Abstract The baseband digital pre‐distortion (DPD) signal processing technique is the most cost‐effective linearisation method among other techniques to address the nonlinearity effect of the power amplifier. For communication systems containing DPD and power amplifier, it is difficult to acquire performance metrics closed‐forms for any DPD architecture since there was no mathematical expression for each DPD coefficient. Usually, researchers look for more efficient DPD algorithms for DPD coefficients (compared to the existing ones) in terms of computational complexity, delay, power consumption etc. Consequently, performance is evaluated through intensive simulation. In this paper, it is shown how one can exploit the results of the recent work to mathematically model the indirect learning architecture DPD and efficiently derive important measures in communication systems. Expressions of the normalised mean square error (NMSE) and achievable rate for the OFDM communication system are derived. The DPD is modelled mathematically by exploiting the DPD coefficients closed‐form expressions. The derived expressions of the NMSE and achievable rate are verified through numerical simulations. Furthermore, closed‐form expressions for the NMSE and achievable rate bounds for the OFDM communication system are derived. The performance measures bounds are found assuming a perfect linearisation scenario. The analytical expressions are validated through numerical simulations.

This study analyses in‐phase and quadrature‐phase imbalance (IQI) in large‐scale multiple antenna systems and Rayleigh fading channel. Specifically, the authors compare between different approaches (using pilot‐based or blind channel estimation processes) to remove the IQI effect at a base station equipped with massive number of antennas. They obtain closed‐form expression for the asymptotic achievable rate when using IQI removal algorithm and zero‐forcing data detection. They also provide complexity analysis for the proposed solutions and show, by means of Monte Carlo simulations, that the proposed algorithm improves the system performance even for small number of antennas.

Massive MIMO relay system promises large spectral and energy efficiencies. It also allows admitting more users in the network with controlled quality of service. In this paper, we seek the answer of the following question: what is the maximum number of users that can be admitted in a two-way relay network with massive number of antennas at the relay side and subject to a minimum quality of service at the user side? In order to answer this question, we develop lower bound on the achievable user rate which we then use to bound the maximum number of the admissible users.We also study the effect of the non orthogonality of the pilot sequences on the user capacity in a small cell (dense) network and propose an interference mitigation scheme which improves the spectral efficiency. It is shown that large number of users can coexist using the proposed scheme.

In this study, the authors analyse and provide new insights into the problem of multi‐cell minimum mean square error (MMSE) detector in massive multiple‐input multiple‐output (MIMO) systems. Their system combines pilot hopping and pilot reuse strategy in the multi‐cell scenario. They obtain a deterministic expression of rate bounds of the uplink system when MMSE is used for channel estimation and data detection. Their result is different from the existing MMSE bounds in massive MIMO literature in that they obtain an achievable rate that is simply a scaled version of that of the matched filter (MF) detection, i.e. the achievable rate of the MF detection can be scaled with a constant, which is a function of the number of antennas and users as well as the power allocation to directly obtain the achievable rate of the MMSE detection. This new finding saves a significant amount of work needed when analysing MMSE detection in massive MIMO since it reduces the problem to obtaining simpler results (using MF analysis) and then extending the result to the MMSE case in a straightforward manner. Simulation results show how tight the achievable rate bound to the actual one at a large number of BS antennas.

In this study, the authors analyse the performance of a massive multiple‐input multiple‐output network with N ‐antenna users. Equipping the user terminal (UT) with a multiple of antennas is usually challenging since it increases the overhead of the channel estimation process (linearly with N ). In this study, the authors use semi‐blind (data‐aided) channel estimation that significantly reduces the pilot overhead and analytically obtains the optimal number of antennas that can be mounted at the UT. The proposed channel estimation algorithm is especially useful in cases where a UT can be assigned a single, or generally a few numbers of, pilot sequence(s) although it might have a number of antennas greater than the number of sequences (as the case of 5G proposed solutions); therefore the network does not have to assign more pilots to the user in order to estimate the additional antennas. The authors also characterise the user outage performance when a part of its data is used for the blind channel estimation.

