The literature review in Section 1.2 highlights the importance of channel estimation and tracking when realising a high-data-rate wireless MC communication system, capable of approaching the maximum capacity of the non-ideal propagation medium. Summarising the main points, the emphasis in the practical system design should be on low-
complexity, robust, scalable and reconfigurable estimator architectures. Comparing properties of training-based and blind channel estimation methods, it should become clear that only pilot-assisted solutions can satisfy these requirements. Indeed, the major drawback, hampering implementation of blind algorithms, is their complexity, which is several orders of magnitude higher than that of linear filtering and interpolation techniques, used in systems relying on training. Furthermore, double selectivity of the fixed and mobile radio channel necessitates frequent CSI updates that can be achieved by means of the reliable pilot-based tracking scheme, utilising temporal correlation properties of the channel rather than independent decisions of the transmitted data symbols.
It is pointed out in Section 1.3 that the performance of pilot-assisted channel estimation algorithms depends on the structure of the training sequence. Thus, channel identification cannot be regarded as a receiver-isolated problem as in the majority of works in the area. Since the objective is the overall system performance improvement, channel estimation effects should be considered jointly with detection of the power-constrained data-bearing signal, yielding a sophisticated transmission optimisation problem. With regard to pilot-assisted MIMO-OFDM optimisation, only a few results are reported in the literature, leaving this topic an open research question.
In this thesis, we propose low-complexity feasible channel estimators for SISO and MIMO-OFDM systems, suitable for a number of application scenarios. Depending on the anticipated dynamic properties of the channel, the filtering part of the estimator architecture can be easily reconfigured, allowing for a ubiquitous receiver implementation. To achieve the best symbol error rate performance, we solve the joint pilot-assisted transmitter-
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receiver optimisation problem for the case of each proposed channel estimation algorithm. Contributions of the thesis are discussed in more detail in the following subsection.
1.4.1 Objectives and contributions
The starting part of the thesis is dedicated to the description of the general MIMO-OFDM system model, including doubly selective channel and basic receiver architectures. As an important part of the low-complexity receiver design, we aim to investigate several SM data symbol detection algorithms, which belong to the two classes:
linear and decision-feedback. Selection of the proper detection algorithm has a direct impact on the system
performance and optimisation since we adopt MSE of the detector’s output as a metric to optimise power allocation between pilot and data symbols. We show that for the higher orders of receive diversity and high SNR regimes, detectors based on the ZF and MMSE criteria exhibit similar performance and hence are equivalent for system optimisation. The decision-feedback detection is closely related to the linear approach since the first (major performance-affecting) iteration output is the same as that of the linear scheme. Therefore there is no difference between these methods from the transmission optimisation standpoint. To reduce computing complexity of the receiver, we employ a suboptimal decision-feedback detector based on the sorted QR decomposition (SQRD). Computer simulations show that its performance is almost the same as that of the optimal V-BLAST detector, whereas the complexity is lower by an order of magnitude.
The central objective of the thesis is the design and performance analysis of efficient channel estimation algorithms. In the considered receiver model, the accuracy of channel identification is critical as the detector relies entirely on the CSI acquired by the channel estimator. Under severe channel estimation errors, recovery of the transmitted data by the detector and demodulator would simply fail. To meet the accurate CSI acquisition objective, we develop a family of the reduced-complexity estimators, which are suitable for both single and multiple-antenna pilot-assisted OFDM(A) systems. The estimators are based on transform-domain processing and have the same order of computational complexity, irrespective of the number of pilot subcarriers and their positioning, thus offering scalability and transceiver reconfiguration flexibility. The common estimator structure represents a cascade of successive small-dimension linear filtering modules. The number of modules, as well as their order inside the cascade, is determined by the class of the estimator (1D or 2D) and availability of the channel statistics (correlation and SNR).
We adopt an analytical approach towards the MSE performance assessment of the presented channel estimation algorithms. In this way we can establish the best and the worst-case estimator performance conditions and investigate filter characteristics, in particular MSE under the design mismatch.
For fine precision estimation in multipath channels, the statistics of which are not known a priori, we propose the recursive design of the filtering modules comprising the channel estimator. Simulation results show that in the steady state, performance of the recursive estimators approaches that of their theoretical counterparts, which are optimal in the MMSE sense.
