LTE PHY Downlink with Spatial Multiplexing

This example shows the Downlink Shared Channel (eNodeB to UE) physical layer (PHY) processing of the Long Term Evolution (LTE) wireless communication system [ 1-3, 7 ].

This example includes:

Refer to the LTE System Toolbox™ product and its set of code examples for specialized LTE compliant building components in MATLAB. Relevant examples from the LTE System Toolbox include:

Keywords: LTE, MIMO-OFDM, spatial multiplexing, codebook-based precoding, MMSE, rate-matching, turbo coding, sphere decoding.


Using the Release 10 specifications of LTE-Advanced (the 4G air interface for mobile communications), this example highlights a multi-antenna transmission scheme that enables dowlink peak data rates in excess of 1Gbps. It employs a multi-codeword spatial multiplexed transmission using closed-loop codebook-based precoding. Using multiple antennas at both transmitter and receiver, the example shows the Release 10 (compatible with Release 8) modes of 2-by-2 and 4-by-4 antenna configurations using UE category 5 parameters. The 4-by-4 mode allows for up to a 300 Mbps downlink transmission rate.

The key components highlighted in the example include

  • Variable-size payload generation

  • CRC insertion per tranport block

  • Code-block segmentation with per code-block CRC insertion

  • Channel (turbo) coding

  • Rate matching with bit selection

  • Bit-level scrambling

  • Data modulation (QPSK, 16QAM or 64QAM)

  • Layer mapping for two and four antennas

  • Codebook-based precoding

  • Resource-element mapping and

  • OFDM signal generation

In addition to the above, the example models a receiver that uses

  • Least-squares channel estimation with interpolation

  • Minimum-mean-squared-error (MMSE) based criteria for codebook selection when precoding matrix indicator (PMI) feedback is enabled,

  • MMSE-based linear MIMO receiver, and

  • Two-stage early termination channel decoder [ 8 ].

The Simulink model uses colors to highlight the purpose of the different model components:

  • blocks highlighted in orange correspond to the downlink channel processing components,

  • blocks highlighted in light blue correspond to the modeling harness,

  • blocks highlighted in cyan aid in verification and visualization, and

  • blocks in yellow allow for user interaction.

The model highlights the frequency division duplex (FDD) mode of the specifications and thus uses a radio frame of 10ms composed of 10 subframes. Each subframe of 1ms duration has two consecutive slots.

The Simulink model processes one subframe per time step.

The downlink shared channel processing at the base station (eNodeB) includes transport channel processing and physical channel processing (PDSCH), with corresponding duality at the receiver (UE) to retrieve the transmitted data bits. The following sub-sections briefly describe the processing involved, with reference to the relevant sections of the specifications [ 1-6 ].

Transport Channel Processing

Transport channels provide the interface between the MAC layer and the physical layer. The Downlink Shared Channel (DL-SCH) is the main downlink transport channel type in LTE. It is used for both user data and dedicated control information as well as part of downlink system information.

This example models a two codeword transmission, i.e. two transport blocks per transmission time interval (TTI), with both codewords having the same size, modulation and code rate. Each codeword corresponds to a single transport block.

CRC insertion per transport block

The example calculates and appends a 24-bit CRC to each generated transport block. This allows for detection of errors at the receive end for the decoded block.

Code-block segmentation and per code-block CRC insertion

Due to the turbo-coding interleaver block lengths supported by LTE (a maximum of 6144 bits), any transport block that exceeds this size is segmented into smaller code-blocks. Based on the link parameters configured and the transport block size determined, the example determines the number of segments (code-blocks) and processes them sequentially (TB Channel Coding blocks). Based on the sizes that Section of [ 3 ] specifies, no filler bits are necessary as part of the segmentation process. For multiple code-blocks per transport block, the example calculates and appends a 24-bit CRC to each code block. This allows for early detection of correctly decoded code blocks, and, as a result, early termination of the iterative decoding for that code block. Refer to commLTETurboDecodercommLTETurboDecoder - a MATLAB-authored System object which implements the decoding per code-block.

Channel coding

DL-SCH uses turbo coding as the channel coder. The Parallel Concatenated Convolutional Coding: Turbo Codes example describes this further in detail.

