lteDLDeprecode

Downlink deprecoding onto transmission layers

Syntax

out = lteDLDeprecode(in,nu,txscheme,codebook)

out = lteDLDeprecode(enb,chs,in)

Description

out = lteDLDeprecode(in,nu,txscheme,codebook) returns a symbol matrix by performing deprecoding using matrix pseudo-inversion to undo processing described in TS 36.211 [1], Section 6.3.4. The overall operation of the deprecoder is to transpose what is defined in the specification.

out = lteDLDeprecode(enb,chs,in) performs deprecoding of the precoded symbol matrix, in, according to cell-wide settings enb and chs (channel transmission configurations).

Examples

Perform Deprecoding on Identity Matrix

Deprecode a precoded identity matrix having codebook index 1 for three layers and four antennas.

in  = lteDLPrecode(eye(3),4,'SpatialMux',1);
out = lteDLDeprecode(in,3,'SpatialMux',1)

out = 3×3 complex

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

Input Arguments

in — Precoded input symbols

numeric matrix

Precoded input symbols, specified as numeric matrix. The size of the matrix is N-by-P, where P is the number of transmission antennas and N is the number of symbols per antenna. Generate the matrix by extracting a PDSCH using ltePDSCHIndices function on a received resource array. You can perform a similar extraction using the index generator for any other downlink channel that utilizes precoding.

nu — Number of layers

integer from 1 to 8

Number of layers, specified as an integer from 1 to 8. The maximum number of layers depends on the transmission scheme, txscheme.

Data Types: double

txscheme — Transmission scheme

'Port0' | 'TxDiversity' | 'CDD' | 'SpatialMux' | 'MultiUser' | 'Port5' | 'Port7-8' | 'Port8' | 'Port7-14'

PDSCH transmission scheme, specified as one of the following options.

Transmission scheme	Description
'Port0'	Single antenna port, port 0
'TxDiversity'	Transmit diversity
'CDD'	Large delay cyclic delay diversity scheme
'SpatialMux'	Closed loop spatial multiplexing
'MultiUser'	Multi-user MIMO
'Port5'	Single-antenna port, port 5
'Port7-8'	Single-antenna port, port 7, when NLayers = 1. Dual layer transmission, ports 7 and 8, when NLayers = 2.
'Port8'	Single-antenna port, port 8
'Port7-14'	Up to eight layer transmission, ports 7–14

Data Types: char | single

codebook — Codebook index

integer from 0 to 15

Codebook index to select the precoding matrix, specified as an integer from 0 to 15. This input is ignored for the 'Port0', 'TxDiversity', and 'CDD' transmission schemes. Find the precoding matrix corresponding to a particular codebook index in TS 36.211 [1], Section 6.3.4. In the case of 'TxDiversity' and nu=1, the function falls back to single port processing.

Data Types: double

enb — eNodeB cell-wide settings

structure

eNodeB cell-wide settings, specified as a structure containing these parameter fields:

Parameter Field	Required or Optional	Values	Description
When chs.TxScheme is set to 'TxDiversity', 'CDD', 'SpatialMux', or 'MultiUser', these parameters are applicable:
CellRefP	Required	1, 2, 4	Number of cell-specific reference signal (CRS) antenna ports
When chs.TxScheme is set to 'SpatialMux', or 'MultiUser' and chs.PMISet is present, these parameters are applicable:.
NCellID	Required	Integer from 0 to 503	Physical layer cell identity
NSubframe	Required	0 (default), nonnegative scalar integer	Subframe number
NDLRB	Required	Scalar integer from 6 to 110	Number of downlink resource blocks. ($$N_{\text{RB}}^{\text{DL}}$$)
CFI	Required	1, 2, or 3 Scalar or if the CFI varies per subframe, a vector of length 10 (corresponding to a frame).	Control format indicator (CFI) value. In TDD mode, CFI varies per subframe for the RMCs ('R.0', 'R.5', 'R.6', 'R.6-27RB', 'R.12-9RB')
CyclicPrefix	Optional	'Normal' (default), 'Extended'	Cyclic prefix length
DuplexMode	Optional	'FDD' (default), 'TDD'	Duplexing mode, specified as: 'FDD' for Frequency Division Duplex or 'TDD' for Time Division Duplex
When DuplexMode is set to 'TDD', these parameters are applicable:
TDDConfig	Optional	0, 1 (default), 2, 3, 4, 5, 6	Uplink–downlink configuration
SSC	Optional	0 (default), 1, 2, 3, 4, 5, 6, 7, 8, 9	Special subframe configuration (SSC)

