Demodulate timedomain OFDM samples and return LTE resource grid
Wireless HDL Toolbox / Modulation
The LTE OFDM Demodulator block implements an algorithm for demodulating LTE signals specified by LTE standard TS 36.212 [1]. The block returns the LTE resource grid that is used for cell ID detection, master information block (MIB) recovery, system information block (SIB)1 recovery, and further decoding.
You can select the number of downlink resource blocks (NDLRB) and choose either normal or extended cyclic prefix (CP), as described in the LTE standard. The block implements a CP fraction to support windowed LTE transmission and provides a parameter to configure the location of prefix removal.
The block provides an interface and architecture suitable for HDL code generation and hardware deployment.
The block accepts input data either at maximum rate of 30.72 MHz, or at a sample rate corresponding to NDLRB. The input sampling rates for NDLRB 6, 15, 25, 50, 75, and 100 are 1.92 MHz, 3.84 MHz, 7.68 MHz, 15.36 MHz, 30.72 MHz, and 30.72 MHz, respectively. The block uses a 2048point fast fourier transform (FFT) for all values of NDLRB and returns the number of resource grid samples needed for the selected NDLRB. By default, the block excludes the direct current (DC) carrier.
The latency from the first input sample to the first output sample depends on your selection of the NDLRB and type of cyclic prefix, as shown in this table.
Maximum Sample Rate  Corresponding to NDLRB Sample Rate  

NDLRB  Latency — Normal CP  Latency — Extended CP  Latency — Normal CP  Latency — Extended CP 
6  5295  5647  6654  6676 
15  5241  5593  6520  6564 
25  5181  5533  6660  6748 
50  5031  5383  6700  6876 
75  4881  5233  6930  7282 
100  4731  5083  6780  7132 
data
— Input dataInput data, specified as a signed real or complex number.
double
and single
data
types are supported for simulation, but not for HDL code generation.
Data Types: single
 double
 int8
 int16
 int32
 signed fixed point
Complex Number Support: Yes
valid
— Indicates valid input dataBoolean
scalarControl signal that indicates when the sample from the
data input port is valid. When this value is
1
(true), the block captures the values on the
data input port. When this value is
0
(false), the block ignores the input
data samples.
Data Types: Boolean
NDLRB
— Number of downlink resource blocks6
 15
 25
 50
 75
 100
Number of downlink resource blocks, specified as 6
,
15
, 25
, 50
,
75
, or 100
. NDLRB must be one
of these six values specified by LTE standard TS 36.212 [1].
The block samples this port at the start of each subframe and ignores
any changes within a subframe.
To enable this port, set the NDLRB source
parameter to Input port
.
Data Types: uint8
 uint16
 uint32
 fixdt(0,K,0), K >= 7
 single
 double
cyclicPrefixType
— Type of CPType of CP, specified as a Boolean
scalar. When this value is
0
(false), the block selects normal CP. When this value is
1
(true), the block selects extended CP. The block samples this
port at the start of each subframe and ignores any changes within a subframe.
To enable this port, set the Cyclic prefix source parameter
to Input port
.
Data Types: Boolean
reset
— Clear internal statesClears internal state, specified as a Boolean
scalar. When this value is 1
(true), the block stops
the current calculation and clears all internal states. When this value
is 0
(false), and the valid
input value is 1
(true), the block begins a new
subframe.
To enable this port, select the Enable reset input port parameter.
Data Types: Boolean
data
— Output dataOutput data, returned as a signed real or complex number. The data type is the same as the data type of the input data port. When you clear the Divide butterfly outputs by two parameter, the output word length increases by 11 bits to avoid overflow.
Data Types: single
 double
 int8
 int16
 int32
 signed fixed point
Complex Number Support: Yes
valid
— Indicates valid output dataControl signal that indicates when the data
output port is valid. The block sets this value to 1
(true) when the resource grid samples are available on the
data output port. When Remove DC
subcarrier is selected, this value is set to
0
(false) at the center of the output samples to
exclude the DC carrier.
