omphybweights

Compute hybrid beamforming weights using orthogonal matching pursuit

Syntax

[wpbb,wprf] = omphybweights(chanmat,ns,ntrf,at)

[wpbb,wprf,wcbb,wcrf] = omphybweights(chanmat,ns,ntrf,at,nrrf,ar)

[___] = omphybweights(chanmat,ns,ntrf,at,nrrf,ar,npow)

Description

[wpbb,wprf] = omphybweights(chanmat,ns,ntrf,at) returns the hybrid precoding weights wpbb and wprf for the channel matrix chanmat. The weights are computed using an orthogonal matching pursuit algorithm. ns is the number of independent data streams propagated through the channel. ntrf specifies the number of RF chains in the transmit array. at is a collection of possible analog weights for wprf. Together, the precoding weights approximate the optimal full digital precoding weights of chanmat.

[wpbb,wprf,wcbb,wcrf] = omphybweights(chanmat,ns,ntrf,at,nrrf,ar) also returns the hybrid combining weights wcbb and wcrf. The input nrrf specifies the number of RF chains in the receive array. ar is a collection of possible analog weights for wcrf.

[___] = omphybweights(chanmat,ns,ntrf,at,nrrf,ar,npow) also specifies the noise power npow in each receive antenna element. All subcarriers are assumed to have the same noise power.

Examples

Calculate Effective Channel Matrix

Assume an 8-by-4 MIMO system with four RF chains in a transmit array and two RF chains in a receive array. Show that the hybrid weights can support transmitting two data streams simultaneously.

Specify the positions of the transmitters and receivers in uniform line arrays.

txpos = (0:7)*0.5;
rxpos = (0:3)*0.5;

Construct the channel matrix.

chanmat = scatteringchanmtx(txpos,rxpos,10);

Specify the number of transmit and receive RF chains.

ntrf = 4;
nrrf = 2;

Specify two data streams.

ns = 2;

Set up the steering vector dictionaries for the transmitting and receiving arrays.

txdict = steervec(txpos,-90:90);
rxdict = steervec(rxpos,-90:90);

Compute the precoding and combining weights.

[Fbb,Frf,Wbb,Wrf] = omphybweights(chanmat,ns,ntrf,txdict,nrrf,rxdict);

Calculate the effective channel matrix from the weights. A diagonal effective channel matrix indicates the capability of simultaneous transmission of multiple data streams.

chan_eff = Fbb*Frf*chanmat*Wrf*Wbb

chan_eff = 2×2 complex

   1.0000 - 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   1.0000 - 0.0000i

Input Arguments

chanmat — Channel response matrix

complex-valued N_t-by-N_r matrix | complex-valued L-by-N_t-by-N_r array

Channel response matrix, specified as an N_t-by-N_r matrix or a complex-valued L-by-N_t-by-N_r array where

• N_t is the number of elements in the transmitting array.

• N_r is the number of elements in the receiving array.

• L is the number of subcarriers.

Data Types: double | single
Complex Number Support: Yes

ns — Number of independent data streams

positive integer

Number of independent data streams propagated through the channel, specified as a positive integer.

Data Types: double | single

ntrf — Number of RF chains in transmit array

positive integer

Number of RF chains in the transmit array, specified as a positive integer.

Data Types: double | single

at — Collection of possible analog transmit array weights

complex-valued N_t-by-P matrix | complex-valued L-by-N_t-by-P array

Collection of possible analog weights for transmit array for wprf, specified as a complex-valued matrix or array.

• When chanmat is an N_t-by-N_r matrix, at is a complex-valued N_t-by-P matrix. Each column represents a vector of analog weights.

• When chanmat is an L-by-N_t-by-N_r array, at is a complex-valued L-by-N_t-by-P array. at has L pages and in each page is a matrix of N_t rows. Each column represents a vector of analog weights.

• N_t is the number of elements in the transmitting array.

• N_r is the number of elements in the receiving array.

• L is the number of subcarriers.

• P is the number of vectors of analog weights in the collection.

Data Types: double | single
Complex Number Support: Yes

nrrf — Number of RF chains in receive array

positive integer

Number of RF chains in the receive array, specified as a positive integer.