Non-orthogonal multiple access (NOMA) emerges as a strong candidate for the next wireless generation as it promises large spectral efficiency. However, as the number of the users increases, the interference increases. This limits the rate per user. In this paper, the maximum number of users that can be admitted in a NOMA system, under a total power constraint and a minimum rate requirement per user, is sought. A lower bound for the achievable sum-rate is first obtained. A power allocation scheme that maximizes the sum-rate, under the aforementioned constraints, is then proposed. Using the proposed scheme, an efficient algorithm to obtain the maximum number of users is developed. The performance is compared with the orthogonal multiple access (OMA) schemes. Our results show that the proposed scheme efficiently computes the number of users and provides significant gain compared to the OMA schemes.

In this paper, we analyze the performance of mas- sive MIMO network with two-antenna users. We show that increasing the number of antennas at the user side is possible without increasing the channel estimation overhead linearly with the number of extra antennas. We propose a simple data-aided channel estimation method for the extra antenna. The proposed method exploits the asymptotic orthogonality of the channel vectors in very large MIMO system and takes advantage of the pilot-aided channel estimation performed for the first antenna. The extra antenna is used for data multiplexing and therefore increases the user throughput. We obtain achievable rates when matched filtering detection is used in uplink multi-cell MIMO system. The rate bounds are tight even at finite (not very large) number of antennas. The proposed algorithm is applicable for more than two antennas.

In this study, the authors develop a pilot assignment algorithm to alleviate the effect of pilot contamination over time‐varying channels. They study the effect of correlated channel states over consecutive blocks under different Doppler frequencies using a moving‐average channel estimation process. They show that it is possible to mitigate the pilot contamination problem by assigning pilot hopping sequences such that each user experiences different contaminating users across time. The proposed algorithm has the advantage that it does not require the cooperation between the base stations, is robust to the channel time‐variations and can significantly increase the spectral efficiency compared to existing algorithms as shown in the simulation results.

In this paper, we analyze the performance of massive MIMO network with two-antenna users. The channel estimation is performed using the pilot sequence for one antenna and a simple data-aided estimation for the extra antenna. The advantage of the proposed method is that the channel estimation overhead does not increase linearly with the number of the user's antennas. We then compare between two schemes using this extra antenna: spatial repetition scheme and a simplified interference-alignment precoding scheme that does not require any coordination between the base stations or the users. It is shown that while the first scheme has the effect of virtually increasing (doubling) the number of antennas at the base station, the second precoding scheme outperforms the first one as it effectively decreases the size of the interference space. We analytically obtain a closed form for the achievable rate of one case using polynomial expansion approximations. The simulations verify the validity and the tightness of the obtained bound even at finite (not very large) number of BS antennas. The proposed algorithm is easily extended for more than two antennas.

In this paper, we analyze the performance of multi-cell least-square (LS) channel estimation using pilot sequence hopping and pilot reuse strategy for pilot decontamination. We obtain achievable rates in uplink synchronous system in L-cell system using LS channel estimation and zero forcing (ZF) detection. Polynomial expansion approximation is performed to obtain a closed form bound of the asymptotic sum-rate. We show that pilot hopping can achieve significant spectral efficiency gain compared to the conventional non-hopping schemes. Moreover, the number of antennas can be also greatly reduced when using the pilot hopping. However, the achieved gains depend on the pilot reuse factor β. It is shown that this gain is not monotonic function of β in some cases and therefore brings to attention that a careful cell planning is required when applying pilot hopping.

In this study, conjugate beamforming lattice‐reduction (LR)‐aided precoding is proposed for block diagonal multiuser multiple‐input–multiple‐output (MU‐MIMO) system. Block diagonalisation (BD), a common precoding for downlink MU‐MIMO is used to eliminate some of the inter‐user interference. In this study, we investigate the performance of conjugate beamforming when partial BD is performed such that a set of users communicates with the base station (BS) without interference from the other sets. We show that the sum‐rate significantly increases by a simplified LR‐aided conjugate beamforming and least‐correlated user‐pairing algorithm. We analytically obtain an upper bound for the achieved rate. We compare between the optimal and the proposed suboptimal user pairing for both cases of perfect and imperfect channel state information at the BS as well as the case of spatially correlated channel.