Data Types: Boolean
ready
— Indicates block is readyControl signal that indicates when the block is ready for new input
data. When this value is 1
(true), the block accepts
input data in the next time step. When this value is
0
(false), the block ignores input data in the
next time step.
To enable this port, set the Input data sample
rate parameter to Match input data
sample rate to NDLRB
.
Data Types: Boolean
NDLRB source
— Source of NDLRBProperty
(default)  Input port
You can set NDLRB with an input port or by selecting a value for the
parameter. To enable the NDLRB parameter, select
Property
. To enable the
NDLRB port, select Input
port
.
NDLRB
— Number of downlink resource blocks6
(default)  15
 25
 50
 75
 100
Number of downlink resource blocks, specified as 6
,
15
, 25
, 50
,
75
, or 100
. NDLRB must be one
of these six values specified by LTE standard TS 36.212 [1].
To enable this parameter, set the NDLRB
source parameter to
Property
.
Cyclic prefix source
— Source of cyclic prefix typeProperty
(default)  Input port
You can set the cyclic prefix by selecting a parameter value or using
an input port. To enable the Cyclic prefix type
parameter, select Property
. To enable the
cyclicPrefixType port, select
Input port
.
Cyclic prefix type
— Type of cyclic prefixNormal
(default)  Extended
Type of cyclic prefix, specified as Normal
or Extended
.
To enable this parameter, set the Cyclic prefix
source parameter to
Property
.
CP fraction
— Percent of cyclic prefix to remove0.55
(default)  value from 0 to 1Cyclic prefix fraction, specified as a value from 0 to 1, inclusive. This parameter specifies the percentage of CP samples that the block removes from the start of the OFDM symbol. The block shifts the remaining CP samples to the end of the OFDM symbol.
When this parameter is 0.55
, the block removes 55%
of the CP from the beginning of the symbol, and shifts 45% to the end of
the symbol. When you set this parameter to 1
, the
block removes 100% of the CP from the start of the OFDM symbol, and does
not shift any samples to the end.
CP fraction provides windowed LTE transmission
support. When a transmitter applies windowing, symbols are cyclically
extended and overlapped. In a receiver design, the best location to
remove the prefix and extract the symbol depends on windowing settings
at the transmitter. For more information on windowing for an LTE
transmitter, see the Algorithms section of lteOFDMModulate
(LTE Toolbox)
function.
Remove DC subcarrier
— Exclude or include DC subcarrieroff
(default)  on
When you select this parameter, the block excludes the DC subcarrier
in the resource grid output. The DC subcarrier is present at the center
of the 12×NDLRB subcarriers. The block excludes the DC subcarrier by
setting the valid signal low
(false
) for the center cycle of the output
subcarriers.
Enable reset input port
— Reset signaloff
(default)  on
Select this parameter to enable the reset port on the block icon.
Input data sample rate
— Input sample rateUse maximum input data sample
rate
(default)  Match input data sample rate to
NDLRB
This parameter specifies the type of sample rate to select for the input data.
To provide an input data sample rate of 30.72 MHz, select
Use maximum input data sample
rate
.
To provide an input data sample rate based on the
NDLRB parameter, select
Match input data sample rate to
NDLRB
. The input sampling rates for
NDLRB values 6
,
15
, 25
,
50
, 75
, and
100
are 1.92 MHz, 3.84 MHz, 7.68 MHz,
15.36 MHz, 30.72 MHz, and 30.72 MHz, respectively.
For more information, see Data Rate Controller.
Divide butterfly outputs by two
— Divide FFT butterfly outputs by twooff
(default)  on
This parameter controls the scaling option of the FFT HDL Optimized (DSP System Toolbox) block inside the LTE OFDM Demodulator.
When you select this parameter, the FFT implements an overall 1/N scale factor by dividing the output of each butterfly multiplication by two. This adjustment keeps the output of the FFT in the same amplitude range as its input. If you disable this parameter, the block avoids overflow by increasing the word length by one bit after each butterfly multiplication.