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In contrast to the majority of the channel estimators developed so far (refer to Section 1.2), our modular-type architectures are well suited for reconfigurable OFDM transceivers. Based on the observed dynamic channel properties, the appropriate filtering scheme can be chosen, and the pilot symbols can be assigned appropriate positions in the time-frequency grid.
Additionally, the thesis includes an extensive comparative analysis of the computational complexity of the developed optimal, suboptimal and recursive estimator architectures. By referring jointly to it and MSE performance results, it should become clear what estimation algorithm is more appropriate to a selected propagation environment and receiver complexity level.
Fig.1.1. Thesis methodology
With reconfigurable channel estimation schemes, the optimal structure of pilot signal to achieve the best detection performance of the MIMO-OFDM system is an important question. The problem of optimal power allocation between the data and the pilot symbols has already been highlighted in Section 1.3. In the final part of the thesis we aim to optimise the pilot-to-data power ratio (PDR) for the case of developed low-complexity 1D and 2D MMSE channel estimators. Note that this section represents our main and original contribution since no attempts have been undertaken so far to optimise MC pilot structure when CSI is acquired by the 2D filtering algorithm in the multiple-antenna receiver. Furthermore, no one working in the field has utilised statistical information of the channel in optimisation. Our work fills up this knowledge gap by deriving the closed-form analytical expressions of the upper bound (suboptimal approximate value) on the optimal PDR as a function of a number of design parameters (number of subcarriers, number of pilots, number of transmit antennas, effective order of the channel model, maximum Doppler shift, SNR, etc.). The resultant PDR equations can be applied to the MIMO-OFDM systems with arbitrary (not only optimal) arrangement of the pilot subcarriers, operating in an arbitrary multipath fading channel. These properties and relatively simple functional representation of the derived analytical PDR expressions are regarded as
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very useful for the reconfigurable SM-MIMO-OFDM system implementation, which is capable of adjusting transmit signal configuration according to the established channel statistics.
Fig.1.1 shows the methodology adopted in the thesis: from basic system model definition towards optimisation of PDR, subject to the selected channel estimation and detection algorithms.
1.4.2 Scope and limitations
In this thesis, we consider a conventional approach towards data symbol detection, i.e. when there is no CSI
feedback from the receiver to the transmitter. The entire computational burden for compensating for channel
distortions lies on the receiver. In the contrary case, depending on whether full or partial CSI can be fed forward to the transmitting side, adaptive loading, pre-equalisation and TB can be employed in the transmitter. If CSI is accurate, i.e. there are no signalling errors and latency is negligible, the aforementioned transmission adaptation techniques yield significant performance improvement over doubly selective channels, while allowing for very simple receiver architectures. Still practical implementations of fully adaptive systems are scarce. In mobile wireless MIMO-OFDM systems in particular, the number of adaptation parameters is large and frequent updates are necessary due to the time-varying nature of the channel. Study of the adaptive transmission methods is outside the scope of this thesis, as they represent a principally different approach to the transceiver design, and necessitate modelling of the feedback channel.
Similar to other block-wise transmission systems, the underlying design assumption is that the channel response remains constant in the interval of one block. In reality, however, the channel response varies continuously due to the Doppler effect inherent to any wireless medium. The approximation of time-varying CFR as time-invariant by means of batch processing at the receiver results in ICI that creates a detection error floor in the higher-SNR regimes. For the maximum normalised Doppler shift of 0.01, which is considered by us as a design-tolerable upper bound, the average signal-to-ICI power ratio per subcarrier is well in excess of 35dB [101]. Thus, the constant channel response assumption is reasonable, and the channel can be modelled as block-wise fading.
Optimised channel estimation architectures, considered in this thesis, are directly applicable to the downlink of OFDMA and linearly precoded GMC systems since the users in these MA schemes are frequency-separated. Thus, pilot and data transmissions can be regarded as channels of separate users. In the GMC systems [29][30], precoding of one user’s data does not affect symbols transmitted on the other users’ subcarriers. Hence, assuming that no precoding is applied to the pilot subcarriers, the functionality of the proposed channel estimation techniques is retained. Since precoded data sequences have a non-constant modulus in the frequency domain, the optimal PDR has to be reformulated with respect to the average power of the data symbol. However, in the uplink, there is a problem since each user has a different SNR and occupies only a small portion of the total bandwidth. Therefore there will be a user-specific optimal PDR due to the different number of data-bearing subcarriers and distinct channel estimation accuracy for different users.
