, 3, 9, 9, 6, 9, 6, 0, 0, 0, 6,
3, 6, 9, 0, 0, 0, 3, 6, 9, 6, 6, 0, 0, 9, 3, 3, 3, 0, 3, 9, 3, 3,
9, 9, 3, 6, 9, 6, 3, 9, 6, 9, 3, 0, 3, 9, 6, 3, 0, 0, 0, 3, 3, 0,
6, 9, 3, 9, 0, 9, 0, 6, 0, 9, 3, 3, 9, 0, 9, 9, 6, 3, 3, 9, 9, 6,
0, 3, 0, 6, 9, 9, 0, 3, 6, 9, 3, 3, 6, 6, 9, 6, 9, 3, 0, 9, 9, 6,
0, 3, 9, 9, 3, 9, 9, 0, 3, 0, 3, 6, 9, 3, 3, 0, 0, 6, 3, 6, 9, 9,
9, 0, 0, 3, 9, 6, 9, 3, 3, 9, 9, 9, 0, 6, 9, 3, 0, 9, 0, 0, 0, 9,
9, 0, 9, 9, 6, 6, 0, 6, 0, 9, 0, 0, 3, 9, 6, 6, 0, 3, 3, 3, 9, 3,
3, 3, 0, 3, 9, 9, 3, 6, 9, 6, 3, 3, 0, 9, 9, 0, 3, 0, 0, 3, 3, 0,
6, 6, 9, 6, 9, 6, 6, 0, 9, 0, 0, 6, 6, 6, 9, 9, 3, 3, 9, 9, 6, 9,
9, 3, 6, 3, 9, 9, 3, 6, 6, 3, 0, 9, 6, 3, 9, 3, 0, 3, 0, 6, 6, 3,
9, 9, 3, 3, 3, 0, 3, 0, 6, 6, 6, 3, 9, 0, 3, 6, 6, 9, 9, 0, 6, 3,
0, 3, 9, 3, 9, 9, 9, 0, 3, 0, 3, 3, 3, 0, 0, 3, 6, 6, 0, 6, 9, 9,
3, 3, 0, 6, 6, 0, 6, 9, 9, 0, 3, 6, 6, 3, 9, 9, 0, 6, 3, 6, 6, 3,
6, 0, 9, 3, 9, 6, 0, 0, 6, 6, 0, 9, 3, 6, 9, 0, 9, 3, 6, 9, 6, 6,
6, 9, 9, 0, 3, 9, 6, 9, 0, 6, 3, 9, 3, 6, 9, 3, 3, 3, 0, 9, 3, 3,
6, 3, 3, 6, 3, 0, 6, 6, 6, 3, 3, 0, 0, 6, 6, 3, 0, 3, 6, 6, 6, 6,
3, 0, 3, 3, 9, 6, 0, 9, 3, 0, 9, 6, 0, 9, 3, 6, 9, 9, 6, 6, 9, 9,
0, 6, 3, 3, 6, 0, 0, 3, 3, 9, 0, 9, 0, 0, 0, 9, 0, 0, 0, 3, 3, 0,
9, 6, 0, 0, 3, 0, 3, 3, 0, 3, 0, 6, 9, 3, 0, 6, 0, 6, 9, 3, 0, 9,
6, 3, 0, 0, 3, 3, 0, 3, 9, 0, 0, 9, 9, 6, 9, 6, 9, 6, 0, 6, 3, 0,
6, 9, 9, 0, 6, 3, 6, 9, 3, 6, 0, 0, 3, 3, 6, 0, 9, 3, 3, 6, 0, 9,
9, 9, 0, 3, 6, 3, 6, 3, 0, 9, 6, 0, 9, 6, 9, 9, 6, 6, 3, 6, 0, 9,
0, 0, 0, 0, 3, 0, 3, 0, 9, 6, 3, 3, 0, 0, 6, 9, 3, 3, 0, 6, 0, 9,
3, 9, 3, 6, 0, 9, 6, 9, 3, 0, 0, 0, 3, 3, 6, 6, 3, 6, 0, 9, 0, 9,
9, 6, 3, 9, 9, 6, 9, 6, 3, 3, 6, 3, 0, 6, 9, 9, 9, 9, 6, 9, 9, 6,
9, 3, 0, 3, 6, 6, 6, 6, 9, 3, 0, 6, 6, 3, 3, 0, 3, 3, 3, 3, 9, 3,
0, 3, 6, 3, 0, 3, 9, 3, 3, 9, 0, 3, 6, 6, 3, 9, 3, 3, 0, 3, 6, 3,
6, 6, 6, 9, 9, 6, 3, 3, 6, 3, 0, 6, 3, 3, 9, 9, 9, 9, 9, 9, 9, 6,
3, 0, 3, 6, 6, 0, 0, 3, 9, 6, 9, 9, 6, 9, 9, 9, 3]),
'2-HARQ')
Information content based on MCS value
This converts the estimated cyclic shift offest value to the information bits based on the control information transmitted
if controlInfo == "1-HARQ" or controlInfo == "SR":
len = 1
else:
len = 2
m_CS[np.where(m_CS==0)] = 0
m_CS[np.where(m_CS==3)] = 1
if controlInfo == '1-HARQ':
m_CS[np.where(m_CS==6)] = 1
elif controlInfo == '2-HARQ':
m_CS[np.where(m_CS==6)] = 3
else:
m_CS[np.where(m_CS==6)] = 2
m_CS[np.where(m_CS==9)] = 3 if controlInfo == 'HARQ+SR' else 2
bin_arr = VectorToBinaryArray(m_CS, len)()
bin_arr.shape
(853, 2)
Simulation
This subsection performs the simulation which involve following steps:
Passing the resource grid through the channel
Adding noise to the grid with a given SNR
PUCCH Format 0 Decoding which involves retrival of sequence from the grid
Followed by estimation of cyclic shift offest, using which the information bits are estimated
BER computation
The bit error rate (BER) is computed for every combination of SNR
\(= \{-30, -20, -10, 0, 10, 20, 30\}\) dB and averaged over
numBatches (monteCarloIterations).