Massive MIMO promises large spectral and power efficiency gains. However, pilot contamination limits these aspired gains. In this paper, we propose a structured, i.e., non-random, pilot hopping and a weighted moving average channel estimation for time-varying massive MIMO systems. The proposed algorithm diversifies the contaminating (interfering) sources, such that all the users enjoy the hopping advantages. We analyze the performance of multi-cell network, where the base stations perform matched filtering or zero-forcing for data detection. Using polynomial expansion approximations, we obtain achievable rates that are tight even at finite (not very large) number of antennas. It is shown that the spectral efficiency gain achieved by pilot hopping is not a monotonic function of the pilot reuse factor β in some cases and, therefore, brings to attention that careful cell planning is required when applying pilot hopping. Moreover, the proposed algorithm involves a weighted moving average that uses the previously obtained channel estimates (of the preceding blocks) if they are correlated with the current one. Due to the massive MIMO properties, the algorithm is robust to channel time-variations and can be used with any previously proposed channel estimation method.

Linear transceivers prove efficiency and sometimes optimality under certain constraints. It is known that receive beamforming (matched filter) is diversity optimal in the case of SIMO channel whereas the MMSE MIMO receiver is diversity optimal for only a small set of spectral efficiency R b/s/Hz for an M × N MIMO channel. In this paper we analyze the matched filter MIMO receiver over a frequency selective channel under cyclic-prefix transmission. It is shown that for a frequency selective channel with ν+1 taps (where ν is the channel memory) the matched filter has a rate-dependent diversity that switches between (ν + 2) modes (with minimum of zero and a maximum of MN(ν + 1)) depending on the value of the operating R.

In this paper we investigate the performance of a densely populated relay network as a massive distributed system. The distributed relaying nodes construct a large set of antennas providing the system with the advantages of both the relays and the massive MIMO systems. We apply large scale analysis to evaluate the performance of the dense relay network as a massive system, and show that the signal-to-noise ratio (SNR) increases almost linearly with the number of relaying devices in the case of amplify-and-forward relaying protocol. In the case of decode-and-forward relaying protocol, we show that the SNR is proportional to the square of number of relaying nodes. We then explore bounds and approximation for the deduced expression. Finally we maximize the energy efficiency of the proposed system by choosing the optimum number of relays.

This paper studies multiple-input multiple-output linear precoding in the high-signal-to-noise-ratio regime under flat fading. The diversity at all fixed rates is analyzed for a number of linear precoders. The diversity-multiplexing tradeoffs (DMTs) are also obtained, discovering that for many linear precoders the DMT gives no direct insight into the intricate behavior of fixed-rate diversity. The zero-forcing (ZF), regularized ZF, matched filtering, and Wiener filtering precoders are analyzed. It is shown that regularized ZF (RZF) or matched filter (MF) suffers from error floors for all positive multiplexing gains. However, in the fixed rate regime, RZF and MF precoding achieve full diversity for spectral efficiencies up to a certain threshold and zero diversity at rates above it. When the regularization parameter in the RZF is optimized in the minimum mean square error sense, the structure is known as the Wiener precoder, which in the fixed-rate regime is shown to have diversity that depends not only on the number of antennas, but also on the spectral efficiency. The diversity in the presence of both precoding and equalization is also analyzed.

MIMO precoding matches the transmission to channel conditions in order to reduce or eliminate interference at the receiver. In this paper, we are interested in the case where the receiver is also equipped with a linear processor, specifically a ZF filter. We analyze the effect of the ZF receive filter on the performance of a variety of MIMO precoders. It is shown that receive-side ZF equalization can remove the error floors that sometimes appear with regularized zero-forcing precoding and matched-filter precoding.

