LTE Downlink PDSCH with Transmit Diversity

This example highlights LTE Downlink PDSCH processing with transmit diversity. It includes both the two transmit antenna and four transmit antenna configurations as per the LTE Release 10 specifications [ 1 ].

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, PDSCH, MIMO-OFDM, transmit diversity, SFBC, FSTD.


Transmit diversity employs multiple antennas at the transmitter to obtain diversity gains with no impact on the data rate. In essence, both schemes specified by LTE are full rate codes and offer increased performance benefits due to the diversity, when compared to single-antenna transmissions.

The key components this example highlights include

  • Variable-size payload generation

  • Bit-level scrambling

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

  • Layer mapping for two or four antennas, with SFBC encoding

  • Resource-element mapping

  • OFDM signal generation and

  • MIMO fading channel

In addition, this example models a receiver that uses

  • Least-squares channel estimation with interpolation. Alternatively, an ideal channel estimate based on the channel gains of the MIMO fading channel is also a configurable option for the link.

  • SFBC-based combining using the channel estimates.

  • Soft-decision demodulation and descrambling.

% Open the LTE Transmit Diversity Example GUI
h = LTETransmitDiversityExample;

The MATLAB GUI provides link configurability by allowing specification of the following parameters:

  • Channel bandwidth - one value out of 1.4, 3, 5, 10, 15 or 20 MHz

  • Control region size - in number of OFDM symbols in a subframe

  • Number of transmit antennas - either of 2 or 4 antennas

  • Number of receive antennas - one of 1, 2 or 4 antennas

  • PDSCH modulation type - one of QPSK, 16QAM, 64QAM for data

  • MIMO Rayleigh fading channel - either of User-defined or Frequency-flat static.

  • Maximum Doppler shift (Hz) - for a user-defined channel, any scalar value denoting the maximum Doppler shift in Hz

  • Path delay vector (Ts) - for a user-defined channel, a vector of integers specifying the path delays in multiples of the channel sample time. The length of this parameter indicates the number of multipaths modeled for the fading channel.

  • Average path gain vector (dB) - for a user-defined channel, a vector of path gain values in dB. The length of this parameter must be the same as the length of the path delay parameter.

  • Correlation level - for a user-defined channel, one of Low, Medium or High as per Section B.2.3 of the LTE specifications [ 3 ]. A frequency-flat static channel uses uncorrelated links with single-path and 0 maximum Doppler shift.

  • SNR (dB) - a scalar value denoting the SNR level for the link

  • Enable channel estimation checkbox. When left unchecked, the link uses the ideal channel estimates based on the channel path gains of the MIMO fading channel. When selected, the link uses least-squares estimates derived as a result of noise averaging over a subframe and interpolation along the frequency axis.

  • Number of subframes to simulate - a scalar that specifies the length of the simulation, measured in steps of 1ms corresponding to a subframe of data.

  • Enable constellation diagrams checkbox when enabled displays the constellation plots for the signals in the receiver processing chain (after OFDM reception and after SFBC-based combining).

  • Enable spectrum analyzer checkbox when enabled displays the spectrum for the transmitted and received signals. The spectrum display corresponds to the last OFDM symbol in a subframe.

The Simulate link button simulates the configured link and the GUI displays the link BER results. The MATLAB command window also displays the progression of the simulation.

The View MATLAB code button opens the simulator code in the Editor allowing for visual inspection and further exploration of the underlying functions used in the simulation.

The transmit diversity simulator 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 script processes one subframe worth of data in one loop iteration.

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 PDSCH processing modeled, with reference to the relevant sections of the LTE specifications [ 1-4 ]. This example omits the transport channel processing in the simulator and assumes the input to the PDSCH are the encoded bits from the transport 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. The Physical Downlink Shared Channel (PDSCH) is the main physical channel used for unicast data transmission. This example uses a single-codeword transmit diversity transmission over two or four transmit antennas, and, as a result, the downlink physical channel processing includes:


The source data bits (transport channel encoded bits) are scrambled by a bit-level scrambling sequence (Section 7.2 and 6.3.1 of LTE standard [ 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.

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 LTE standard [ 1 ]). You select the modulation scheme using the PDSCH modulation type parameter on the MATLAB GUI.

Layer Mapping and Precoding

The lteTDEncode.mlteTDEncode.m function combines the transmit diversity layer mapping and precoding as per Sections and of [ 1 ]). This function uses complex notation for signals and employs the comm.OSTBCEncodercomm.OSTBCEncoder System object from the Communications System Toolbox to implement the space-frequency block coding specified for LTE. For both two and four antenna schemes, the LTE specifications make use of the basic Alamouti code [ 6 ], applied over space and frequency dimensions with no rate reduction.

