mimo_channel.m

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function [Channel, Fading] = MIMO_Channel(FadingMatrixType, ...
			     FadingOversamplingFactor, Speed_ms, ...
			     CarrierFrequency_Hz, ...
			     RunningTimeInstant, ChipOversamplingFactor, ...
			     ChipRate_Hz, NumberOfChipsPerIteration, PDP_linear,...
                 NumberOfTxAntennas, NumberOfTransmittedSamples, ...
                 NumberOfRxAntennas, NumberOfReceivedSamples);
             
% function [Channel, Fading] = MIMO_Channel(FadingMatrixType, ...
%			      FadingOversamplingFactor, Speed_ms, ...
%		 	      CarrierFrequency_Hz, ...
%	 		      RunningTimeInstant, ChipOversamplingFactor, ...
% 			      ChipRate_Hz, NumberOfChipsPerIteration, PDP_linear,...
%                 NumberOfTxAntennas, NumberOfTransmittedSamples, ...
%                 NumberOfRxAntennas, NumberOfReceivedSamples);
%
% Generates the correlated tap coefficients of the MIMO tapped delay line
% model to be used during one iteration of the main loop. The function
% performs a double interpolation, first in the fading vector domain,
% to collect the fading samples corresponding to the (sub)chip-spaced time
% samples, then in the tap domain, to match the delays of the PDP to
% the sample instants of the simulation. This second interpolation complies
% with the description in TR 25.869 v 0.1.1, p.23.
%
% The correlated tap coefficients are delivered through two different
% matrices Channel and Fading which embed the same information but
% exhibit two different structures.
%
% Inputs
%
% * 2-D matrix FadingMatrixType of size (NumberOfPaths * NumberOfTxAntennas
%   * NumberOfRxAntennas) x FadingNumberOfIterations containing the spatially
%   correlated fading process of the NumberOfPaths * NumberOfTxAntennas
%   * NumberOfRxAntennas tap coefficients of the MIMO model, including
%   an optional Rice component.
% * Variable FadingOversamplingFactor, oversampling factor of the fading
%   processes, used by the first interpolation to match fading instants
%   with simulation instants.
% * Variable Speed_ms, speed of the UE in m/s
% * Variable CarrierFrequency_Hz, carrier frequency in Hz
% * Variable RunningTimeInstant, time reference
% * Variable ChipOversamplingFactor, oversampling factor of the main loop
% * Variable ChipRate_Hz, chip rate
% * Variable NumberOfChipsPerIteration, span of an iteration in chips
% * Variable PDP_linear, PDP of the channel
% * Variable NumberOfTxAntennas, number of antenna elements at Tx
% * Variable NumberOfTransmittedSamples, time span of the main loop at Tx
% * Variable NumberOfRxAntennas, number of antenna elements at Rx
% * Variable NumberOfReceivedSamples, time span of the main loop at Rx,
%   equals to NumberOfReceivedSamples plus the maximum delay expressed
%   in samples (refer to IST METRA D3.2 for more details).
%
% Outputs
%
% * 2-D matrix Fading of size (NumberOfTxAntennas * NumberOfRxAntennas *
%   NumberOfPaths) x (NumberOfChipsPerIteration * ChipOversamplingFactor)
%   containing the fading samples of an iteration for all taps of the PDP.
% * 3-D matrix Channel of size NumberOfTxAntennas x (NumberOfRxAntennas *
%   NumberOfReceivedSamples) x NumberOfTransmittedSamples to be used to
%   perform channel filtering according to the formalism described in
%   IST METRA Deliverable D3.2, pp. 22-28.
%
%
% STANDARD DISCLAIMER
%
% CSys is furnishing this item "as is". CSys does not provide any
% warranty of the item whatsoever, whether express, implied, or
% statutory, including, but not limited to, any warranty of
% merchantability or fitness for a particular purpose or any
% warranty that the contents of the item will be error-free.
%
% In no respect shall CSys incur any liability for any damages,
% including, but limited to, direct, indirect, special, or
% consequential damages arising out of, resulting from, or any way
% connected to the use of the item, whether or not based upon
% warranty, contract, tort, or otherwise; whether or not injury was
% sustained by persons or property or otherwise; and whether or not
% loss was sustained from, or arose out of, the results of, the
% item, or any services that may be provided by CSys.
%
% (c) Laurent Schumacher, AAU-TKN/IES/KOM/CPK/CSys - February 2002

% First interpolation
% Interpolation in the fading vector domain

TimeStep_s   = 1/(ChipOversamplingFactor*ChipRate_Hz);
FadingStep_s = 3e8/(2*Speed_ms*CarrierFrequency_Hz*FadingOversamplingFactor);
TimeInstants = RunningTimeInstant:TimeStep_s:RunningTimeInstant+ ...
               ((NumberOfChipsPerIteration*ChipOversamplingFactor)-1)*TimeStep_s;

% The mod(ulo) operator enables to loop on the fading vector along simulation.
% This requires that the length of this fading vector is at least 40 wavelengths,
% to be able to claim decorrelation between successive samples.
FadingInstants         = mod(TimeInstants./FadingStep_s, size(FadingMatrixType,2)-1);
FloorFadingInstants    = floor(FadingInstants);
RemainerFadingInstants = FadingInstants - FloorFadingInstants;
% Actual interpolation
for ii = 1:(NumberOfChipsPerIteration*ChipOversamplingFactor)
    Fading(:,ii) = (1-RemainerFadingInstants(ii))...
                   .*FadingMatrixType(:,FloorFadingInstants(ii)+1)+...
                   RemainerFadingInstants(ii)...
                   .*FadingMatrixType(:,FloorFadingInstants(ii)+2);
end;

% Second interpolation
% Interpolation in the tap domain
% The delay values of the PDP do not necessarily match with the sampling instants
% of the simulation. This second interpolation step derives the values of the taps
% by linearly interpolating the correlated fadings. Note that the coefficients
% of the linear interpolation are given as square root values of the distance
% between samples, since the interpolation is linear in powers to maintain
% the property that sum(PDP) = 1
%
% Note: this step could be optimised. Indeed, the interpolation in the tap domain
% Could be performed out of the loop, since it always delivers the same result.
% Tap delays and sampling instants do not change from iteration to the other.
PDPInstants         = PDP_linear(2,:)./TimeStep_s;
FloorPDPInstants    = floor(PDPInstants);
RemainerPDPInstants = PDPInstants - FloorPDPInstants;
Channel             = zeros(NumberOfTxAntennas,...
	                  NumberOfRxAntennas*NumberOfReceivedSamples,...
	                  NumberOfTransmittedSamples);
% Actual interpolation
for ii = 1:NumberOfTransmittedSamples
    for jj = 1:size(PDP_linear,2)
        shift = ((ii-1)*ChipOversamplingFactor) + FloorPDPInstants(jj) + 1;
        for kk = 1:NumberOfTxAntennas
            for ll = 1:NumberOfRxAntennas
                Channel(kk, shift + (ll - 1) * NumberOfReceivedSamples, ii) = ...
                    Channel(kk, shift + (ll - 1) * NumberOfReceivedSamples, ii) + ...
                    sqrt(1 - RemainerPDPInstants(jj)) * Fading((kk - 1) * NumberOfRxAntennas + ll, ii);
                Channel(kk, shift + (ll - 1) * NumberOfReceivedSamples + 1, ii) = ...
                    Channel(kk, shift + (ll - 1) * NumberOfReceivedSamples + 1, ii) + ...
                    sqrt(RemainerPDPInstants(jj)) * Fading((kk - 1) * NumberOfRxAntennas + ll, ii);
            end;
        end;
    end;
end;