Data Types: struct

chs — Channel-specific transmission configuration

structure

Channel-specific transmission configuration, specified as a structure that can contain the following parameter fields:

Parameter Field	Required or Optional	Values	Description
TxScheme	Required	'Port0', 'TxDiversity', 'CDD', 'SpatialMux', 'MultiUser', 'Port5', 'Port7-8', 'Port8', 'Port7-14'.	PDSCH transmission scheme, specified as one of the following options. Transmission scheme Description 'Port0' Single antenna port, port 0 'TxDiversity' Transmit diversity 'CDD' Large delay cyclic delay diversity scheme 'SpatialMux' Closed loop spatial multiplexing 'MultiUser' Multi-user MIMO 'Port5' Single-antenna port, port 5 'Port7-8' Single-antenna port, port 7, when NLayers = 1. Dual layer transmission, ports 7 and 8, when NLayers = 2. 'Port8' Single-antenna port, port 8 'Port7-14' Up to eight layer transmission, ports 7–14
NLayers	Required	Integer from 1 to 8	Number of transmission layers.
The following parameters are applicable when TxScheme is set to 'SpatialMux' or 'MultiUser'. Include either CodebookIdx field or both PMISet and PRBSet fields. For more information, see Algorithms.
CodebookIdx	Required	Integer from 0 to 15	Codebook index used during precoding
PMISet	Required	Integer vector with element values from 0 to 15.	Precoder matrix indication (PMI) set. It can contain either a single value, corresponding to single PMI mode, or multiple values, corresponding to multiple or subband PMI mode. The number of values depends on CellRefP, transmission layers and TxScheme. For more information about setting PMI parameters, see ltePMIInfo.
PRBSet	Required	Integer column vector or two-column matrix	Zero-based physical resource block (PRB) indices corresponding to the slot wise resource allocations for this PDSCH. PRBSet can be assigned as: a column vector, the resource allocation is the same in both slots of the subframe, a two-column matrix, this parameter specifies different PRBs for each slot in a subframe, a cell array of length 10 (corresponding to a frame, if the allocated physical resource blocks vary across subframes). PRBSet varies per subframe for the RMCs 'R.25'(TDD), 'R.26'(TDD), 'R.27'(TDD), 'R.43'(FDD), 'R.44', 'R.45', 'R.48', 'R.50', and 'R.51'.
The fields PMISet and PRBSet are used to determine the frequency-domain position occupied by each precoded symbol in out. This step is performed to apply the correct subband precoder when multiple PMI mode is used. Alternatively, you can provide the CodebookIdx parameter field. CodebookIdx is a scalar specifying the codebook index to use across the entire bandwidth. Therefore, the CodebookIdx field does not support subband precoding. The relationship between PMI values and codebook index is given in TS 36.213 [2], Section 7.2.4.

Data Types: struct

Output Arguments

out — Deprecoded downlink output

matrix

Deprecoded downlink output, returned as N_SYM-by-v matrix, containing v layers, with N_SYMN_SYM symbols in each layer. The symbols for layers and antennas lie in columns rather than in rows.

Data Types: double
Complex Number Support: Yes

Algorithms

For transmission schemes 'CDD', 'SpatialMux', and 'MultiUser', and degenerately 'Port0',

• Precoding involves multiplying a P-by-v precoding matrix, F, by a v-by-N_SYM matrix, representing N_SYM symbols on each of v transmission layers. This multiplication yields a P-by-N_SYM matrix, representing N_SYM precoded symbols on each of P antenna ports. Depending on the transmission scheme, the precoding matrix can be composed of multiple matrices multiplied together. But the size of the product, F, is always P-by-v.