This paper investigates the performance of the minimum mean-square error (MMSE) equalizers in MIMO frequency selective channels under zero-padding (ZP) transmission. It was previously known that the SISO linear ZP receiver achieves full diversity; this paper shows that the MIMO version of this receiver is suboptimal in diversity. It is shown that the MMSE MIMO receiver exhibits an intricate error behavior that depends not only on channel memory and antenna configuration, but also on transmission rate. This behavior is fully characterized in closed form, revealing that the MMSE ZP receiver attains the (optimal) diversity of a ML receiver but only at small spectral efficiencies.

Single-carrier (SC) block transmission with cyclic prefix (CP) is a method with several advantages that has been incorporated into standards. This paper investigates the performance of multi-antenna SC-FDE under cyclic-delay diversity (CDD) and Alamouti signaling. Our analysis fully characterizes the diversity, showing that it depends not only on the antenna configuration and channel memory, but also on data block length and data transmission rate. Below a certain rate threshold, full diversity is available to both CDD and Alamouti signaling, while at higher rates their diversity diminishes, albeit not quite in the same way. Our analysis shows that at high rates the CDD diversity degenerates to the diversity of the SISO SC-FDE, while Alamouti signaling provides twice the diversity of SISO SC-FDE.

This paper investigates the performance of the zero-forcing (ZF) and minimum mean-square error (MMSE) equalizers in MIMO frequency selective channels under zero-padding (ZP) transmission. It was previously known that the SISO zero-forcing ZP receiver achieves full diversity; this paper shows that the MIMO version of this receiver is suboptimal in diversity. The MMSE ZP is also investigated, showing that it exhibits an intricate error behavior that depends not only on channel memory and antenna configuration, but also on transmission rate. This behavior is fully characterized in closed form, revealing that the MMSE ZP receiver attains the (optimal) diversity of a ML receiver but only at small spectral efficiencies. Thus MMSE ZP works better than ZF ZP, but not quite as well as ML. To further improve the performance, lattice-reduction aided equalization in the frequency-selective channel is investigated. It is shown that lattice-reduction-aided zero forcing equalizer as well as MMSE equalizer achieve the maximum spatial and temporal diversity at all spectral efficiencies.

We characterize the DMT of finite-length linear equalizers in the MIMO frequency-selective channel. We obtain the DMT in the case of cyclic-prefix transmission and provide an upper bound for the DMT in the case of zero-padding transmission. We also provide in-depth analysis for the diversity of the MMSE receiver in the fixed rate regime (i.e. zero multiplexing gain) in the cyclic-prefix transmission and obtain a lower bound on diversity. This gives better insight about the diversity of the MMSE in this regime since only upper bound exists in the literature. The MMSE diversity in this regime is function of the spectral efficiency, the data block length and the number of transmit and receive antennas.

Cyclic Delay Diversity (CDD) is a simple method that converts transmit antenna diversity into frequency selectivity, thus allowing simple operation and use of conventional receivers to capture the diversity. This paper shows that single-carrier CDD methods are capable of producing diversity without channel coding or linear precoding, and that this is made possible via the appropriate design and use of linear equalizers. At the heart of our result is the establishment of a functional equivalence between effective channels seen by the CDD MISO system and the cyclic-prefix SISO ISI system. Specifically, we show that in an M×1 CDD MSIO system, the MMSE receiver achieves maximum diversity for rate values R ≤ log L/M(ν+1)-1, where L is the data block length, R the spectral efficiency in b/s/Hz, and ν is the channel memory. The equivalence between the delay diversity (DD) system and a zero-padding single-carrier system can be also established (as long as the DD delay taps are carefully chosen) for which linear equalizers can achieve maximum diversity with no constraint on rate.

For linear MIMO precoders, the diversity is an important parameter affecting broad tradeoffs in system design, however, the diversity of many MIMO precoders has not been available in the open literature. This paper analyzes the diversity of the following MIMO precoders: the zero-forcing (ZF), regularized ZF, matched filtering and Wiener filtering. Several interesting properties of these precoders are revealed by this analysis. It is shown that regularized ZF (RZF) and the matched filter (MF) exhibit two-mode diversity: full diversity at low rates R and error floor at high rates. The rate threshold of this two-mode behavior is analytically determined. The Wiener precoder is also shown to produce a diversity that depends on the spectral efficiency and can be as small as one and as large as the product of the number of transmit and receive antennas.

