We consider the uplink of a cell-free (CF) massive multi-input multi-output (MIMO) system with superimposed pilot (SP) transmission, wherein user equipments (UEs) superimpose low-powered pilots onto data signals. This is unlike regular pilot (RP) transmission, where data and pilots use orthogonal spectral resources. Our CF mMIMO system has hardware impairments which occur due to i) low-quality radio frequency (RF) chains at the access points (APs) and UEs; and ii) dynamic analog-to-digital converter (ADC) architecture at the APs, which enables each RF chain to be connected to different resolution ADC. We derive a closed-form spectral efficiency (SE) expression for this CF system, wherein UEs observepracticalspatially-correlated Rician-faded channels. The derived lower-bound is generic, and reduces to the ones in the existing CF mMIMO SP works,which have only considered ideal hardware. Using this lower-bound, we optimally balance pilot and data transmit powers to maximize the SE. We analytically show that the optimal power balance is insensitive to AP impairments, but sensitive to that of UEs. We numerically show that SP can provide a higher SE than RP for low-to-severe hardware impairment levels, when supported by dynamic ADC architecture at the APs. With low resolution ADCs, RP always outperforms SP. The RP is also shown to be suitable for low UE speeds.

In this study, the authors consider robust transceiver design for amplify‐and‐forward relay aided multiple‐input multiple‐output interference systems assuming direct transmitter–receiver links and imperfect channel state information (CSI). The imperfect CSI of each link consists of the estimated channel and the covariance matrix of the channel estimation error. The authors address two transceiver optimisation problems: one is minimising the sum of averaged mean squared error (MSE) at all the receivers and the other is minimising the maximum averaged MSE among all the receivers, both of which are subject to power constraints at the transmitter and relay nodes. The formulated sum‐MSE minimisation and max‐MSE minimisation based optimisation problems are non‐convex with matrix variables and therefore a globally optimal solution is difficult to obtain. To solve these non‐convex optimisation problems, they develop sub‐optimal iterative algorithms based on alternating minimisation approach to jointly optimise the precoding matrices at the transmitter and relay nodes and the receiver filter matrices. Simulation results demonstrate the effectiveness of the proposed algorithms and their improved performance against CSI uncertainties at similar computational cost as the existing non‐robust designs.

Neighborhood search algorithms have been proposed for low complexity detection in large/massive multipleinput multiple-output systems. They iteratively search for the vector, which minimizes the maximum likelihood (ML) cost in a fixed neighborhood. However, the ML solution may not lie in the searched space and also the search may go through a large number of intermediate vectors. Motivated by this, we first propose to cut down the size of the neighborhood so that the complexity of such algorithms can be reduced. Second, we also look for an update which is not restricted to be in a fixed neighborhood. This helps in improving the error performance. For the first purpose, we propose a metric and a few selection rules to decide whether or not to include a vector in the neighborhood. We use the indices of, say K, largest components of the metric for generating a reduced neighborhood set, which is used to reduce the complexity of the existing algorithms while maintaining their error performance. Furthermore, this reduced set facilitates the proposal of two new search algorithms. Simulation results show that the proposed algorithms have a much better error performance and also lower complexity compared with the existing algorithms.

In this work, the authors investigate a multi‐user multi‐input multi‐output (MIMO) interference relay system, where several transmitter nodes simultaneously communicate with their respective receiver nodes through half‐duplex MIMO amplify and forward (AF) relay nodes. For this system configuration, they address the problem of linear transceiver–relay design to achieve max–min fairness among all the users' data streams. Assuming perfect channel state information, this problem is formulated as the maximisation of the minimum signal‐to‐interference‐plus‐noise ratio (SINR) per stream among all the users subject to transmit power constraints at the transmitter and relay nodes. Since the formulated problem of jointly optimising all the transmitters, relays and receivers is non‐convex, a globally optimal solution cannot be easily obtained. Therefore, they propose a quasi‐optimal iterative algorithm to jointly optimise the transmitter precoders, relay precoding matrices and receiver filters for all the users and relays such that the minimum per stream received SINR is improved at each iteration. Simulation results show that the proposed algorithm improves fairness among data‐streams of all users and outperforms existing strategies in terms of minimum user rate and bit error rate.

