10-4 10-3 10-2 10-1 100 0 5 10 15 20 BER SNR [dB] analytic-conclusion : 31-Oct-2006 1 2 3 4
Figure 6.2: BER versus SNR performance of an iterative multi-antenna multicarrier system in dispersive
Rayleigh fading channel. We consider the scenarios of 1. low diversity rank, 2. high diversity rank and suboptimum SDM detector, 3. high diversity rank and optimum SDM detector and 4. high diversity rank and iterative optimum SDM detector and decoder.
iniscent of the OHRSA method derived in Chapter 4. This phenomenon is exemplified, for instance, by Figure 3.11 of Section 3.6.
• Finally, the iterative gain region corresponds to the interval of the SNR values located between the performance curves 3 and 4 of Figure 6.2, which correspond to the systems employing a single as well as eight detection and decoding iterations. Correspondingly, the attainable iterative gain may be realized by employing iterative detection and decoding, which invokes iterative exchange of the soft bit-related information and thus facilitates the efficient exploitation of the diversity rank avail- able. This phenomenon is exemplified, for instance, by Figures 5.3 and 5.6 of Sections 5.2 and 5.3, respectively.
6.2
Future work
6.2.1 Semi-Analytical Model
The family of state-of-the-art communication systems invokes a conglomerate of complex mathematical algorithms. The analytical expressions describing the behaviour of these algorithms are often hard to de- rive. Correspondingly, the performance of complex systems is typically evaluated using extensive software
6.2.1. Semi-Analytical Model 181
Figure 6.3: Mobile wireless communication system analysis methodology.
simulations. Unfortunately however, the multiplicity of effects imposed by the different phenomena in the complex systems considered tend to obscure the important trends and trade-offs, which have to be consid- ered in the process of system design and optimization.
Consequently, we propose a semi-analytic methodology, which facilitates the prediction of the perfor- mance achievable by a system characterised by a specific ensemble of system and channel parameters.
The proposed semi-analytical technique attempts to dissect the complex problem of system performance analysis into a set of factors originating from different aspects of both the channel and the waveform char- acteristics, thus exposing the various trends and trade-offs inherent in the design of an efficient wireless mobile smart-antenna-aided multicarrier communication system.
Let us consider the system analysis methodology characterized in the stylised illustration of Figure 6.3, where we identify two sets of parameters, which characterize our system. Firstly, at the left of the figure we have a set of channel parameters, which comprizes the Doppler frequency fD, the RMS delay spreadτrms, the angular spread σa2 as well as the AWGN variance σw2. Additionally, we have to consider the statistical
distribution of the CIR taps-related fading coefficients. Secondly, for each channel-related parameter, we have the corresponding waveform parameter, as seen at the right of Figure 6.3. Namely, we have the bit- interleaver depth T, the signal bandwidth B, the numbers mt and nr of transmit and receive antennas as
6.2.1. Semi-Analytical Model 182 10-5 10-4 10-3 10-2 10-1 100 0 10 20 30 40 50 BER SNR [dB]
uncoded-qam ber-snr : 10-Oct-2006
M=4 M=16 M=64 Gaussian simul. Rayleigh simul. Gaussian analytic Rayleigh analytic
Figure 6.4: BER versus SNR performance of uncodedM-QAM in Gaussian and Rayleigh channels. The markers characterize the simulated results corresponding to M = 4, 16and64. The solid and dashed lines show the corresponding calculated BER versus SNR for Gaussian and Rayleigh channels, respectively, obtained using the semi-analytical model.
well as the signal to noise ratioγ. Additionally, we have the statistical distribution of the energy associated with the transmitted symbols, which is determined by the particular coding, spreading and modulation scheme. Some examples of the possible symbol-power distributions include the constant power in the case of a PSK modulation, the quantized multi-level uniform distribution in the case ofM-QAM as well as the near-Rayleigh power distribution in the cases of CDMA and OFDM.
Consequently, our aim is to derive a set of semi-analytical expressions, which would describe the in- terdependencies between the aforementioned system parameters and a set of criteria characterizing the per- formance of the mobile wireless communication system considered. Specifically, we choose four major performance criteria, which form the performance metric depicted in Figure 6.3, namely we consider the
BER, Complexity, Throughput as well as Latency.
We have completed a feasibility study and our preliminary results suggest that a semi-analytical model may be devised for characterizing the various phenomena, which is capable of accounting for the majority of the effects featuring in Figures 6.4–6.9, which determine the performance of a complex mobile wireless communication system. Some examples of these aspects, which may be taken into account in a correspond- ing model include
6.2.1. Semi-Analytical Model 183 10-5 10-4 10-3 10-2 10-1 100 0 5 10 15 20 25 30 BER SNR [dB] uncoded-ray-divber-snr : 11-Oct-2006 Rayleigh D=2 D=4 D=8 D=16 D=32 Gauss analytic
Figure 6.5: BER versus SNR performance of an uncoded QPSK system communicating over a χ2D- distributed flat-fading channel. The markers portray the simulated results associated with the diversity ranks
D = 1, 2,· · ·, 32. The solid lines show the corresponding calculated BER versus SNR curves obtained using the semi-analytical model.
• Coding scheme, e.g. block, convolutional, turbo code with a given number of decoding iterations (Figure 6.6).
• MIMO system dimensions, i.e. number of transmit and receive antennas (Figure 6.7).
• Multi-user environment, i.e. number of coherent and non-coherent users (Figures 6.7 and 6.8).
• Channel correlation properties, i.e. Doppler frequency, delay spread (Figure 6.5).
• MIMO detection complexity (Figures 6.8 and 6.9).