Numerical performance analysis of the system with perfect CSI at the receiver

This section aims to illustrate by means of simulation examples the effects of the block-wise doubly selective channel on system performance, assuming that the receiver has perfect CSI knowledge. In Subsection 2.4.2, we study frequency-selective behaviour and impact of the channel models with different delay spreads on the symbol error

rate (SER) of the SISO-OFDM system. Subsection 2.4.3 presents SER performance results for the SM-MIMO configuration, which help to identify the most efficient detector. Note that the results presented in this section will serve as a benchmark for the simulation performance analysis in the subsequent chapters of the thesis, which deal with a more complicated system model, incorporating channel estimator.

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2.4.1 System configuration

Consider a discrete-time baseband MC system with the processing block length N =64 (i.e. 64 subcarriers in the effective bandwidth B) and QAM modulation of the subcarriers (i.e. OFDM type). CP length is set to Ncp =7 to accommodate CIR with a modelled length of L=8 samples.

It should be noted that N =64 is selected here and in the subsequent experiments as it is the smallest radix-4 FFT adopted in the standardised systems [7]. Hence it ensures faster execution of Monte Carlo simulations. For the same processing block duration higher block lengths will broaden the system bandwidth and increase sampling resolution, but CIR energy spread and Doppler variation will not alter. Hence the block length is not a vital parameter in the context of performance evaluation of the selected system model.

The modelled channel is block-wise time-variant, with the Doppler spectrum given by the Jakes model [118] and the maximum angular shift ωD =0.025π , which represents the tolerable maximum according to (2.41). Two different multipath models have been adopted for simulation:

Ch.1) K=3 equipowered IID components (i.e. uniform MIP) underlying bandlimited CIR (2.9), with non-sample- spaced excess delays τ0 =0,

1 1 1.7 − = B τ and 1 2 4.4 − = B τ (illustrated in Fig.2.8);

Ch.2) L sample-spaced IID components with the exponential power decay defined in (2.14) by the factor α =2. Note that Ch.1 has 1

rms 1.81 − = B τ , and Ch.2 is characterised by 1 rms 0.425 − = B τ .

The modelled MIMO channel properties are in full accordance with the assumptions made in Subsection 2.3.1.

2.4.2 Symbol error rate in SISO transmission mode

Doubly selective behaviour of the channel is clearly visible in Fig.2.13, where CFR magnitude corresponding to Ch.1 is plotted for a sequence of blocks. One can see that some subcarriers may be subject to strong attenuation in a few blocks in the plotted sequence, while for the other blocks their gains are sufficient to guarantee reliable symbol transmission through the channel.

In the example studied here, OFDM subcarriers are modulated by QPSK and 16QAM. The elementary single- tap ZF equaliser performs CFR compensation at the receiver.

Fig.2.14 shows that SER of the QPSK-modulated system is about 8.5dB lower than SER of the system with 16QAM. Although CIR length is the same for both Ch.1 and Ch.2, there is a growing performance difference at higher SNRs at the receiver input. Thus, the plotted results confirm the major dependence of system performance on the rms delay spread of the channel, which has been theoretically stated in Subsection 2.2.2. Fig.2.14 shows that SER is higher for Ch.1, which has smaller number of underlying multipath components than Ch.2, but at the same time a more dispersive profile.

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Fig.2.13. Example of CFR magnitude of the doubly selective channel

Fig.2.14. SER of the SISO-OFDM system with perfect CSI at the receiver

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2.4.3 Symbol error rate in MIMO transmission mode

The SM-MIMO configuration is tested in two modes to demonstrate receive diversity impact on performance: with 4 Tx and 4 Rx antennas (4x4) and with 4 Tx and 6 Rx antennas (4x6). Selected channel model is Ch.1. The experiment compares detectors of various complexity levels, described in Subsection 2.3.3.

The square system (4x4) with the linear ZF detector is seen (Fig.2.15) to have about 5.5dB-6dB worse performance than SISO-OFDM (1x1). As explained in Subsection 2.3.3, this is caused by ill-conditioned realisations of the MIMO transform matrix. Adoption of MMSE weighting instead of ZF considerably reduces the loss (< 2dB). At higher SNRs this gap diminishes.

Increase of the receive diversity by introduction of 6 antennas instead of the minimum 4 greatly improves SER at higher SNRs. Note that the difference between ZF and MMSE becomes quite small as the additional rows in the MIMO transform matrix guarantee that it has full column rank. Hence ZF weighting in the detector is suitable for higher diversity orders and will be used in the subsequent analysis of the 4x6 configuration. Furthermore, the use of ZF detector does not imply the necessity of noise power tracking, inherent to the MMSE design.

One can also see from Fig.2.15 that using the V-BLAST detector leads to the large performance gain at higher SNRs in contrast to the linear detector (>5dB for SER 10-4). The smaller SER difference at lower SNRs can be explained by propagation of the V-BLAST decisions errors, occurring in the starting recursion steps.

Fig.2.15. SER of the QPSK-modulated SM-MIMO-OFDM system with perfect CSI at the receiver and different detectors

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SER of the system with the low-complexity V-BLAST alternative implemented as the SQRD algorithm (Tab.2.3) with post-detection ordering is shown in Fig.2.16 in comparison with the classical V-BLAST detector (Tab.2.1). Despite the suboptimal ordering, SQRD performance degradation with regard to V-BLAST is very negligible and is visible only at very high SNRs. A channel with slower variation than the simulated Doppler spread, equal to the tolerable maximum (2.41), would lead to even better results, as then the ordering is indeed the same for successive blocks.

It is interesting to note that for the case of 16QAM modulation SQRD detector with MMSE weighting exhibits almost the same performance as with ZF weighting. This is in contrast to the QPSK case, for which 0.6dB-0.7dB difference is observed between the corresponding curves.

Fig.2.16. Comparative performance of the optimal and suboptimal decision feedback detection algorithms for the case of 4x6 system