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 GUI, as per the table below (reproduced from LTE standard [ 4 ])

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 LTE standard [ 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, via using the comm.OFDMModulator System object. The number of FFT points depends on the channel bandwidth specified, as per Table F.5.3-1 of LTE standard [ 3 ]. For normal cyclic prefix, the seven OFDM symbols in a slot use different cyclic prefix lengths.

MIMO Channel

The simulator uses the comm.MIMOChannelcomm.MIMOChannel System object to model the Rayleigh fading over multiple links. You can select from a choice of frequency-flat static characteristic to one where the Maximum Doppler shift, path gains, path delays and correlation levels can be individually specified for each link. The path delays are constrained to be integer multiples of the channel input sample time.

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 comm.OFDMDemodulator System object.

Channel Estimation when selected, 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. As an alternative, an ideal channel estimation scheme is also provided which uses the channel gains from the MIMO fading channel. This ideal scheme can be used as a reference for performance evaluation of the actual estimation scheme.

Transmit Diversity Combining for the multiple transmitted signals is folded into the lteTDCombine.mlteTDCombine.m function which, similar to the encoder, uses complex notation for signals and employs the comm.OSTBCCombinercomm.OSTBCCombiner System object from the Communications System Toolbox.

The combined data stream is further demodulated and descrambled to get the received data bits.

Assumptions and Simplifications

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

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

  • Normal cyclic prefix which specifies seven OFDM symbols per slot.

  • Full bandwidth data allocation based on user selection of the channel bandwidth.

  • Constant, user-specifiable control region size 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.

  • Baseband processing only with no RF component modeling.

  • The multi-path delays for the fading channel are constrained to be multiples of the input channel sample time.

  • Aside from the variable-size data payloads, the simulator does not adapt any other attribute during a simulation run.

Results and Displays

For the chosen parameters, the following displays (if enabled) validate the processing during simulation:

  • Spectrum analyzer displays the transmitted and received signal spectrum. Comparing both the spectrum plots per subframe highlights the frequency selective-ness in the fading channel over time. Note, that only the last OFDM symbol in a subframe is displayed.

  • Received signal constellation diagrams - Comparing the pre- and post transmit diversity combining signals gives a visual cue to the link performance and the benefits of combining.

At the end of the simulation, the final bit-error-rate (BER) is displayed both on the GUI and the MATLAB command window, along with the total number of errors observed and the total number of bits processed.

% Suppress displays
handles = guidata(h);
handles.showSpectrum.Value = 0;
LTETransmitDiversityExample('showSpectrum_Callback', handles.showSpectrum, [], handles);
handles = guidata(h);
handles.showScopes.Value = 0;
LTETransmitDiversityExample('showScopes_Callback', handles.showScopes, [], handles);

% Simulate the default link
handles = guidata(h);
handles.simulate.Value = 1;
LTETransmitDiversityExample('simulate_Callback', handles.simulate, [], handles);
Simulating LTE Downlink PDSCH with Transmit Diversity
    Creating objects for simulation.
        Ideal channel gains will be used.
    Processing #1 subframe.
    Processing #2 subframe.
    Processing #3 subframe.
    Processing #4 subframe.
    Processing #5 subframe.
    Processing #6 subframe.
    Processing #7 subframe.
    Processing #8 subframe.
    Processing #9 subframe.
    Processing #10 subframe.
    Processing #11 subframe.
    Processing #12 subframe.
    Processing #13 subframe.
    Processing #14 subframe.
    Processing #15 subframe.
    Processing #16 subframe.
    Processing #17 subframe.
    Processing #18 subframe.
    Processing #19 subframe.
    Processing #20 subframe.
    Processing #21 subframe.
    Processing #22 subframe.
    Processing #23 subframe.
    Processing #24 subframe.
    Processing #25 subframe.
    Processing #26 subframe.
    Processing #27 subframe.
    Processing #28 subframe.
    Processing #29 subframe.
    Processing #30 subframe.
Elapsed time is 4.039235 seconds.
BER:              5.8571e-05
Number of errors: 46
Number of bits:   785376

Further Exploration

Use the simulator script LTETransmitDiversitySim.mLTETransmitDiversitySim.m to explore alternate link configurations on your own, to include either of

  • Single antenna transmission,

  • A different channel estimation scheme or

  • Full downlink processing, including the transport channel processing.

LTE PHY Downlink with Spatial Multiplexing describes a similar MATLAB-based simulator for LTE using spatial multiplexing: LTEDownlinkSim.mLTEDownlinkSim.m.

For complete LTE link modeling in MATLAB 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 v10.0.0 (2010-12)

  2. 3GPP Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Physical layer procedures (Release 10)", 3GPP TS 36.213 v10.0.0 (2010-12).

  3. 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 v10.0.0 (2010-10).

  4. 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 v10.0.0 (2010-09).

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

  6. S. M. Alamouti, "A simple transmit diversity technique for wireless communications," IEEE® Journal on Selected Areas in Communications, vol. 16, no. 8, pp. 1451-1458, Oct. 1998.

Was this topic helpful?