Breadth first tree search (BFTS) algorithms are known to provide a close to maximum likelihood (quasi-ML) solution at a low-complexity if the received sequence is detected in the right sequence order. However, finding the right sequence order has an exponential overhead. In view of this, we propose to repeatedly apply a BFTS algorithm to all sequence orders. Since it will test all the orders, it is expected to achieve quasi-ML performance. However, this will increase the complexity because of redundant iterations. The complexity can be reduced if we can stop the iterations as soon as a quasi-ML solution is achieved. For this, we propose two stopping rules, one relies on a constellation based heuristic and the other one uses the distribution of ML cost. It is found that their complexity curves have a cross-over point. Thus, a combination of the two rules provides a quasi-ML error performance at a low-complexity for uncoded as well as coded systems. We further show that the proposed stopping rule can reduce the complexity of depth first tree search algorithms also. Last, for large MIMO systems, compared with existing algorithms, it is found to be exceptionally better in terms of both error performance and complexity.

Neighborhood search algorithms have been proposed for detection in large multiple-input multiple-output systems. They iteratively search for the best vector in a fixed neighborhood. A better way could be to look for an update which is not restricted to a fixed neighborhood. Motivated by this, we formulate a problem to maximize the reduction in maximum likelihood (ML) cost and use it to derive an expression for updating the current solution. Using this update and a likelihood function regarding the locations of errors, we propose an unconstrained likelihood ascent search (ULAS) algorithm. ULAS seeks to provide the maximum reduction in ML cost by finding an update which is not restricted to be in a fixed neighborhood. Using simulations, the proposed algorithm has been shown to provide better error performance for uncoded systems than existing algorithms, at lower complexity. We also show that ULAS is amenable to lattice reduction, which helps in obtaining two variants leading to further improvements in performance.

Neighborhood search algorithms have been proposed for detection in large/massive multiple-input multiple-output (MIMO) systems. They iteratively search for the best vector in a fixed neighborhood. However, the ML solution may not lie in the searched space or the search may take a large number of intermediate vectors to converge. Instead of searching in a fixed neighborhood, a better way will be to look for an update which is not restricted to be in a fixed neighborhood. Motivated by this, we formulate an optimization problem to maximize the reduction in ML cost and use it to derive an expression for updating the solution. We use a metric based on the channel matrix and the error vector to determine the likelihood of a symbol being in error. Using this likelihood and the update, we propose a likelihood ascent search (LAS) algorithm to find an update which is not restricted to be in a fixed neighborhood and seeks to provide maximum reduction in ML cost. This process continues till there is a reduction in the ML cost. Compared to existing LAS based algorithms, it is found to provide better error performance, that too at a lower complexity.

Neighborhood search algorithms such as likelihood ascent search (LAS) and reactive tabu search (RTS) have been proposed for low complexity detection in multiple-input multiple-output (MIMO) systems having a large number of antennas. Both these algorithms are iterative and search for the vector which minimizes the maximum likelihood (ML) cost in the neighborhood. In this paper we propose a way to reduce the size of the neighborhood. For this, we propose a metric and a selection rule to decide whether or not to include a vector in the neighborhood. We use the indices of, sayK, largest components of the metric for generating a reduced neighborhood set. This reduced set is used to evaluate the performance of the resulting LAS and RTS algorithms. Simulation results show that this reduces the complexity significantly while maintaining the error performance. We also show that the proposed reduced neighborhood algorithms can make MIMO systems with several hundred antenna pairs feasible.

In this study, the authors consider the min–max mean squared error (MSE)‐based linear transceiver–relay design for multiple‐input–multiple‐output (MIMO) interference relay channel, where a finite number of half‐duplex MIMO amplify and forward relays assist the communication between multiple source–destination pairs. The problem is formulated as minimising the maximum MSE among all data streams of all users subject to individual transmit power constraints at each source and relay node. Since the optimisation problem is non‐convex, globally optimal solution cannot be guaranteed. They propose a suboptimal solution based on alternating minimisation, where the beamforming matrices at all the source, relay and destination nodes are jointly computed in an iterative manner. Numerical simulations show that the proposed algorithm not only ensures fairness among all users’ data streams, but also achieves good sum‐rate and bit error rate performance.

