This example shows how the LTE System Toolbox™ can be used to model a TS36.104 "PRACH Detection Requirements" conformance test. The probability of correct detection of the Physical Random Access Channel (PRACH) preamble is measured when the preamble signal is present.
The Random Access Channel (RACH) is an uplink transmission used by the User Equipment (UE) to initiate synchronization with the eNodeB. TS36.104, Section 126.96.36.199 [ 1 ] defines the probability of Physical Random Access Channel (PRACH) detection must be greater than or equal to 99% at an SNR of -8.0 dB. There are several detection error cases:
Detecting an incorrect preamble
Not detecting a preamble
Detecting the correct preamble but with the wrong timing estimation
For channel propagation conditions ETU70, a timing estimation error occurs if the estimation error of the timing offset of the strongest path is larger than 2.08 us. The strongest path has a delay of 310 ns for ETU70.
In this example, a PRACH waveform is configured and passed through an appropriate channel. At the receiver PRACH detection is performed and the PRACH detection probability is calculated. The example is executed for the parameters defined in TS36.104, Section 8.4.1 [ 1 ] and TS36.141, Table A.6-1 [ 2 ]; i.e. normal mode, 2 receive antennas, ETU70 channel, normal cyclic prefix, burst format 0, SNR -8.0dB.
The test is carried out over 10 subframes at a number of SNRs.
foffset is the frequency offset which will be modeled between transmitter and receiver and is specified for the test in TS36.104, Table 188.8.131.52-1 [ 1 ]. A large number of
numSubframes should be used to produce meaningful results.
SNRdB can be an array of values or a scalar.
numSubframes = 10; % Number of subframes frames to simulate at each SNR SNRdB = [-14.0 -12.0 -10.0 -8.0 -6.0]; % SNR points to simulate foffset = 270.0; % Frequency offset in Hertz
User Equipment (UE) settings are specified in the structure
ue.NULRB = 6; % 6 Resource Blocks ue.DuplexMode = 'FDD'; % Frequency Division Duplexing (FDD) ue.CyclicPrefixUL = 'Normal'; % Normal cyclic prefix length ue.NTxAnts = 1; % Number of transmission antennas
The PRACH configuration is defined in the structure
prach. This configuration is used to create a second structure
info by calling ltePRACHInfo. This provides information about the PRACH generated given a specified configuration. Some of this information will be used later in the example.
prach.Format = 0; % PRACH format: TS36.104, Table 184.108.40.206-1 prach.SeqIdx = 22; % Logical sequence index: TS36.141, Table A.6-1 prach.CyclicShiftIdx = 1; % Cyclic shift index: TS36.141, Table A.6-1 prach.HighSpeed = 0; % Normal mode: TS36.104, Table 220.127.116.11-1 prach.FreqOffset = 0; % Default frequency location prach.PreambleIdx = 32; % Preamble index: TS36.141, Table A.6-1 info = ltePRACHInfo(ue, prach); % PRACH information
Configure the propagation channel model using a structure
chcfg as per TS36.104, Table 18.104.22.168-1 [ 1 ].
chcfg.NRxAnts = 2; % Number of receive antenna chcfg.DelayProfile = 'ETU'; % Delay profile chcfg.DopplerFreq = 70.0; % Doppler frequency chcfg.MIMOCorrelation = 'Low'; % MIMO correlation chcfg.Seed = 1; % Channel seed chcfg.NTerms = 16; % Oscillators used in fading model chcfg.ModelType = 'GMEDS'; % Rayleigh fading model type chcfg.InitPhase = 'Random'; % Random initial phases chcfg.NormalizePathGains = 'On'; % Normalize delay profile power chcfg.NormalizeTxAnts = 'On'; % Normalize for transmit antennas chcfg.SamplingRate = info.SamplingRate; % Sampling rate
A loop is used to run the simulation for a set of SNR points, given by the vector
SNRdB. The SNR vector configured here is a range of SNR points including a point at -8.0 dB, the SNR at which the test requirement for PRACH detection rate (99%) is to be achieved.
ltePRACH generates an output signal normalized to the same transmit power as for an uplink data transmissions within the LTE System Toolbox. Therefore the same normalization must take place on the noise added to the PRACH. The noise added before SC-FDMA demodulation will be amplified by the IFFT. The amplification is the square root of the size of the IFFT (), thus to ensure the power of the noise added is normalized after demodulation, to achieve the desired SNR the desired noise power is divided by . In addition, as real and imaginary parts of the noise are created separately before being combined into complex additive white Gaussian noise, the noise amplitude must be scaled by so the generated noise power is 1.
