blkdiagbfweights

MIMO channel block diagonalized weights

Since R2020a

Syntax

[wp,wc] = blkdiagbfweights(chanmat,ns)

[wp,wc] = blkdiagbfweights(chanmat,ns,pt)

Description

[wp,wc] = blkdiagbfweights(chanmat,ns) returns precoding weights, wp, and combining weights, wc, derived from the channel response matrices contained in a MATLAB^® cell array chanmat.

• You can specify multiple user channels by putting each channel in a chanmat cell. chanmat{k} represents the k^thchannel from the transmitter to the user.

• • For a single frequency, specify the channel cell as a matrix.

  • For multiple frequencies, specify the channel cell as a three-dimensional array where the rows represent different subcarriers.

• Specify multiple subchannels per channel using the ns argument. Subchannels represent different data streams. ns specifies the number of subchannels for each user channel. Multiply the data streams by the precoding weights, wp.

The precoding and combining weights diagonalize the channel into independent subchannels so that for the k^thuser, the matrix wp*chanmat{k}*wc{k} is diagonal for each subcarrier.

[wp,wc] = blkdiagbfweights(chanmat,ns,pt) also specifies the total transmitted power, pt, per subcarrier.

Examples

Spatial Multiplexing with Block Diagonal Weights

Start with a base station consisting of a uniform linear array (ULA) with 16 antennas, and two users having receiver ULA arrays with 8 and 4 antennas, respectively. Show that using block diagonalization-based precoding and combining weights achieves spatial multiplexing, where the received signal at each user can be decoded without interference from the other user. Specify two data streams for each user.

Specify the transmitter location in txpos and two user receiver locations in rxpos1 and rxpos2. Array elements are spaced one-half wavelength apart.

txpos = (0:15)*0.5;
rxpos1 = (0:7)*0.5;
rxpos2 = (0:3)*0.5;

Create the channel matrix cell array using scatteringchanmtx and then compute the beamforming weights wp and wc. Each channel corresponds to a user. Assume that the channels have 10 scatterers. Each channel has two subchannels specified by the vector ns.

chanmat = {scatteringchanmtx(txpos,rxpos1,10), ...
    scatteringchanmtx(txpos,rxpos2,10)};
ns = [2 2];
[wp,wc] = blkdiagbfweights(chanmat,ns);

The weights diagonalize the channel matrices for each user.

For channel 1:

disp(wp*chanmat{1}*wc{1})

   8.2269 - 0.0000i   0.0000 + 0.0000i
  -0.0000 + 0.0000i   6.1371 - 0.0000i
   0.0000 - 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i  -0.0000 - 0.0000i

For channel 2:

disp(wp*chanmat{2}*wc{2})

  -0.0000 - 0.0000i  -0.0000 + 0.0000i
  -0.0000 + 0.0000i  -0.0000 + 0.0000i
   8.7543 + 0.0000i   0.0000 + 0.0000i
  -0.0000 - 0.0000i   4.4372 - 0.0000i

First create four subchannels to carry the data streams: two subchannels per channel. Each data stream contains 20 samples of $\pm 1$. Precode the input streams and combine the streams to produce the recovered signals.

x = 2*round(rand([20,4])) - 1;
xp = x*wp;
y1 = xp*chanmat{1} + 0.1*randn(20,8);
y2 = xp*chanmat{2} + 0.1*randn(20,4);
y = [y1*wc{1},y2*wc{2}];

Overlay stem plots of the input and recovered signals to show that the received user signals are the same as the transmitted signals.

for m = 1:4
    subplot(4,1,m)
    s = stem([x(:,m) 2*((real(y(:,m)) > 0) - 0.5)]);
    s(1).LineWidth = 2;
    s(2).MarkerEdgeColor = 'none';
    s(2).MarkerFaceColor = 'r';
    ylabel('Signal')
    title(sprintf('User %d Stream %d',ceil(m/2),rem(m-1,2) + 1))
    if m==1
        legend('Input','Recovered','Location','best')
    end
end
xlabel('Samples')

Spatial Multiplexing with Specified Power

Start with a base station consisting of a uniform linear array (ULA) with 16 antennas, and two users having receiver ULA arrays with 8 and 5 antennas, respectively. Show how to use three-dimensional arrays of channel matrices to handle two subcarriers. Then, the channel matrix for the first user takes the form 2-by-16-by-8 and the channel matrix for the second user takes the form 2-by-16-by-5. Also assume that there are two data streams for each user.

Specify the transmitter location in txpos and two user receiver locations in rxpos1 and rxpos2. Array elements are spaced one-half wavelength apart.

nr1 = 8;
nr2 = 5;
txpos = (0:15)*0.5;
rxpos1 = (0:(nr1-1))*0.5;
rxpos2 = (0:(nr2-1))*0.5;

Create the channel matrices using scatteringchanmtx and put them in a cell array. To create a second subchannel for each receiver, duplicate each channel matrix. Assume 10 point scatterers in computing the channel matrix.

smtmp1 = scatteringchanmtx(txpos,rxpos1,10);
smtmp2 = scatteringchanmtx(txpos,rxpos2,10);
sm1 = zeros(2,16,8);
sm2 = zeros(2,16,5);
sm1(1,:,:) = smtmp1;
sm1(2,:,:) = smtmp1;
sm2(1,:,:) = smtmp2;
sm2(2,:,:) = smtmp2;
chanmat = {sm1,sm2};

Specify that there are two data streams for each user.

ns = [2 2];

Specify the transmitted powers for each subcarrier.

pt = [1.0 1.5];

Compute the beamforming weights.