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Since we focus on optimal filtering applied to channel estimation, we do not consider the effect of CFR interpolation errors. In particular, we assume error-free interpolation in the frequency domain that is indeed true when CIR has a finite length and is constructed by sample-spaced multipath components, which can be correlated in general. It has been mentioned in Subsection 1.2.1 that filtering and interpolation can be regarded as independent linear problems, where interpolation errors do not depend on the additive noise, in contrast to filtering errors. Interpolation error independence on SNR implies that optimal power allocation between pilots and data should account only for the filtering gain.
Finally, we consider an idealised spatial propagation model, assuming that channel responses between different transmit-receive antenna pairs are statistically independent. The reader is referrred to Subsection 1.1.1 for the grounding of such a theoretical assumption, as well as a discussion of the non-ideal MIMO environments.
1.4.3 List of publications
Material presented in this thesis is partially included in the series of publications listed below in chronological order. Note that the earlier articles (I-VI) address the problem of low-complexity channel estimation, whereas the later ones (VII-X) are dedicated to the optimisation of the pilot-assisted SISO- and MIMO-OFDM systems.
I. E. Golovins and N. Ventura, “Comparative analysis of low complexity channel estimation techniques for the pilot-assisted wireless OFDM systems,” in Proceedings of the 9th South African Telecommunications
and Networking Applications Conference (SATNAC), Sep. 2006.
II. E. Golovins and N. Ventura, “Low-complexity channel estimation for the wireless OFDM systems,” in
Proceedings of the 12th European Wireless (EW) conference, Apr. 2007.
III. E. Golovins and N. Ventura, “Design and performance analysis of low-complexity pilot-aided OFDM channel estimators,” in Proceedings of the 6th International Workshop on Multi-Carrier and Spread
Spectrum (MC-SS), published in Springer Lecture Notes in Electrical Engineering, vol. 1, May 2007. IV. E. Golovins and N. Ventura, “Modified order-recursive least squares estimator for the noisy OFDM
channels,” in Proceedings of the 5th IEEE Communications and Networking Services Research (CNSR)
conference, May 2007.
V. E. Golovins and N. Ventura, “Low-complexity constrained LMMSE estimator for the sparse OFDM channels,” in Proceedings of the 8th IEEE African Conference (AFRICON), Oct. 2007.
VI. E. Golovins and N. Ventura, “Reduced-complexity recursive MMSE channel estimator for the wireless OFDM systems,” in Proceedings of the IEEE Wireless Communications and Networking Conference
(WCNC), Apr. 2008.
VII. E. Golovins and N. Ventura, “Optimisation of the pilot-to-data power ratio in the MQAM-modulated OFDM systems with MMSE channel estimation,” in Proceedings of the 10th
South African Telecommunications and Networking Applications Conference (SATNAC), Sep. 2007.
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VIII. E. Golovins and N. Ventura, “Optimal training for the SM-MIMO-OFDM systems with MMSE channel estimation,” in Proceedings of the 6th IEEE Communications and Networking Services Research (CNSR)
conference, May 2008.
IX. E. Golovins and N. Ventura, “Optimisation of the pilot-to-data power ratio in the wireless MIMO-OFDM system with low-complexity MMSE channel estimation,” Elsevier Computer Communications Journal,
Special Issue on Adaptive Multicarrier Communications and Networks, vol. 32, pp. 465-476, Feb. 2009.
X. E. Golovins and N. Ventura, “Robust recursive two-dimensional channel estimators for the MIMO-OFDM systems,” in Proceedings of the 1st Wireless Communication Society, Vehicular Technology, Information
Theory and Aerospace & Electronics Systems Technology (Wireless VITAE) conference, May 2009. XI. E. Golovins and N. Ventura, “Performance evaluation of low-complexity decision-feedback detector for
SM-MIMO-OFDM Systems,” in Proceedings of the 12th South African Telecommunications and
Networking Applications Conference (SATNAC), Aug.-Sep. 2009.
XII. E. Golovins and N. Ventura, “Impact of multipath channel parameters on channel estimation performance in OFDM systems,” in Proceedings of the 9th
IEEE African Conference (AFRICON), Sep. 2009.