Rounding Method
— Rounding mode for internal fixedpoint calculationsFloor
(default)  Ceiling
 Convergent
 Nearest
 Round
 Zero
This parameter specifies the type of rounding mode for internal
fixedpoint calculations. For more information about rounding modes, see
Rounding
Modes (DSP System Toolbox). When the input is any integer data type or fixedpoint
data type, the FFT algorithm uses fixedpoint arithmetic for internal
calculations. This parameter does not apply when the input is of data
type single
or double
. Rounding
applies to twiddlefactor multiplication and scaling operations.
The LTE OFDM Demodulator block operation sequence is carried over using these blocks: Data Rate Controller, CP Prefix Removal, Sample Repeater, FFT Shift, FFT, and Resource Grid Selection. The Data Rate Controller block helps in controlling the input data rate by generating a ready signal. The CP Removal block removes the part of the CP at the start of a symbol and the remainder of the CP at the end of the symbol. The Sample Repeater block repeats the samples based on the NDLRB values. The block repeats the samples until they form 2048 samples and converts the input data rate to the maximum rate supported by LTE. The FFT Shift block performs a timedomain FFT shift. The FFT block converts the frequencydomain signal to a timedomain signal. The Resource Grid Selection block extracts the resource grid elements based on the NDLRB and the input data sample rate, and provides the demodulated output. The parameters shown in this figure configure the behavior of the block.
The block accepts input data either at maximum rate of 30.72 MHz, or at a sample rate corresponding to NDLRB. The input sampling rates for NDLRB values 6, 15, 25, 50, 75, and 100 are 1.92 MHz, 3.84 MHz, 7.68 MHz, 15.36 MHz, 30.72 MHz, and 30.72 MHz, respectively.
When you set the Input data sample rate parameter to
Use maximum input data sample rate
, the block
operates based on the demodulation parameters (NDLRB and
CP prefix type) and provides output data along with an
output valid signal to the next block.
When you set the Input data sample rate parameter to
Match input data sample rate to NDLRB
, the block
generates an output ready signal and controls the input at a
rate with respect to the NDLRB. The block accepts data samples with respect to the
NDLRB when the ready signal is 1
(true).
This figure shows the timing diagram of the ready signal
generation for a continuous input when NDLRB is
6
and CP prefix type is
Normal
, having FFT length as 128 and CP length as
10.
numHigh = FFT length + CP length = 128 +10 = 138 clock cycles.
numLow = Maximum FFT length + Maximum CP length  (numHigh) = 2048 + 160  (138) = 2070 clock cycles.
This figure shows the timing diagram of the ready signal
generation for a discrete input with 1
(high) for 16 clock cycles
when NDLRB is 6
and CP
prefix type is Normal
, having FFT length
as 128 and CP length as 10.
numHigh = (FFT length + CP length 1) * Maximum FFT length / FFT length + 1 = (128 +10 1) * 16 + 1 = 2193 clock cycles.
numLow = Maximum FFT Length + Maximum CP Length  (numHigh) = 2048 + 160  (2193) = 15 clock cycles.
This block supports windowed LTE transmission by implementing fractional cyclic prefix removal. Windowing reduces outofband emissions. A transmitter performs windowing by overlapping the tail of each OFDM symbol with the head of the next OFDM symbol. A receiver must avoid these overlapped samples in the FFT calculation. Fractional CP solves this problem by removing part of the CP at the start of a symbol and the remainder of the CP at the end of the symbol. Implementing a CPfraction algorithm also makes the LTE OFDM Demodulator block less sensitive to timing offset.
The Cyclic prefix type parameter controls whether the block expects normal or extended CP. When the block operates at a maximum sample rate of 30.72 MHz, it assumes that each symbol is 2048 samples plus the cyclic prefix size associated with that rate. When using normal CP, the prefix of the first symbol in each slot has 160 samples, while subsequent symbols have a prefix of 144 samples. The extended CP has 512 samples.