Single-carrier frequency domain equalization (SC-FDE) has many advantages, but in the MIMO frequency selective channel its performance has not been fully characterized and several important open questions remain. This paper analyzes the diversity of zero-forcing MIMO SC-FDE. It is shown that the diversity of the ZF receiver over this channel is the same as that of the ZF receiver in the frequency-flat channel. To improve the performance, a lattice-reduction (LR) aided ZF equalization is proposed and analyzed. It is shown that the full spatial and temporal diversity is achieved by he LR-aided ZF receiver for the uncoded transmission. This is the first analytical proof for the LR-aided equalization for MIMO frequency selective channel.

In most multiple-input multiple-output (MIMO) systems, the family of waterfall error curves, calculated at different spectral efficiencies, are asymptotically parallel at high signal-to-noise ratio. In other words, most MIMO systems exhibit a single diversity value for all fixed rates. The MIMO minimum mean square error (MMSE) receiver does not follow this pattern and exhibits a varying diversity in its family of error curves. This paper analyzes this interesting behavior of the MMSE MIMO receiver and produces the MMSE MIMO diversity at all rates. The diversity of the quasi-static flat-fading MIMO channel consisting of any arbitrary number of transmit and receive antennas is fully characterized, showing that full spatial diversity is possible if and only if the rate is within a certain bound which is a function of the number of antennas. For other rates, the available diversity is fully characterized. At sufficiently low rates, the MMSE receiver has a diversity similar to the maximum likelihood receiver (maximal diversity), while at high rates, it performs similarly to the zero-forcing receiver (minimal diversity). Linear receivers are also studied in the context of the MIMO multiple-access channel. Then, the quasi-static frequency selective MIMO channel is analyzed under zero-padding and cyclic-prefix (CP) block transmissions and MMSE reception, and lower and upper bounds on diversity are derived. For the special case of SIMO under CP, it is shown that the aforementioned bounds are tight.

Cyclic-prefix (CP) insertion in a single or multi-carrier system transforms the frequency-selective channel into a set of parallel flat channels, thus reducing the equalization complexity considerably. To harness the channel multipath diversity in this parallelized system the use of error control codes and/or linear precoding are proposed in the literature. A more recent result shows that maximum diversity can be achieved by lattice-reduction aided equalization together with precoded OFDM transmission. In this paper, we show that full diversity lattice-reduction is possible {\em without} requiring either precoding or error control codes. In earlier work it was shown that some cyclic-prefix systems have a diversity that is rate-dependent; we show that lattice-reduction diversity does not follow the same pattern of behavior. We also explore and expose important distinctions between diagonal and non-diagonal equalization for cyclic prefix systems.

This paper analyzes the MMSE receiver in MIMO frequency-selective channels. This expands our understanding of the MMSE MIMO channel, whose diversity was only recently characterized in the MIMO flat-fading regime. Specifically, in this paper lower and upper bounds on the diversity of the MMSE receiver operating over frequency selective MIMO channel under block transmission with zero-padding (ZP) or cyclic-prefix (CP) are produced. The tightness of the bounds is demonstrated for both ZP/CP for the special case of SIMO channel.

This work settles a long-standing open problem by providing a complete characterization of the diversity of the MMSE MIMO receiver for all fixed rates (spectral efficiencies). The MMSE MIMO receivers exhibit a complicated behavior in the fixed-rate regime that cannot be obtained via DMT analysis. Specifically, we show that in a system with M transmit antennas, N receive antennas, and rate R, the diversity is given by d = ⌈M2-R/M⌉2+ (N - M)⌈M2-R/M⌉. This verifies and refines earlier results that were obtained only for two extremal operating points: diversity MN at very low rates and diversity N - M + 1 at very high rates.