Rate Matching

Rate matching extracts the exact set of bits to be transmitted within a subframe from the encoded bits. This example implements the sub-block interleaving, creation of the circular buffer and the actual bit selection using UE Category 5 parameters (Table 4.1-1 of [ 5 ]). The multiple code-blocks are then concatenated together for downstream physical channel processing.

Physical Channel (PDSCH) Processing

A physical channel corresponds to a set of time-frequency resources used for transmission of a particular transport channel. Each transport channel maps to a corresponding physical channel. The Physical Downlink Shared Channel (PDSCH) is the main physical channel used for unicast data transmission. This example uses spatial multiplexed codebook-based transmission, and, as a result, the downlink physical channel processing includes:


The transport channel encoded bits are scrambled by a bit-level scrambling sequence (Section 7.2 and 6.3.1 of [ 1 ]). The scrambling sequence depends on the physical layer cell identity to ensure interference randomization between cells. For the single-user single cell downlink transmission, the example assumes a cell ID, but differentiates the sequence per transmitted codeword.

Data Modulation

Downlink data modulation converts the scrambled bits into complex modulated symbols. The set of modulation schemes supported include QPSK, 16QAM and 64QAM, corresponding to two, four, and six bits per modulation symbol respectively (Section 7.1 and 6.3.2 of [ 1 ]). The modulation scheme is chosen by the PDSCH modulation type parameter on the Model Parameters block.

Layer Mapping

The complex modulated symbols from both codewords are mapped to layers (antenna ports) as per Section of [ 1 ]. Since full rank transmission is assumed, the number of layers is equal to the number of transmit antennas (the latter determined from the Antenna configuration parameter on the Model Parameters block).

Codebook-based Precoding

The modulated symbols per layer are precoded using the codebooks specified in Section of [ 1 ]. For two antennas (layers), the DFT-based codebook is used which allows for only two entries, while for four antennas (layers) 16 entries from the Householder matrix are used. The parameters Enable PMI feedback and Codebook index on the Model Parameters block allow selection of the codebook based on feedback from UE or initial user-specification. This example does not model any of the control signals used to convey the codebook index from eNodeB to UE and in the case of feedback, from UE back to eNodeB (i.e. assumes an error free transmission for the index).

Resource Element Mapping

The precoded symbols to be transmitted on each antenna are mapped to the resource elements of the resource blocks available for transmission. The number of available resource blocks is a function of the Channel bandwidth parameter on the Model Parameters block, as per the table below (reproduced from [ 6 ])

For the chosen configuration, each resource block corresponds to 12 sub-carriers, which at 15 KHz subcarrier spacing amounts to 180 KHz of spectrum. Hence, at 20 MHz channel bandwidth, the 100 available resource blocks occupy 18 MHz of channel bandwidth.

The actual number of data symbols mapped to resource elements per subframe depends on the

  • resource elements occupied by Cell-Specific Reference (CSR) signals used for channel estimation

  • control signaling region (PDCCH)

  • resource elements occupied by primary (PSS) and secondary (SSS) synchronization signals

  • resource elements occupied by transmission of the broadcast channel (PBCH).

Since some of these signals are not transmitted every subframe, the size of the data payload varies over the subframes in a radio frame.

Cell-Specific Reference Signals

The most basic of the LTE reference signals, Cell-Specific Reference (CSR) signals are specified for one, two, or four antennas in a cell and used for channel estimation at the receiver.

This example models the structure of CSR signals, per resource block, used for two and four antennas, as shown below (reproduced from [ 1 ])

Note that for the resource element carrying the reference signal for an antenna, the corresponding resource elements in other antennas have null transmissions. This allows the CSR signals to transmit without interference from the other antenna transmissions.

Also observe the reference-symbol density of the reference signals for third and fourth antennas is lower, compared to the density of the first and second antennas. This has the effect of reducing the overhead for higher number of antennas and also limiting the ability to track fast channel variations.

