# Schriftenreihe des Instituts für Nachrichtentechnik

Band 3

Massive multiple-input/multiple-output communication systems are a great solution to satisfy the demand of high-throughput, reliable information transfer, without the need of increasing the required frequency spectrum. In such systems, the base stations are equipped with a very large number of antennas in comparison to the number of users served. Using linear techniques, such as maximum-ratio combining or zero-forcing linear equalization, the effective channels between the base station and the users become almost deterministic, an effect known as channel hardening, even though the actual channel realizations are random.

However, to reap these benefits, accurate estimates of the channel coefficients are required, a problem which is very challenging, due to the very large number of these coefficients. Additionally, when pilot-sequence-based techniques are applied, the estimates may suffer from additional interference due to the pilot contamination problem, that arises from the reuse of the limited number of these sequences in the multi-cellular environment.

To completely avoid these aforementioned drawbacks, noncoherent detection approaches in massive MIMO systems were proposed. Using differentially-encoded transmit data, and high-performing detection algorithms at the receiver, results that compete with the conventional coherent detection schemes that are typically employed in these systems are achieved. Moreover, only statistical knowledge of the situation, and not the actual conditions, are required. However, a problem still remains.

With the hundreds, if not more, radio front-ends, the hardware may become impractical to implement using the state-of-the-art components that are typically designed for single-antenna, or multi-antenna systems that employ only a handful of them. Additionally, to obtain the competitive results, processing is performed on large-dimensional data. This adds to the operational costs, as powerful signal-processing hardware becomes mandatory, when, e.g., latency is critical.

Hence, in this dissertation, the design of noncoherent receivers is explored. In the first part, the goal is achieving the best power efficiency possible. This includes improvements in the various steps of the receiver; starting with the antennas, and the radiation pattern they exhibit, the feedback gain in the detection algorithms, the metric utilized to decide which symbols are the most reliable, and decode them, and the combination of differential encoding with error-correction codes to reduce the error rates further. These advanced receiver concepts highlight the potential of noncoherent detection in massive MIMO systems.

In the second part of the dissertation, the main focus lies on reducing the algorithmic and hardware complexity of the noncoherent massive MIMO receiver. First, low-complexity alternatives or implementations are adopted for particular computationally-demanding processing tasks, e.g., the SVD for subspace tracking, at the receiver. Next, the structure of the different matrices involved in the detection process are exploited to reduce the numerical complexity from the start. Then, low-resolution analog-to-digital converters are investigated and optimized, to obtain as-good results as the unquantized case. Finally, the special case of one-bit quantization is studied, with the accompanying derivations to obtain a quantization-aware receiver. This entails a solution for acquiring the statistical knowledge needed for detection at the receiver. In contrast to coherent detection employing one-bit converters, it can be proven that at a very high signal-to-noise ratio, it is possible for noncoherent detection to have no error floor.

The theoretical insights in this work are supported by numerical results obtained from Monte--Carlo simulations. Additionally, when possible, analytic expressions of the required complexity are derived.

Band 2

Hardware-intrinsic security studies cryptographic methods, whose implementations are assisted by some specific physical properties of the hardware on which they are executed. Physical Unclonable Functions (PUFs) are a predominant part of that field and currently an active research area. The most investigated type of PUF is the so-called silicon PUF, representing an electronic device, which is embedded in an integrated circuit (IC) with some cryptographic functions. PUFs are used to generate a highly secret, time-invariant, true random bit sequence, referred to as PUF response. This randomly generated PUF response is unique for each individual PUF device and can easily be reproduced on request inside the IC over its entire lifetime. The PUF response is derived from the inherent randomness of some physical properties occurring from variations in the IC manufacturing process. These variations cannot be controlled with todays technologies. For example, the propagation delay of logic gates or the initialization state of memory cells can be used in order to generate a PUF response. Since such behaviors cannot be controlled, it is extremely unlikely to produce two PUFs with the same response. This is the reason why PUFs are called unclonable. Even the IC manufacturer cannot predict the individual response of an embedded PUF without performing a readout after IC manufacturing. If the IC manufacturer prevents the possibility to readout a PUF response in any way, not even by using any kind of IC tampering, the PUF response becomes secret to everyone.

Since PUFs can be interpreted as highly secret, true random bit sources, they are predestined for a variety of cryptographic applications such as, for example, secret key generation and storage, identification and authentication of various entities. A PUF response exists in its binary form only for a very short active time period during execution of the cryptographic function in which it is involved. Otherwise, in predominantly inactive periods, it is hidden in its analog form, consisting of unclonable analog physical parameter values of the PUF device. Every attempt to manipulate these parameter values uncontrollably changes the binary PUF response. Consequently, the PUF response is inseparably merged with the IC hardware and it is not possible to reconstruct its binary value during inactive periods. In the very short active periods, when the PUF response exists in its binary form, its secret can be protected by additional methods. Due to external influences like changes of temperature, supply voltage or IC aging, many PUF variants cannot reproduce their binary responses error-free. For such error-prone PUFs, methods from the field of error-correcting codes have to be applied to reliably reproduce binary PUF responses.

In current applications, however, all PUF types are only equipped with classical errorcorrecting codes, which are not tailored to the specific properties of individual PUF types. Consequently, the possibilities of reliability improvements of error-prone PUFs are not completely exhausted.