For the 'TxDiversity' transmission scheme,

• A P ²-by-2v precoding matrix, F, is multiplied by a 2v-by-N_SYM matrix, formed by splitting the real and imaginary components of a v-by-N_SYM matrix of symbols on layers. This multiplication yields a P ²-by-N_SYM matrix of precoded symbols, which is then reshaped into a P-by-PN_SYM matrix for transmission. Since v is P for the 'TxDiversity' transmission scheme, F is of size P ²-by-2P, rather than P ²-by-2v.

When v is P in 'CDD', 'SpatialMux', and 'MultiUser' transmission schemes, and when P and v are 2 in the 'TxDiversity' transmission scheme,

• The precoding matrix, F, is square. Its size is 2P-by-2P for the transmit diversity scheme and P-by-P otherwise. In this case, the deprecoder takes the matrix inversion of the precoding matrix to yield the deprecoding matrix F ^–1. The matrix inversion is computed using LU decomposition with partial pivoting (row exchange):

  1. Perform LU decomposition P_xF = LU.

  2. Solve LY = I using forward substitution.

  3. Solve UX = Y using back substitution.

  4. F ^–1 = XP_x.

The degenerate case of the 'Port0' transmission scheme falls into this category, with P = v = 1.

For the 'CDD', 'SpatialMux', and 'MultiUser' transmission schemes,

• The deprecoding is then performed by multiplying F ^–1 by the transpose of the input symbols (symbols is size N_SYM-by-P, so the transpose is a P-by-N_SYM matrix). This multiplication recovers the v-by-N_SYM (equals P-by-N_SYM) matrix of transmission layers.

For the 'TxDiversity' transmission scheme,

• The deprecoding is performed, multiplying F ^–1 by the transpose of the input symbols (symbols is size PN_SYM-by-P, so the transpose is a P-by-PN_SYM matrix), having first been reshaped into a 2P-by-N_SYM matrix. This multiplication yields a 2v-by-N_SYM, matrix which is then split into two v-by-N_SYM matrices. To recover the v-by-N_SYM matrix of transmission layers multiply the second matrix by j and add the two matrices together (thus recombining real and imaginary parts).

For the other cases, specifically 'CDD', 'SpatialMux', and 'MultiUser' transmission schemes with v ≠ P and the 'TxDiversity' transmission scheme with P = 4,

• The precoding matrix F is not square. Instead, the matrix is rectangular with size P-by-v, except in the case of 'TxDiversity' transmission scheme with P = 4, where it is of size P ²-by-(2P = 16)-by-8. The number of rows is always greater than the number of columns in the matrix F is size m-by-n with m > n.

• In this case, the deprecoder takes the matrix pseudo-inversion of the precoding matrix to yield the deprecoding matrix F ⁺. The matrix pseudo-inversion is computed as follows.

  1. Perform LU decomposition P_xF = LU.

  2. Remove the last m − n rows of U to give $$\overline{U}$$.

  3. Remove the last m − n columns of L to give $$\overline{L}$$.

  4. $$X={\overline{U}}^H{\left(\overline{U}{\overline{U}}^H\right)}^{-1}{\left({\overline{L}}^H\overline{L}\right)}^{-1}{\overline{L}}^H$$ (the matrix inversions are carried out as in the previous steps).

  5. F ⁺ = XP_x

The application of the deprecoding matrix F ⁺ is the same process as described for deprecoding the square matrix case with F ⁺ in place of F ^–1.

This method of pseudo-inversion is based onLinear Algebra and Its Application [3], Chapter 3.4, Equation (56).

References

[1] 3GPP TS 36.211. “Evolved Universal Terrestrial Radio Access (E-UTRA); Physical Channels and Modulation.” 3rd Generation Partnership Project; Technical Specification Group Radio Access Network. URL: https://www.3gpp.org.

[2] 3GPP TS 36.213. “Evolved Universal Terrestrial Radio Access (E-UTRA); Physical layer procedures.” 3rd Generation Partnership Project; Technical Specification Group Radio Access Network. URL: https://www.3gpp.org.

[3] Strang, Gilbert. Linear Algebra and Its Application. Academic Press, 1980. 2nd Edition.