PRACH Detection Conformance Test

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This example shows how the LTE 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.

Introduction

The Random Access Channel (RACH) is an uplink transmission used by the User Equipment (UE) to initiate synchronization with the eNodeB. TS36.104, Section 8.3.4.1 [ 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.

Simulation Configuration

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 8.4.2.1-1 [ 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 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

UE Configuration

User Equipment (UE) settings are specified in the structure ue.

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

PRACH Configuration

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 8.4.2.1-1
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 8.4.2.1-1
prach.FreqOffset = 0;      % Default frequency location
prach.PreambleIdx = 32;    % Preamble index: TS36.141, Table A.6-1

info = ltePRACHInfo(ue, prach);  % PRACH information

Propagation Channel Configuration

Configure the propagation channel model using a structure chcfg as per TS36.104, Table 8.4.2.1-1 [ 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

Loop for SNR Values

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 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 ( $N_{\mathrm{FFT}}$ ), 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 $N_{\mathrm{FFT}}$ . 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 $1/\sqrt{2}$ 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 TS 36.141 Section 8.4.1.4.2 [ 2 ], the preambles are sent with certain timing offsets defined in TS36.141, Figure 8.4.1.4.2-2 [ 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 to ensure the implementation delay is not 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.

PRACH Detection: Perform PRACH detection using ltePRACHDetect for all cell preamble indices (0-63). The detected PRACH index and offset is returned and used to determine where a detection was successful according to the constraints discussed in the Introduction.

% 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 8.4.1.4.2-2
        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

Analysis

At the end of the SNR loop, the calculated detection probabilities for each SNR value are plotted against the target probability.

targetSNR = -8.0;
PRACHDetectionResults(SNRdB, numSubframes, pDetection, targetSNR);

References

3GPP TS 36.104 "Base Station (BS) radio transmission and reception" 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA).
3GPP TS 36.141 "Base Station (BS) conformance testing" 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA).

Local Functions

function PRACHDetectionResults(SNRdB,numSubframes,pDetection,targetSNR)
    % Plot detection probability
    figure('NumberTitle','off','Name','PRACH Detection Probability');
    plot(SNRdB,pDetection,'b-o','LineWidth',2,'MarkerSize',7);
    title(['Detection Probability for ',num2str(numSubframes),' subframe(s)']);
    xlabel('SNR (dB)'); ylabel('Detection Probability');
    grid on; hold on;

    % Plot target probability
    plot(targetSNR,0.99,'rx','LineWidth',2,'MarkerSize',7);
    legend('Simulation Result', 'Target 99% Probability','Location','best');
    minP = 0;
    if(~isnan(min(pDetection)))
        minP = min([pDetection(:); 0.99]);
    end
    axis([SNRdB(1)-0.1, SNRdB(end)+0.1, minP-0.05, 1.05]);
end