OFDM Transmission

The complex-valued time-domain OFDM signal per antenna is generated from the fully populated resource grid, using the OFDM Modulator block. The number of FFT points depends on the channel bandwidth specified, as per Table F.5.3-1 of [ 4 ]. For normal cyclic prefix, the seven OFDM symbols in a slot use different cyclic prefix lengths.

MIMO Channel Model

The MIMO Fading Channel block implements the MIMO fading profiles as per Annex B.2 of [ 4 ]. The higher mobility profiles are excluded as the closed-loop spatial multiplexing mode would be applicable to high data rate and low mobility scenarios only. It uses the comm.LTEMIMOChannelcomm.LTEMIMOChannel System object and the comm.MIMOChannelcomm.MIMOChannel System object, with low correlation setting between the multiple links.

Refer to the accompanying component model LTEPDSCHExample.slxLTEPDSCHExample.slx for parameteric control of the correlation levels for LTE MIMO channel profiles.

Receiver (UE) Processing

The main elements of the receiver processing (at the UE) modeled in this example include:

OFDM receiver - undoes the unequal cyclic prefix lengths per OFDM symbol in a slot and converts back to the time- and frequency-domain grid structure, using the OFDM Demodulator block.

MIMO receiver subsystem which includes:

  1. Channel Estimation employs least-squares estimation using averaging over a subframe for noise reduction for the reference signals, and linear interpolation over the subcarriers for the data elements. This uses the CSR signals for the channel estimates.

  2. Codebook selection employs the minimum-mean-squared-error (MMSE) criterion to calculate the codebook index per subframe [ 9 ]. When the Enable PMI Feedback parameter is on, this index is fed back to the transmitter for use at the next time step. Otherwise, the user-specified codebook index is used for the duration of the simulation. The feedback granularity modeled is once for the whole subframe (wideband) and applied to the next transmission subframe.

  3. MIMO receiver employs a linear MMSE receiver to combat the interference from the multiple antenna transmissions.

Soft-decision demodulation is employed per codeword to facilitate downstream turbo decoding.

Two-stage early termination channel decoding to decode the received blocks of data (TB Channel Decoding blocks). The Disable transport-block level early termination parameter on the Model Parameters block controls whether to fully decode the transport block. The per code-block early termination of the iterative decoding is always on. Refer to the accompanying component model LTEDLSCHExample.mdlLTEDLSCHExample.mdl for direct parametric control on the transport block length, the two-stage decoding and its effect on simulation.

Assumptions and Simplifications

For the simulation, the following assumptions and simplifications are made:

  • Single-user downlink transmission (NcellID = 0, RNTI = 1)

  • No HARQ support (redundancy version number, rvIdx = 0)

  • Normal cyclic prefix which specifies seven OFDM symbols per slot

  • Full bandwidth data allocation based on user selection of the channel bandwidth via the Model Parameters block

  • Constant, user-specifiable control region for the duration of the simulation

  • Localized resource mapping only

  • Resource grid filling accounts for PDCCH, PBCH channels and PSS, SSS signals but does not model the individual signals. This allows for data throughput measurements without affecting the receiver processing for the data symbols.

  • Full rank modeling only, i.e. a 2-by-2 antenna configuration has 2 layers and a 4-by-4 antenna configuration has 4 layers. As a consequence, rank estimation is not modeled.

  • The transport block size is predetermined based on the specified parameters, using min|R -(A+24)/N| where R is the target coding rate, A is the transport block size as per Section of [ 3 ] and N is the number of PDSCH data bits available for the given allocation and configuration.

  • Baseband processing only with no RF component modeling.

  • Aside from the feedback of the precoding matrix indicator and variable-size data payloads, the model does not adapt any other attribute during a simulation run.

Results and Displays

For the chosen parameters, the following displays validate and verify the modeling during simulation:

  • Bit error rate meters for PDSCH bits per codeword (PBER)

  • Block error rate meters for the transport blocks (BLER)

  • Bit error rate meters for the data bits per codeword (CBER)

  • Received signal scatter plots per received antenna after OFDM receiver processing

and after MIMO receiver processing.

The figures above show the results for the default configuration of the model. Comparing the two sets of plots enables you to gauge the signal separation the MIMO receiver achieves, which directly impacts the PDSCH bit error rate performance.