Interference alignment aims to achieve maximum degrees of freedom in an interference system. For achieving Interference alignment in interfering broadcast systems a closed-form solution is proposed in which is an extension of the grouping scheme in . In a downlink scenario where there are a large number of users, the base station is required to select a subset of users such that the sum rate is maximized. To search for the optimal user subset using brute-force approach is computationally exhaustive because of the large number of possible user subset combinations. We propose a user selection algorithm achieving sum rate close to that of optimal solution. The algorithm employs coordinate ascent approach and exploits orthogonality between the desired signal space and the interference channel space in the reciprocal system to select the user at each step. For the sake of completeness, we have also extended the sum rate approach based algorithm to Interfering broadcast channel. The complexity of both these algorithms is shown to be linear with respect to the total number of users as compared to exponential in brute-force search.

We propose a family of Secondary User (SU) power allocation schemes in spectrum sharing OFDM cognitive radio networks. The SU sum rates are maximized subject to a protection criterion for the Primary Users (PU) expressed through a utility function. We demonstrate that a specific choice of utility function leads to the maximization of weighted sum rate of all users, the weight being linked to a guarantee on the PU sum rate. Our formulation also allows trading off individual PU guarantees for higher SU sum rates, with a recently proposed scheme imposing individual PU Rate Loss guarantees being a limiting case.

This paper addresses the problem of fractional timing offset and channel estimation in Multiple input Multiple output orthogonal frequency division multiplexing (MIMO OFDM) systems. The estimators have been derived assuming a flat fading channel and using the maximum likelihood criterion. Closed form Cramer Rao bound (CRB) expressions for fractional timing offset and channel response are also derived. Simulation results have been used to cross-check the accuracy of the proposed estimation algorithm.

The authors propose a new multi-tone (MT) code division multiple access (CDMA) design which has a superior bit error rate (BER) performance than conventional MT CDMA in the presence of frequency offset. The design involves multiplexing of Walsh codes onto the sub-carriers in conjunction with double differential modulation. To exploit the full potential of the design a partial correlation receiver has been proposed. Depending on the signal-to-noise ratio (SNR) and frequency offset it is possible to tune this receiver for the best possible performance. The simulated BER performance of the proposed system has been found to be better than MT CDMA for small as well as large frequency offsets for both single and multi-user systems in additive white Gaussian noise (AWGN) and Rayleigh fading channels.

Training sequences for data-aided timing estimation in multi-input multi-output systems are designed. It is observed that for low complexity implementation, the sequences must necessarily satisfy the zero cross-correlation zone property. By restricting our search to a more tractable subset of this class of sequences, we are able to minimize the modified Cramer-Rao bound in closed form and obtain sequences whose mean square error performance is close to that of the optimal orthogonal sequences. Two constant modulus sequences with even lower implementation complexity are also proposed.

Recently Golay complementary sets were shown to exist in the subsets of second-order cosets of a 𝑞-ary generalization of the first-order Reed–Muller (RM) code. We show that mutually orthogonal Golay complementary sets can also be directly constructed from second-order cosets of a 𝑞-ary generalization of the first-orderRMcode. This identification can be used to construct zero correlation zone (ZCZ) sequences directly and it also enables the construction of ZCZ sequences with special subsets.

A new expression for the probability density function of the signal-to-noise ratio (SNR) at the output of a predetection dual-equal-gain-combining (dual-EGC) receiver over independent but non-identical Rayleigh fading paths with different noise levels is derived. A closed-form expression for the average bit error rate (ABER) for coherent binary modulation schemes is also derived. The effect of the degree of noise imbalance on ABER is studied. From the results we determine the ranges of noise imbalance for a given average SNR per path over which the performance of predetection dual-EGC is better or worse than SC and single path receivers.

We present two maximum likelihood (ML) based estimators for non-data-aided (NDA) symbol timing recovery in MIMO systems. These estimators are based on the classical unconditional ML and the stochastic ML (SML) methods. The proposed estimators utilize information about the particular space-time code used and give performance comparable to data aided estimators, though for a relatively higher complexity. An approximate version of the SML estimator which requires lower implementation complexity is also presented. The loss in SNR due to timing estimation error is also analyzed.