When the block operates at sample rates with respect to the NDLRB value, for example, if the NDLRB is 6, the block receives 128 samples plus the cyclic prefix size associated with that rate. When using normal CP, the prefix of the first symbol in each slot has 10 samples, while subsequent symbols have a prefix of nine samples. The extended CP has 32 samples.
The block handles the CP in two stages. First, the block calculates the number of CP samples to remove, Nr, and removes those samples from the input samples. Next, it calculates the number of samples to shift, Ns, and shifts those samples to the end of OFDM symbol in the time domain. These two segments together make up the total cyclic prefix length, Ncp = Ns + Nr.
The CP fraction parameter controls how many samples the block
removes at the beginning of the symbol. The block shifts the remainder of the cyclic
prefix from the start of the symbol to the end of the symbol. The block quantizes
CP fraction to fi(0,11,10)
. To achieve
an integer number of samples, the block calculates Nr =
floor
(Ncp * CP
fraction).
The waveform shows the control signals for the two stages of CP removal. The block
is configured for a normal CP, so the CP of the first symbol is 160 samples. The CP
for subsequent symbols is 144 samples. The CP fraction is
0.55
.
In stage one, the block sets the internal valid signal to
0
(false
) to exclude the first
Nr samples of the symbol. For the first symbol,
Nr = 88. Manipulation of the valid
signal also excludes the final Ns samples, which are replaced by
the shifted samples in the next stage. For the first symbol, Ns =
72. In stage two, the block writes the Ns samples to a RAM, and
then reads and returns these samples at the end of the symbol. The block shifts the
internal valid signal to include the shifted samples in their
new location. The result is 2048 samples, properly aligned in the time domain in
preparation for an FFT.
For the second symbol, with a cyclic prefix of 144 samples, Nr = 80 and Ns = 64.
For more information on LTE transmitter windowing, see the Algorithms section of
the lteOFDMModulate
(LTE Toolbox) function.
As the LTE OFDM Demodulator block uses a maximum FFT length of 2048. So, when the input samples corresponding to the actual FFT length are provided, the Sample Repeater block repeats the samples until it forms 2048 samples. For this operation, the block buffers the input samples first, and then repeats the samples based on the NDLRB value. This repetition mechanism helps avoid scaling at the FFT block input. For example, if the NDLRB is 6, each OFDM symbol consists of 128 samples. The block converts these 128 samples to 2048 samples by repeating them 16 times. After the block generates 2048 data samples, it sends data and valid signals to the next block.
Conventionally, receivers perform FFT shift in the frequency domain. However, this method requires memory and introduces latency related to the size of the FFT. Instead, a receiver can execute the same operation in the time domain using the frequency shifting property of Fourier transforms. Shifting a function in one domain corresponds to a multiplication by a complex exponential function in the other domain. To reduce hardware resources and latency, this block performs the FFT shift by multiplying the timedomain samples by a complex exponential function.
These equations describe an FFT shift. The equation for an Npoint FFT is
$$X(k)=F[x(n)]={\displaystyle \sum _{n=0}^{N1}x(n){e}^{\frac{j2\pi nk}{N}}}$$
For an FFT shift of N/2 carriers in either direction, substitute $$k=k\frac{N}{2}$$, resulting in
$$X(k{\scriptscriptstyle \frac{N}{2}})={\displaystyle \sum _{n=0}^{N1}x(n){e}^{\frac{j2\pi n(k{\scriptscriptstyle \frac{N}{2}})}{N}}}$$
This equation simplifies to
$$X(k\frac{N}{2})={\displaystyle \sum _{n=0}^{N1}{e}^{j\pi n}x(n){e}^{\frac{j2\pi nk}{N}}}$$
Since $$\sum _{n=0}^{N1}x(n){e}^{\frac{j2\pi nk}{N}}$$ is equivalent to $$F[x(n)]$$, and $${e}^{j\pi}=1$$, this equation simplifies to
$$X(k\frac{N}{2})=F[{{\displaystyle (1)}}^{n}x(n)]$$
The final equation shows that an FFT shift in the time domain simplifies to multiplication by (1)^{n}. Therefore, the block implements the FFT shift by multiplying the timedomain samples by either +1 or –1.