SNRdB = np.linspace(-30, 30, 20)
SNR = 10**(SNRdB/10)
isChannelPerfect = True
BER1 = np.zeros(SNR.size)
BER2 = np.zeros(SNR.size)
BER = np.zeros(SNR.size)
i = 0
for snr in SNR:
print("SNR-Index: "+str(i)+"| SNR: "+str(snr))
n = np.sqrt(0.5/snr)*(np.random.standard_normal(size=pucchFormat0Grid.shape)+1j*np.random.standard_normal(size=pucchFormat0Grid.shape))
y = pucchFormat0Grid + n
pucchFormat0DecoderObj = PUCCHFormat0Decoder(numofSymbols, symbolIndex_start, verbose = False)
pucchFormat0DecoderOp = pucchFormat0DecoderObj(y, intraSlotFreqHopping, interlacedTransmission, pucch_ResourceCommon, indexPUCCH, numInterlacedRBs, startingPRB, secondHopPRB, numOfInterlaces, interlaceIndex_0, interlaceIndex_1)
Obj_mcs = MCSEstimation(interlacedTransmission, pucch_ResourceCommon, hardout = True)
estimatem_CS = Obj_mcs(pucchFormat0DecoderOp, controlInfo, indexPUCCH, nID, slotNumber, symbolIndex_start, numofSymbols, initialCycShift, numInterlacedRBs)
if Obj_mcs.numberOfSymb == 1 or Obj_mcs.numberOfSymb == 2:
BER1[i] = np.mean(np.abs(estimatem_CS[0] - bin_arr))
print("*************************************************************")
print("BER1 : "+str(BER1[i]))
BER2[i] = 0
if Obj_mcs.numberOfSymb == 2:
BER2[i] = np.mean(np.abs(estimatem_CS[1] - bin_arr))
print("-------------------------------------------------------------")
print("BER2 : "+str(BER2[i]))
BER[i] = np.mean((BER1[i], BER2[i]))
print("-------------------------------------------------------------")
print("BER : "+str(BER[i]))
i = i+1
SNR-Index: 0| SNR: 0.001 ********************************************************* BER1 : 0.5023446658851114 ------------------------------------------------------------- BER : 0.2511723329425557 SNR-Index: 1| SNR: 0.00206913808111479 ********************************************************* BER1 : 0.4806565064478312 ------------------------------------------------------------- BER : 0.2403282532239156 SNR-Index: 2| SNR: 0.004281332398719396 ********************************************************* BER1 : 0.5005861664712778 ------------------------------------------------------------- BER : 0.2502930832356389 SNR-Index: 3| SNR: 0.008858667904100823 ********************************************************* BER1 : 0.5046893317702228 ------------------------------------------------------------- BER : 0.2523446658851114 SNR-Index: 4| SNR: 0.018329807108324356 ********************************************************* BER1 : 0.4783118405627198 ------------------------------------------------------------- BER : 0.2391559202813599 SNR-Index: 5| SNR: 0.0379269019073225 ********************************************************* BER1 : 0.4859320046893318 ------------------------------------------------------------- BER : 0.2429660023446659 SNR-Index: 6| SNR: 0.07847599703514611 ********************************************************* BER1 : 0.48182883939038684 ------------------------------------------------------------- BER : 0.24091441969519342 SNR-Index: 7| SNR: 0.16237767391887217 ********************************************************* BER1 : 0.4349355216881594 ------------------------------------------------------------- BER : 0.2174677608440797 SNR-Index: 8| SNR: 0.3359818286283782 ********************************************************* BER1 : 0.36518171160609614 ------------------------------------------------------------- BER : 0.18259085580304807 SNR-Index: 9| SNR: 0.6951927961775608 ********************************************************* BER1 : 0.1776084407971864 ------------------------------------------------------------- BER : 0.0888042203985932 SNR-Index: 10| SNR: 1.4384498882876635 ********************************************************* BER1 : 0.016998827667057445 ------------------------------------------------------------- BER : 0.008499413833528723 SNR-Index: 11| SNR: 2.976351441631318 ********************************************************* BER1 : 0.0 ------------------------------------------------------------- BER : 0.0 SNR-Index: 12| SNR: 6.158482110660259 ********************************************************* BER1 : 0.0 ------------------------------------------------------------- BER : 0.0 SNR-Index: 13| SNR: 12.742749857031342 ********************************************************* BER1 : 0.0 ------------------------------------------------------------- BER : 0.0 SNR-Index: 14| SNR: 26.366508987303583 ********************************************************* BER1 : 0.0 ------------------------------------------------------------- BER : 0.0 SNR-Index: 15| SNR: 54.55594781168523 ********************************************************* BER1 : 0.0 ------------------------------------------------------------- BER : 0.0 SNR-Index: 16| SNR: 112.88378916846895 ********************************************************* BER1 : 0.0 ------------------------------------------------------------- BER : 0.0 SNR-Index: 17| SNR: 233.57214690901213 ********************************************************* BER1 : 0.0 ------------------------------------------------------------- BER : 0.0 SNR-Index: 18| SNR: 483.2930238571757 ********************************************************* BER1 : 0.0 ------------------------------------------------------------- BER : 0.0 SNR-Index: 19| SNR: 1000.0 ********************************************************* BER1 : 0.0 ------------------------------------------------------------- BER : 0.0
Performance Evaluation
The script plots SNR in dB vs BER performance for . It can be observed that the control information is received with a reliablilty of
BER = \(10^{-2}\) at an SNR value of 0 dB.
Performance Plot
fig, ax = plt.subplots()
ax.semilogy(SNRdB, BER1, "-b", label="Symbol 1 - BER1")
ax.semilogy(SNRdB, BER2, "-r", label="Symbol 2 - BER2")
ax.semilogy(SNRdB, BER, "*-g",label="BER")
ax.legend(loc="upper right")
ax.set_xlabel("Signal to Noise Ratio (dB)", fontsize = 9)
ax.set_ylabel("Bit Error Rate", fontsize = 9)
ax.set_title("BER Performance of PUCCH Format 0")
Text(0.5, 1.0, 'BER Performance of PUCCH Format 0')