This dissertation considers several aspects of PUFs from the perspective of coding theory. Traditionally, for error correction in PUFs, a worst-case bit error probability is used in order to model the binary symmetric channel. As existing results in the literature indicate, this is a very conservative and sometimes even pessimistic assumption. In the theory of error-correcting codes, knowing characteristics of a channel is always beneficial in order to design codes that lead to an improvement of the error-correction performance. We derive channel models for two different PUF variants, namely Ring Oscillator PUFs (ROPUFs) and Dynamic Random Access Memory (DRAM) PUFs. Using DRAM to construct PUFs is a comparatively new approach proposed in the literature. In contrast to the established variants, PUF responses extracted from DRAM are heavily biased towards either “0” or “1”, and hence, debiasing methods have to be applied in addition to error correction. We propose methods that can be applied to solve the debiasing problem.

When dealing with noisy responses, secure sketches are a widely used concept. When reproducing a PUF response based on an erroneous re-extracted response, so-called helper data which are calculated and stored during initialization have to be used to map responses to codewords, such that decoding algorithms can be applied. We propose and analyze a new secure sketch that only uses an error-correcting code, but no further helper data. Also, we use our channel model, which we derived for ROPUFs, to construct new secure sketches.

Furthermore, we propose specific code constructions that can be used for error correction in the context of PUFs. Block codes and convolutional codes are considered for that purpose and we explain how to improve existing results from literature by using code classes (Reed–Muller codes, Reed–Solomon codes), decoding techniques (generalized minimum-distance decoding, power decoding, list decoding, using soft information at the input of the decoder, sequential decoding) or coding techniques (generalized concatenated codes), that have not been applied to PUFs before. Our code constructions result in a smaller block error probability, decoding complexity or codeword length in comparison to existing implementations.

The final part of this dissertation deals with security aspects. In particular, we consider timing attacks on the decoding algorithm, as a representative of the huge family of side-channel attacks. We study two techniques to prevent such attacks, namely a masking technique, as well as a modified decoding algorithm with a runtime that is constant and independent of the received word.

Band 1

Advanced equalization and coded-modulation strategies for multiple-input/multiple-output (MIMO) communication are considered. The focus is on techniques that are suited for the application in multiuser MIMO uplink transmission (MIMO multiple-access channel) or multiuser MIMO downlink transmission (MIMO broadcast channel). This particularly includes lattice-reduction-aided (LRA) schemes which have become popular in recent years.

In LRA schemes, the MIMO channel matrix is factorized into two parts: a unimodular integer matrix and a residual non-integer matrix. Given that factorization, only the non-integer part is conventionally equalized, either by means of linear equalization or the application of the principle of successive interference cancellation (SIC). In contrast to that, the integer interference can be resolved without any performance-harming noise enhancement. From a mathematical point of view, the integer matrix describes a change to a more suited basis for channel equalization. Consequently, the channel factorization can be obtained by well-known lattice-basis-reduction algorithms, e.g., the Lenstra–Lenstra–Lovász (LLL) algorithm. However, concentrating on the treatment of the multiuser MIMO interference, LRA schemes have most often been treated uncoded, i.e., neglecting the combination with a convenient coded-modulation approach. This situation has changed with the concept of integer-forcing (IF) equalization. In IF schemes, the channel matrix is factorized, too. Nevertheless, the integer interference is resolved over the finite field of the channel code—creating a close coupling between channel equalization and coded modulation. For the finite-field integer matrix, the unimodularity constraint as present in LRA schemes can be relaxed to a full-rank constraint. This not only brings up the question if, in classical LRA schemes, the unimodularity constraint is really necessary, but also if the LRA techniques have really been operated in an optimum or at least in a close-to-optimum way.

Hence, in this thesis, strategies and approaches are identified that enable a performance gain over the state-of-the-art application of LRA receiver- or transmitter-side equalization. First, this involves the choice of the signal constellation. In particular, constellations over the Eisenstein integers—the hexagonal lattice over the complex plane—are studied. These signal constellations as well as conventional quadrature amplitude modulation (QAM) ones are combined with coded-modulation schemes that are suited for the application in multiuser MIMO communications using binary or non-binary low-density parity-check (LDPC) codes. Moreover, criteria and algorithms for lattice basis reduction are reviewed and extended for lattices over Eisenstein integers. These considerations also include the abovementioned relaxation to full-rank integer matrices, which is specifically known as successive minima problem. A recapitulation of conventional linear and SIC-based equalization schemes is provided, where the famous V-BLAST detection strategy is regarded from the perspective of lattice theory. Following this, optimum or close-to-optimum channel factorization strategies and related algorithms are worked out for LRA transmitter- and receiver-side schemes. It is shown that the classical unimodularity constraint can indeed be relaxed—generalizing the “lattice-reduction-aided” to “lattice-aided” (LA) schemes. The combination of these LA approaches with coded-modulation strategies is studied and the differences to the corresponding IF schemes are clarified; a discussion on the convenience of both philosophies in multiuser MIMO uplink and downlink transmission is given. The theoretical derivations in this thesis are supported by results obtained from Monte-Carlo simulations. This particularly includes the evaluation of the transmission performance if binary source symbols are transmitted.