The output of the FFT shift subsystem is fed to an FFT HDL Optimized (DSP System Toolbox) block. The sample rate of the timedomain samples must be 30.72 MHz. The block calculates a 2048point FFT for all NDLRB values.
The Divide butterfly outputs by two parameter controls whether the FFT implements an overall 1/N scale factor by dividing the output of each butterfly multiplication by two. This adjustment keeps the output of the FFT in the same amplitude range as its input. When you disable scaling (default), the block avoids overflow by increasing the word length by one bit after each butterfly multiplication.
This part of the algorithm selects the appropriate number of subcarriers based on the NDLRB. Out of 2048 subcarriers, the block selects the center 12xNDLRB subcarriers for output.
If the Remove DC subcarrier parameter is selected, the block
excludes the DC subcarrier from the final resource grid output. The block excludes
the DC subcarrier by setting the valid signal to
0
(false) for the center cycle of the output
subcarriers.
For NDLRB 25, the block returns 12×25=300 resource grid samples. The block
indicates the location of these output samples with the
validOut signal set to 1
(true). The
validOut signal is 0
(false) at the
center of the output samples, to exclude the DC carrier.
This waveform shows the output when you set the Input data sample
rate parameter to Use maximum input data sample
rate
and select an NDLRB of 25 with normal CP.
This waveform shows the output of the block when you set the Input data
sample rate parameter to Match input data sample rate to
NDLRB
and select an NDLRB of 25 with normal CP. The block repeats
four times at the input of FFT for computing 2048point FFT. The actual FFT samples
are taken for every one in four samples at the output of FFT. The block chooses the
center (12×25 = 300) resource grid elements and outputs them along with valid
signal.
The performance of the synthesized HDL code varies with your target and synthesis
options. The input data type used for generating HDL code is
fixdt(1,16,14)
.
This table shows the resource and performance data synthesis results when using the block with default configuration. The generated HDL targeted to Xilinx^{®} Zynq^{®} XC7Z045IFFG9002L FPGA. The design achieves a clock frequency of 280 MHz.
Resource  Number Used 

LUTs  6072 
Registers  8291 
DSPs  16 
Block RAM  23 
F7 Muxes  0 
F8 Muxes  0 
RAMB36/FIFO  6 
RAMB18  18 
[1] 3GPP TS 36.212. "Multiplexing and channel coding." 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (EUTRA). URL: https://www.3gpp.org.
[2] Sesia, S., I. Toufik, and M. Baker, eds. LTE  The UMTS Long Term Evolution : From Theory to Practice. Hoboken, NJ: John Wiley & Sons Ltd., 2009.
This block supports C/C++ code generation for Simulink^{®} accelerator and rapid accelerator modes and for DPI component generation.
HDL Coder™ provides additional configuration options that affect HDL implementation and synthesized logic.
This block has a single, default HDL architecture.
ConstrainedOutputPipeline  Number of registers to place at
the outputs by moving existing delays within your design. Distributed
pipelining does not redistribute these registers. The default is

InputPipeline  Number of input pipeline stages
to insert in the generated code. Distributed pipelining and constrained
output pipelining can move these registers. The default is

OutputPipeline  Number of output pipeline stages
to insert in the generated code. Distributed pipelining and constrained
output pipelining can move these registers. The default is

You cannot generate HDL for this block inside a Resettable Synchronous Subsystem (HDL Coder).
LTE OFDM
Modulator  lteOFDMDemodulate
(LTE Toolbox)  lteOFDMModulate
(LTE Toolbox)
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