jsdmrfweights

Create RF precoding weights

Since R2023a

Syntax

wprf = jsdmrfweights(hcov,ns)

wprf = jsdmrfweights(hcov,ns,ntrf)

Description

wprf = jsdmrfweights(hcov,ns) returns the RF precoding weights, wprf, for the channel covariance matrix, hcov, to achieve orthogonality among users by Joint Spatial Division Multiplexing (JSDM). JSDM uses RF precoding weights to divide users into groups by their location information. The RF precoding weights, wprf, beamform the transmitted signal into each group.

wprf = jsdmrfweights(hcov,ns,ntrf) also specifies the desired number of RF chains ntrf.

Examples

Find JSDM RF Precoding Weights

Find RF precoding weights for a JSDM beamformer based on a base station with a 64-element linear antenna array. Assume there are two user groups. The first group has two users and the second group has three users. Array elements are 1/2 wavelength apart.

Set the number of array elements to 64.

Nt = 64;

Find the array steering weights in the direction of the first user group. The user group is centered at $+{10}^{\circ }$ azimuth.

v1 = steervec((0:Nt-1)*0.5,[9 11]);
rc1 = v1*v1'; 

Find the array steering weights in the direction of the second user group. The user group is centered ${-5}^{\circ }$ azimuth.

v2 = steervec((0:Nt-1)*0.5,[-4 -5 -6]);
rc2 = v2*v2';

Then, compute the RF weights from the channel covariance matrix.

hcov = {rc1,rc2};
wprf = jsdmrfweights(hcov,[2 3]);

Verify the orthogonality between the two user groups.

snr1 = pow2db(real(trace(wprf{1}*rc1*wprf{1}'))/real(trace(wprf{1}*rc2*wprf{1}')))

snr1 = 
26.1255

snr2 = pow2db(real(trace(wprf{2}*rc2*wprf{2}'))/real(trace(wprf{2}*rc1*wprf{2}')))

snr2 = 
26.1632

Input Arguments

hcov — Channel covariance matrix

1-by-G cell array

Channel covariance matrix, specified as 1-by-G cell array where G is the number of groups. Each cell in hcov an N_t-by-N_t matrix representing the covariance of the channel between the base station and the corresponding group of the users. N_t is the number of elements in the base station array. Assume that hcov is the same for all users in the corresponding group across all subcarriers.

hcov for the g^th user group is defined as the expected value of H*H', where H is an N_t-by-N_r(g) matrix representing the instantaneous channel for that user group. N_r(g) is the number of receiving elements in theg^th group.

Data Types: double | single
Complex Number Support: Yes

ns — Number of data streams

G-element row vector | 1-by-G cell array

Number of data streams, specified as a G-element row vector or a 1-by-G cell array.

• If ns is a vector, each element specifies the total number of data streams in the corresponding user group.

• If ns is a cell array, each element in the cell array is a K_g-element row vector where K_g is the number of users in the g^th group. The elements in K_g-element row vector specify the number of receiving data streams for each user in that group.

This function assumes that the number of receiving elements in the g^th user group, N_r(g), matches the total number of data streams for that group.

Data Types: double | single

ntrf — Desired number of RF chains

number of data streams per group (default) | 1-by-G integer vector

Desired number of RF chains for each group, specified as a 1-by-G integer vector. Note that if nrtf is specified, then the dimension of wprf(g) becomes nrtf(g)-by-N_t.

Data Types: double | single

Output Arguments

wprf — RF precoding weights

1-by-G cell array

RF precoding weights for the channel covariance matrix, returned as a 1-by-G cell array.

• When ns is a vector, each cell in wprf is an ns(g)-by-N_t matrix that maps the ns(g) RF chain to Nt antennas in the base station.

• When ns is a cell array, each cell in wprf is a sum(NS{g})-by-Nt matrix that maps the total number of RF chains in the g^th group to Nt antennas in the base station.

Algorithms

Precision

This function supports single and double precision floating point values for input arguments. If the input arguments are single precision, the outputs are single precision. If the input arguments are double precision, the outputs are double precision.

References

[1] Adhikary A., J. Nam, J-Y Ahn, and G. Caire. "Joint Spatial Division and Multiplexing - The Large-Scale Array Regime." IEEE Transactions on Information Theory, Vol. 59, No. 10, October 2013, pp. 6441-6463.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2023a