NonSquareDifferentialMIMO-IdealRayleigh-BER.py

This webpage introduces an API example for the noncohrent scenario, which uses NonSquareDifferentialMLDSimulator. Other examples are found in NonSquareDifferentialMLDSimulatorTest.

This example compares the BER performance of the differential star-QAM (SQAM), square diagonal unitary code (DUC), and nonsquare DUC schemes. The simulation parameters are given in the table below.

Performance Results

Simulation Parameters

Parameter	Value
Channel	Ideal Rayleigh fading
Number of transmit antennas	\(M=4\)
Number of receive antennas	\(N=4\)
Constellation size	\(L=16,65536\)
Transmission rate	\(R=4\) [bit/symbol]

Reproducible Code

import os
import sys
import numpy as np
import matplotlib.pyplot as plt
from imtoolkit import Parameters, Modulator, OSTBCode, DiagonalUnitaryCode, ADSMCode, IdealRayleighChannel, Basis, DifferentialMLDSimulator, SemiUnitaryDifferentialMLDSimulator, NonSquareDifferentialMLDSimulator

plt.switch_backend('agg')
plt.rcParams['xtick.direction'] = 'in'
plt.rcParams['ytick.direction'] = 'in'
plt.rcParams['markers.fillstyle'] = 'none'

def simulateBER(argstr):
    params = Parameters(argstr)
    if params.code == "symbol":
        codes = np.array(Modulator(params.mod, params.L).symbols).reshape(params.L, 1, 1)
    elif params.code == "OSTBC":
        codes = OSTBCode(params.M, params.mod, params.L).codes
    elif params.code == "DUC":
        codes = DiagonalUnitaryCode(params.M, params.L).codes
    elif params.code == "ADSM":
        codes = ADSMCode(params.M, params.mod, params.L).codes

    if params.mode == "BER":
        channel = IdealRayleighChannel(1, params.M, params.N)
    else:
        channel = IdealRayleighChannel(params.ITi, params.M, params.N)

    if params.sim == "diff":
        sim = DifferentialMLDSimulator(codes, channel)
    elif params.sim == "sudiff":
        sim = SemiUnitaryDifferentialMLDSimulator(codes, channel)
    elif params.sim == "nsdiff":
        bases = Basis(params.basis, params.M, params.T).bases
        sim = NonSquareDifferentialMLDSimulator(codes, channel, bases)

    if params.mode == "BER":
        return sim.simulateBERReference(params, outputFile=False, printValue=False)
    else:
        return sim.simulateBERParallel(params, outputFile=False, printValue=False)

if __name__ == '__main__':
    fig, ax = plt.subplots()
    ax.set_xlabel("SNR [dB]")
    ax.set_ylabel("BER")
    ax.set_xlim(0, 30)
    plt.ylim(1e-7, 1e0)
    plt.yscale("log")
    ax.tick_params(pad=8)

    ret = simulateBER("BERP_sim=sudiff_channel=rayleigh_code=symbol_M=1_N=4_L=16_mod=SQAM_ITo=1e3_ITi=1e5_snrfrom=0.00_to=30.00_len=16")
    ax.plot(ret["snr_dB"], ret["ber"], color="k", marker="s", linestyle="-", label="Differential SQAM [1]")

    os.environ['USECUPY'] = "0"
    ret = simulateBER("BER_sim=diff_channel=rayleigh_code=DUC_M=4_N=4_T=4_L=65536_IT=1e4_snrfrom=0.00_to=30.00_len=16")
    ret["ber"][ret["ber"] <= 1e-8] = np.NaN
    ax.plot(ret["snr_dB"], ret["ber"], color="b", marker="o", linestyle="-", label="Square DUC [2]")

    ret = simulateBER("BER_sim=diff_channel=rayleigh_code=ADSM_M=4_N=4_T=4_L=4096_mod=PSK_IT=1e3_snrfrom=0.00_to=30.00_len=16")
    ax.plot(ret["snr_dB"], ret["ber"], color="b", marker="+", linestyle="-", label="Square ADSM [3]")
    os.environ['USECUPY'] = "1"

    ret = simulateBER("BERP_sim=nsdiff_channel=rayleigh_code=DUC_basis=d_M=4_N=4_T=1_L=16_W=80_ITo=1e3_ITi=1e4_snrfrom=0.00_to=30.00_len=16")
    ax.plot(ret["snr_dB"], ret["ber"], color="r", marker="^", linestyle="-", label="Nonsquare DUC [5]")

    handles, labels = ax.get_legend_handles_labels()
    legend = ax.legend(handles, labels, loc="best", frameon=True)
    frame = legend.get_frame()
    frame.set_facecolor('white')
    frame.set_edgecolor('white')

    #plt.show()
    plt.savefig(sys.argv[0].replace(".py", ".svg"))

Related Publications

• [1] W. T. Webb, L. Hanzo, and R. Steele, “Bandwidth efficient QAM schemes for Rayleigh fading channels,” IEE Proc., vol. 138, no. 3, pp. 169–175, 1991.

• [2] B. M. Hochwald and W. Sweldens, “Differential unitary space-time modulation,” IEEE Trans. Commun., vol. 48, no. 12, pp. 2041–2052, 2000.

• [3] R. Rajashekar, C. Xu, N. Ishikawa, S. Sugiura, K. V. S. Hari, and L. Hanzo, “Algebraic differential spatial modulation is capable of approaching the performance of its coherent counterpart,” IEEE Trans. Commun., vol. 65, no. 10, pp. 4260–4273, 2017.

• [4] N. Ishikawa and S. Sugiura, “Rectangular differential spatial modulation for open-loop noncoherent massive-MIMO downlink,” IEEE Trans. Wirel. Commun., vol. 16, no. 3, pp. 1908–1920, 2017.

• [5] N. Ishikawa, R. Rajashekar, C. Xu, S. Sugiura, and L. Hanzo, “Differential space-time coding dispensing with channel-estimation approaches the performance of its coherent counterpart in the open-loop massive MIMO-OFDM downlink,” IEEE Trans. Commun., vol. 66, no. 12, pp. 6190–6204, 2018.

• [6] N. Ishikawa, R. Rajashekar, C. Xu, M. El-Hajjar, S. Sugiura, L. L. Yang, and L. Hanzo, “Differential-detection aided large-scale generalized spatial modulation is capable of operating in high-mobility millimeter-wave channels,” IEEE J. Sel. Top. Signal Process., in press.

• [7] N. Ishikawa, “IMToolkit: An open-source index modulation toolkit for reproducible research based on massively parallel algorithms,” IEEE Access, vol. 7, pp. 93830–93846, July 2019.