Data Types: double | single

ar — Collection of possible receive analog array weights

complex-valued N_r-by-Q matrix | complex-valued N_r-by-Q-by-L array

Collection of possible analog weights for receive array wcrf, specified as a complex-valued matrix or array.

• When chanmat is an N_t-by-N_r matrix, ar is a complex-valued N_r-by-Q matrix. Each column represents a vector of analog weights.

• When chanmat is an L-by-N_t-by-N_r array, ar is a complex-valued N_r-by-Q-by-L array. Each page is an N_r-by-Q matrix. Each column represents a vector of analog weights.

• N_t is the number of elements in the transmitting array.

• N_r is the number of elements in the receiving array.

• L is the number of subcarriers.

• Q is the number of vectors of analog weights in the collection.

Data Types: double | single
Complex Number Support: Yes

npow — Noise power

0 (default) | nonnegative scalar

Noise power in each receive antenna element, specified as a nonnegative scalar. All subcarriers have the same noise power.

Data Types: double | single

Output Arguments

wpbb — Hybrid baseband precoding weights

complex-valued N_s-by-N_trf matrix | complex-valued L-by-N_s-by-N_trf array

Hybrid baseband precoding weights, returned as a complex-valued matrix or array.

• When chanmat is an N_t-by-N_r matrix, wpbb is a complex-valued N_s-by-N_trf matrix.

• When chanmat is an L-by-N_t-by-N_r array, wpbb is a complex-valued L-by-N_s-by-N_trf array.

• N_s is the number of independent data streams specified by the ns argument.

• N_trf is the number of RF chains in the transmit array specified by the ntrf argument.

• L is the number of subcarriers.

wprf — Hybrid RF precoding weights

complex-valued N_trf-by-N_t matrix | complex-valued L-by-N_trf-by-N_t array

Hybrid RF precoding weights, returned as a complex-valued matrix or array.

• When chanmat is an N_t-by-N_r matrix, wprf is a complex-valued N_trf-by-N_t matrix.

• When chanmat is an L-by-N_t-by-N_r array, wprf is a complex-valued L-by-N_trf-by-N_t array.

• N_t is the number of elements in the transmitting array.

• N_trf is the number of RF chains in the transmit array specified by the ntrf argument.

• L is the number of subcarriers.

wcbb — Hybrid baseband combining weights

complex-valued N_rrf-by-N_s matrix | complex-valued L-by-N_rrf-by-N_s array

Hybrid baseband combining weights, returned as a complex-valued matrix or array.

• When chanmat is an N_t-by-N_r matrix, wcbb is a complex-valued N_rrf-by-N_s matrix.

• When chanmat is an L-by-N_t-by-N_r array, wcbb is a complex-valued L-by-N_rrf-by-N_s array.

• N_s is the number of independent data streams specified by the ns argument.

• N_rrf is the number of RF chains in the receive array specified by the nrrf argument.

• L is the number of subcarriers.

wcrf — Hybrid RF combining weights

complex-valued N_r-by-N_rrf | complex-valued L-by-N_r-by-N_rrf array

Hybrid RF combining weights, returned as a complex-valued matrix or array.

• When chanmat is an N_t-by-N_r matrix, wcrf is a complex-valued N_r-by-N_rrf matrix.

• When chanmat is an L-by-N_t-by-N_r array, wcrf is a complex-valued L-by-N_r-by-N_rrf array.

• N_t is the number of elements in the transmitting array.

• N_rrf is the number of RF chains in the receive array specified by the nrrf argument.

• L is the number of subcarriers.

More About

Precoding Weights

The matrix product of the precoding weights wpbb x wprf approximates the optimal full digital precoding weights of the channel matrix chanmat.

Combining Weights

The combining weights wcbb and wcrf, together with the precoding weights, diagonalize the channel into independent subchannels. The matrix product wpbb x wprf x chanmat x wcrfx wcbb is approximately diagonal.

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] Ayach, Omar El et al. "Spatially Sparse Precoding in Millimeter Wave MIMO Systems" IEEE Trans on Wireless Communications. Vol. 13, No. 3, March 2014.

Extended Capabilities

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

Version History

Introduced in R2019b