[wp,wc] = blkdiagbfweights(chanmat,ns,pt);

Show that the channels are diagonalized for the first subcarrier.

ksubcr = 1;
wpx = squeeze(wp(ksubcr,:,:));
chanmat1 = squeeze(chanmat{1}(ksubcr,:,:));
chanmat2 = squeeze(chanmat{2}(ksubcr,:,:));
wc1 = squeeze(wc{1}(ksubcr,:,:));
wc2 = squeeze(wc{2}(ksubcr,:,:));
wpx*chanmat1*wc1

ans = 4×2 complex

   8.2104 + 0.0000i  -0.0000 - 0.0000i
  -0.0000 + 0.0000i   5.9732 + 0.0000i
  -0.0000 + 0.0000i   0.0000 + 0.0000i
  -0.0000 - 0.0000i   0.0000 + 0.0000i

wpx*chanmat2*wc2

ans = 4×2 complex

   0.0000 - 0.0000i  -0.0000 - 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i
   8.8122 - 0.0000i  -0.0000 - 0.0000i
  -0.0000 + 0.0000i   4.8186 + 0.0000i

Propagate the signals to each user and then decode. Generate four streams of random data containing -1's and +1's and having two columns for each user. Each stream is a subchannel.

x = 2*(round(rand([20 4]))) - 1;

Precode the data streams.

xp = x*wpx;
y1 = xp*chanmat1 + 0.1*randn(20,8);
y2 = xp*chanmat2 + 0.1*randn(20,5);

Decode the data streams.

y = [y1*wc1,y2*wc2];

Overlay stem plots of the input and recovered signals to show that the received user signals are the same as the transmitted signals.

for m = 1:4
    subplot(4,1,m)
    s = stem([x(:,m) 2*((real(y(:,m)) > 0) - 0.5)]);
    s(1).LineWidth = 2;
    s(2).MarkerEdgeColor = 'none';
    s(2).MarkerFaceColor = 'r';
    ylabel('Signal')
    title(sprintf('User %d Stream %d',ceil(m/2),rem(m-1,2) + 1))
    if m==1
        legend('Input','Recovered','Location','best')
    end
end
xlabel('Samples')

Input Arguments

chanmat — Channel response matrices

N_u-element cell array

Channel response matrices, specified as an N_u-element cell array. N_u is the number of receive arrays. Each cell corresponds to a different channel and contains a channel response matrix or a three dimensional MATLAB array. The cell array must contain either all matrices or all arrays. For matrices, the number of rows for all matrices must be the same. For three-dimensional arrays, the number of rows and columns must be the same.

• If the k^th cell is a matrix, the matrix has the size N_t-by-N_r(k). N_t is the number of elements in the transmitting array and N_r(k) is the number of elements in the k^th receiving array.

• If the k^th cell is an array, the array has the size L-by-N_t-by-N_r(k). L is the number of subcarriers. N_t is the number of elements in the transmit array and N_r(k) is the number of elements in the k^th receive array.

Data Types: double | single
Complex Number Support: Yes

ns — Number of data streams per receive array

N_u-element row vector of positive integers

Number of data streams per receive array, specified as an N_u-element row vector of positive integers. N_u is the number of receive arrays.

Data Types: double | single

pt — Total transmitted power per subcarrier, in linear units

1 (default) | positive scalar | L-element vector of positive values

Total transmitted power per subcarrier, in linear units, specified as a positive scalar or an L-element vector of positive values. L is the number of subcarriers. If pt is a scalar, all subcarriers have the same transmitted power. If pt is a vector, each vector element specifies the transmitted power for the corresponding subcarrier.

Data Types: double | single

Output Arguments

wp — Precoding weights

complex-valued N_st-by-N_t matrix | complex-valued L-by-N_st-by-N_t MATLAB array

Precoding weights, returned as a complex-valued N_st-by-N_t matrix or a complex-valued L-by-N_st-by-N_t MATLAB array.

• If chanmat contains matrices, wp is a complex-valued N_st-by-N_t matrix where N_st is the total number of data channels (sum(ns)).

• If chanmat contains three-dimensional MATLAB arrays, wp is a complex-valued L-by-N_st-by-N_t MATLAB array where N_st is the total number of data channels (sum(ns)).

Units are dimensionless.

Data Types: double
Complex Number Support: Yes

wc — Combining weights

N_u-element cell array

Combining weights, returned as an N_u-element cell array. Units are dimensionless.

• If chanmat contains matrices, the k^th cell in wc contains a complex valued N_r(k)-by-N_s(k) matrix. N_s(k) is the value of the argument ns for the k^th receive array.

• If chanmat contains three-dimensional MATLAB arrays, the k^th cell of wc contains a complex-valued L-by-N_r(k)-by-N_s(k) MATLAB array. N_s(k) is the value of the k^th entry of the ns vector.

Data Types: double
Complex Number Support: Yes

References

[1] Heath, Robert W., et al. “An Overview of Signal Processing Techniques for Millimeter Wave MIMO Systems.” IEEE Journal of Selected Topics in Signal Processing, vol. 10, no. 3, Apr. 2016, pp. 436–53. DOI.org (Crossref), doi:10.1109/JSTSP.2016.2523924. Bibliography

[2] Tse, D. and P. Viswanath, Fundamentals of Wireless Communications, Cambridge: Cambridge University Press, 2005.

[3] Paulraj, A. Introduction to Space-Time Wireless Communications, Cambridge: Cambridge University Press, 2003.

[4] Spencer, Q.H., et al. "Zero-Forcing Methods for Downlink Spatial Multiplexing in Multiuser MIMO Channels." IEEE Transactions on Signal Processing, Vol. 52, No. 2, February 2004, pp. 461-471. DOI.org (Crossref), doi:10.1109/TSP.2003.821107.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• Does not support variable-size inputs.

Version History

Introduced in R2020a