At each SNR test point the probability detection is calculated on a subframe by subframe basis using the following steps:
PRACH Transmission: A PRACH waveform is generated using ltePRACH with a specified timing offset. As per TS36.141, Section 22.214.171.124.2 [ 2 ] the preambles are sent with certain timing offsets defined in TS36.141, Figure 126.96.36.199.2-2 [ 2 ]. A timing offset base value is set to 50% of the number of cyclic shifts for PRACH generation. This offset is increased for each preamble, adding a step value of 0.1 us, until the end of the tested range, which is 0.9 us. This pattern then repeats.
Noisy Channel Modeling: The waveform is passed through a fading channel and additive white Gaussian noise added. An additional 25 samples are added to the end of the waveform to cover the range of delays expected from the channel modeling (a combination of implementation delay and channel delay spread). This implementation delay is then removed the to ensure the implementation delay is interpreted as an actual timing offset in the preamble detector.
Application of Frequency Offset: The frequency offset defined by the standard is also applied at this stage by performing a simple FM modulation of the received waveform.
% Initialize the random number generator stream rng('default'); % Initialize variables storing probability of detection at each SNR pDetection = zeros(size(SNRdB)); for nSNR = 1:length(SNRdB) % Scale noise to ensure the desired SNR after SC-FDMA demodulation ulinfo = lteSCFDMAInfo(ue); SNR = 10^(SNRdB(nSNR)/20); N = 1/(SNR*sqrt(double(ulinfo.Nfft)))/sqrt(2.0); % Detected preamble count detectedCount = 0; % Loop for each subframe for nsf = 1:numSubframes % PRACH transmission ue.NSubframe = mod(nsf-1, 10); ue.NFrame = fix((nsf-1)/10); % Set PRACH timing offset in us as per TS36.141, Figure 188.8.131.52.2-2 prach.TimingOffset = info.BaseOffset + ue.NSubframe/10.0; % Generate transmit wave txwave = ltePRACH(ue, prach); % Channel modeling chcfg.InitTime = (nsf-1)/1000; [rxwave, fadinginfo] = lteFadingChannel(chcfg, ... [txwave; zeros(25, 1)]); % Add noise noise = N*complex(randn(size(rxwave)), randn(size(rxwave))); rxwave = rxwave + noise; % Remove the implementation delay of the channel modeling rxwave = rxwave((fadinginfo.ChannelFilterDelay + 1):end, :); % Apply frequency offset t = ((0:size(rxwave, 1)-1)/chcfg.SamplingRate).'; rxwave = rxwave .* repmat(exp(1i*2*pi*foffset*t), ... 1, size(rxwave, 2)); % PRACH detection for all cell preamble indices [detected, offsets] = ltePRACHDetect(ue, prach, rxwave, (0:63).'); % Test for preamble detection if (length(detected)==1) % Test for correct preamble detection if (detected==prach.PreambleIdx) % Calculate timing estimation error. The true offset is % PRACH offset plus channel delay trueOffset = prach.TimingOffset/1e6 + 310e-9; measuredOffset = offsets(1)/chcfg.SamplingRate; timingerror = abs(measuredOffset-trueOffset); % Test for acceptable timing error if (timingerror<=2.08e-6) detectedCount = detectedCount + 1; % Detected preamble else disp('Timing error'); end else disp('Detected incorrect preamble'); end else disp('Detected multiple or zero preambles'); end end % of subframe loop % Compute final detection probability for this SNR pDetection(nSNR) = detectedCount/numSubframes; end % of SNR loop
Detected multiple or zero preambles Detected multiple or zero preambles
At the end of the SNR loop, the calculated detection probabilities for each SNR value are plotted against the target probability.
hPRACHDetectionResults(SNRdB, numSubframes, pDetection);
This example uses the helper function:
3GPP TS 36.104 "Base Station (BS) radio transmission and reception"
3GPP TS 36.141 "Base Station (BS) conformance testing"