Space-Time Block Codes

Space-Time Block codes distribute communication symbols over multiple antennas and time slots. They can be configured by adding an instance to the SymbolPrecoding of a Modem exposed by the precoding attribute.

The following example shows how to configure a modem with a Alamouti precoder within a \(2\times 2\) MIMO communication link:

# Create a new simulation featuring a 2x2 MIMO link between two devices
simulation = Simulation()
tx_device = simulation.new_device(
    antennas=SimulatedUniformArray(SimulatedIdealAntenna(AntennaMode.TX), 0.1, (2,)),
)

rx_device = simulation.new_device(
    antennas=SimulatedUniformArray(SimulatedIdealAntenna(AntennaMode.RX), 0.1, (1,)),
)

# Create a link between the two devices
link = SimplexLink()
link.connect(tx_device, rx_device)

# Configure a single carrier waveform
waveform = RootRaisedCosineWaveform(
    oversampling_factor=4,
    symbol_rate=1e6,
    num_preamble_symbols=16,
    num_data_symbols=32,
    modulation_order=64,
    roll_off=.9,
    channel_estimation=SingleCarrierIdealChannelEstimation(simulation.scenario.channel(tx_device, rx_device), tx_device, rx_device),
)
link.waveform = waveform

# Configure the precoding
link.transmit_symbol_coding[0] = Alamouti()
link.receive_symbol_coding[0] = Alamouti()

Note that Alamouti precoding requires channel state information at the receiver, therefore waveform’s channel_estimation attribute must be configured.

The following example shows how to configure a modem with a Ganesan precoder within a \(4\times 4\) MIMO communication link:

# Create a new simulation featuring a 4x4 MIMO link between two devices
simulation = Simulation()
tx_device = simulation.new_device(
    antennas=SimulatedUniformArray(SimulatedIdealAntenna(AntennaMode.TX), 0.1, (4,)),
)

rx_device = simulation.new_device(
    antennas=SimulatedUniformArray(SimulatedIdealAntenna(AntennaMode.RX), 0.1, (4,)),
)

# Create a link between the two devices
link = SimplexLink()
link.connect(tx_device, rx_device)

# Configure a single carrier waveform
waveform = RootRaisedCosineWaveform(
    oversampling_factor=4,
    symbol_rate=1e6,
    num_preamble_symbols=16,
    num_data_symbols=32,
    modulation_order=64,
    roll_off=.9,
    channel_estimation=SingleCarrierIdealChannelEstimation(simulation.scenario.channel(tx_device, rx_device), tx_device, rx_device),
)
link.waveform = waveform

# Configure the precoding
link.transmit_symbol_coding[0] = Ganesan()
link.receive_symbol_coding[0] = Ganesan()

Note that Ganesan precoding requires channel state information at the receiver, therefore waveform’s channel_estimation attribute must be configured.

class Alamouti

Bases: TransmitSymbolEncoder, ReceiveSymbolDecoder, Serializable

Alamouti precoder distributing symbols in space and time.

Support for 2 transmit antennas only. Refer to Alamouti[1] for further information.

decode_symbols(symbols, num_output_streams)

Decode data for STBC with 2 antenna streams

Received signal with equal noise power is assumed, the decoded signal has same noise level as input.

Parameters:

• symbols (StatedSymbols) – Input signal with \(N \times K\) symbol blocks.

• num_output_streams (int) –

  Number of required streams resulting from the decoding process.

  Will be ignored by this decoder.

Return type:

StatedSymbols

Returns: Decoded data with size \(N \times K\)

encode_symbols(symbols, num_output_streams)

Encode data into multiple antennas with space-time/frequency block codes.

Parameters:

• symbols (StatedSymbols) – Input signal featuring \(K\) blocks.

• num_output_streams (int) – Number of required streams resulting from the encoding process. Should always be 2 for Alamouti encoding.

Return type:

StatedSymbols

Returns: Encoded data with size \(2 \times K\) symbols

Raises:

• ValueError – If more than a single symbol stream is provided.

• ValueError – If the number of transmit antennas is not two.

• ValueError – If the number of data symbols is not even.

num_receive_output_streams(num_input_streams)

Get required number of output streams during decoding.

Parameters:

num_input_streams (int) – Number of input streams.

Return type:

int

Returns: The number of output streams. Negative numbers indicate infeasible configurations.

property num_receive_input_symbols: int

Required number of input streams during decoding.

property num_receive_output_symbols: int

Resulting number of output streams after decoding.

property num_transmit_input_symbols: int

Required number of input streams during encoding.

property num_transmit_output_symbols: int

Resulting number of output streams after encoding.

class Ganesan

Bases: TransmitSymbolEncoder, ReceiveSymbolDecoder, Serializable

Girish Ganesan and Petre Stoica general precoder distributing symbols in space and time.

Supports 4 transmit antennas. Features a \(\frac{3}{4}\) symbol rate. Refer to Ganesan and Stoica[2] for further information.

decode_symbols(symbols, num_output_streams)

Decode data for STBC with 4 antenna streams Note that Ganesan schema’s symbol rate is \(\frac{3}{4}\) so the decoding process decreases the number of blocks by \(\frac{3}{4}\).

Parameters:

• symbols (StatedSymbols) – Input signal with \(4 \times N\) symbol blocks.

• num_output_streams (int) – Number of required streams resulting from the decoding process. Will be ignored by this decoder.

Return type:

StatedSymbols

Returns:

Decoded data with size \(3 \times N\) Returned channel states are initialized with ones (np.ones is used).

encode_symbols(symbols, num_output_streams)

Encode data into multiple antennas with space-time/frequency block codes. Note that Ganesan schema’s symbol rate is \(\frac{3}{4}\) so the encoding process increases the number of blocks by \(\frac{4}{3}\).

Parameters:

• symbols (StatedSymbols) – Input signal featuring \(K\) blocks.

• num_output_streams (int) – Number of required streams resulting from the encoding process. Should always be 4 for Ganesan encoding.

Return type:

StatedSymbols

Returns:

Encoded data with size \(\frac{4}{3} \times K\) symbol blocks. Thus num_blocks is changed to num_blocks / 3 * 4. Returned channel states are initialized with ones (np.ones is used).

Raises:

• ValueError – If more than a single symbol stream is provided.

• RuntimeError – If the number of transmit antennas is not four.

• ValueError – If the number of data symbols blocks is not divisable by three.

num_receive_output_streams(num_input_streams)

Get required number of output streams during decoding.

Parameters:

num_input_streams (int) – Number of input streams.

Return type:

int

Returns: The number of output streams. Negative numbers indicate infeasible configurations.

property num_receive_input_symbols: int

Required number of input streams during decoding.

property num_receive_output_symbols: int

Resulting number of output streams after decoding.

property num_transmit_input_symbols: int

Required number of input streams during encoding.

property num_transmit_output_symbols: int

Resulting number of output streams after encoding.

[1]

S.M. Alamouti. A simple transmit diversity technique for wireless communications. IEEE Journal on Selected Areas in Communications, 16(8):1451–1458, 1998. doi:10.1109/49.730453.

[2]

G. Ganesan and P. Stoica. Space-time block codes: a maximum snr approach. IEEE Transactions on Information Theory, 47(4):1650–1656, 2001. doi:10.1109/18.923754.