  • Transmitted and received signal spectrum. Comparing both the spectrum plots per subframe highlights the frequency selectivity in the fading channel over time. Note that only the last OFDM symbol in a subframe is displayed.

  • Codebook index signal scope - allows you to see the variation in the applied codebook when feedback is enabled

  • Maximum throughput per codeword over a simulation run

Upon completion of the simulation, two 3D plots display the number of decoding iterations used per code-block per transport block over time (less than or equal to the maximum default value of eight).

These plots help you validate the maximum decoding iterations parameter value used for turbo decoding.

Also, the workspace variables cbFlags1 and cbFlags2 hold the error status for each code-block per transport block over time (1 for an error, 0 for no error, for each of the code blocks in the transport blocks). For the example's default settings, observe the transport blocks in error per codeword, for the whole simulation run.

errCW1 =

   Empty matrix: 0-by-30

errCW2 =

   Empty matrix: 0-by-30

These values also match the displayed transport block error rate per codeword.

Further Exploration

This example offers insight into the required processing of the 4G LTE system with some parameter control on the transmitter, channel and receiver subsystems. It enables one to study the dependent attributes and their effect on the link performance with bit error rate and block error rate as the figure of merits. The example showcases features such as

  • Variable-sized signals in Simulink,

  • Communications System Toolbox System objects and blocks,

  • MATLAB-authored System objects, and

  • MATLAB Function block for simpler control flow modeling in Simulink.

Some areas of user exploration include

  • Use the Model Parameters block to configure different fixed reference measurement channels as per Tables A. and A. of [ 4 ] and analyze the system performance for different channel conditions and receiver parameters. Since the example does not model the transmission of system information blocks (SIB) in subframe 5, the throughput measures are higher for the example than shown in the tables. Also for four antenna ports, since Table A. assumes transmit diversity, the payload sizes are different for the example.

  • Use the component model LTEPDSCHExample.slxLTEPDSCHExample.slx to analyze the physical channel processing without the effects of channel coding. It additionally offers control of the correlation levels between the multiple fading links and allows you to assess the BER performance over the multiple LTE MIMO channel profiles.

  • Use the component model LTEDLSCHExample.mdlLTEDLSCHExample.mdl to analyze the transport channel processing without the effects of physical channel processing. It additionally offers control on the transport block length allowing verification of the channel coding at the individual code-block level.

  • Experiment with the alternate algorithms provided (e.g. codebook selection criteria and/or the linear MIMO receiver functions) by uncommenting the code or trying one of your own. The use of MATLAB code enables you to study the existing implementation and modify algorithms with ease.

For complete LTE link modeling in MATLAB, including uplink processing and TDD support, refer to the LTE System Toolbox product.

Selected References

  1. 3GPP Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Physical channels and Modulation (Release 10)", 3GPP TS 36.211 v10.7.0 (2013-02)

  2. 3GPP Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Multiplexing and channel coding (Release 10)", 3GPP TS 36.212 v10.8.0 (2013-06).

  3. 3GPP Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Physical layer procedures (Release 10)", 3GPP TS 36.213 v10.12.0 (2014-03).

  4. 3GPP Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); User Equipment(UE) radio transmission and reception (Release 10)", 3GPP TS 36.101 v10.14.0 (2014-03).

  5. 3GPP Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); User Equipment(UE) radio access capabilities (Release 10)", 3GPP TS 36.306 v10.11.0 (2013-12).

  6. 3GPP Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Base station radio transmission and reception (Release 10)", 3GPP TS 36.104 v10.11.0 (2013-07).

  7. E. Dahlman, S. Parkvall, and J. Skold, "4G LTE/LTE-Advanced for Mobile Broadband", Elsevier, 2011.

  8. Cheng, J.-F., "Two-Level Early Stopping Algorithm for LTE Turbo Decoding", IEEE 68th Vehicular Technology Conference, 2008, pp. 1-5.

  9. D. J. Love & R. W. Heath, "Limited Feedback Unitary Precoding for Spatial Multiplexing Systems", IEEE Trans. Info. Theory, Vol. 51, No. 8, Aug 2005, pp. 2967-2976.

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