A new linear complexity algorithm using weighted combining is proposed for multiuser detection (MUD) in macrodiversity for synchronous DS-CDMA. Error probability expression is derived for weighted combining based receivers and a framework for finding optimal weights is proposed. Simulation results show that the performance of the proposed algorithm compares with the optimal maximum-likelihood (ML) MUD under various situations.

In this correspondence, we consider the class of finite-state Markov channels (FSMCs) in which the channel behaves as a binary symmetric channel (BSC) in each state. Upper bounds on the rate of LDPC codes for reliable communication over this class of FSMCs are found. A simple upper bound for all noninverting FSMCs is first derived. Subsequently, tighter bounds are derived for the special case of Gilbert–Elliott (GE) channels. Tighter bounds are also derived over the class of FSMCs considered. The latter bounds holdalmost-surelyfor any sequence ofrandomly constructedLDPC codes of given degree distributions. Since the bounds are derived for optimal maximum-likelihood decoding, they also hold for belief propagation decoding. Using the derivations of the bounds on the rate, some lower bounds on the density of parity check matrices for given performance over FSMCs are derived.

Using the approximate Fourier series technique we obtain expressions for the probability of error for bandlimited BPSK signalling in the presence of timing errors and fading. The derived results can be used to compute the error probabilities to any desired accuracy for Nakagami-m and Weibull fading channels. The effect of timing error on the performance of the raised cosine pulse has been evaluated for several fading parameters. We also compare the performance of some useful Nyquist pulses known

We study multicarrier on-off keying (MCOOK) for fast frequency-hopping (FFH) multiple-access systems. The performance of a sub-optimum receiver is analyzed for Rayleigh fading channels and a closed form expression for bit error rate (BER) has been derived for the binary case. We find that the number of chips per symbol required to optimize the perfor- mance of the system varies from system to system. Comparison with FFH M-ary frequency shift keying (MFSK) shows that in the interference-limited region (large MAI), MCOOK performs better than MFSK and further, the gain in the performance increases with increase in the value of modulation index M.

In UWB systems, FCC mask puts a constraint on the Maximum Allowable Transmit Power (MATP) of a pulse. The transmit power of a pulse is an important parameter that determines the BER performance and range. In this paper a subspace based approach has been found to make the MATP optimization easier which otherwise seems intractable due to mask constraints. The design procedure begins with some pulse width and then we optimize for MATP. The obtained pulses turn out to have higher MATP than the known pulses of the same width. We show that using the proposed pulses, a lower BER than that of the existing pulses can be achieved. The proposed approach is applicable to the FCC mask or any other piecewise constant mask that may be proposed in future.

The maximum-likelihood multiuser detection problem in code-division multiple-access is known to be an optimization problem with an objective function that is required to be optimized over a combinatorial decision region. Conventional suboptimal detectors relax the combinatorial decision region by a convex region, without altering the objective function to be optimized. We take an approach wherein the objective function is reduced to a form appropriate for the application of a polynomial complexity algorithm in computational geometry, while keeping the decision region combinatorial. The resulting detector allows a tradeoff between performance and computational complexity. The bit-error rate performance of the detector has been found to be better than the decorrelator and the linear minimum mean-square error detectors, for the same level of complexity.

In this correspondence, new characterizations for the construction of zero correlation zone (ZCZ) sequences from mutually orthogonal Golay complementary sets (MOGCS) is presented. It is shown that the recursive construction of MOGCS is inherent in these characterizations. Previously known constructions of ZCZ sequences and MOGCS are shown to be special cases of this characterization. The notion of mutually orthogonal ZCZ sequence sets is also introduced

Simultaneous down-conversion of multiple band-pass signals is desirable for a number of wireless applications. Bandpass sampling technique can be used for this purpose, but it is difficult to implement and has several drawbacks. In this paper we propose a novel front-end technique to directly down-convert multiple frequency- division multiplexed (FDM) signals separated by certain minimum frequency. A special downconversion function is derived to achieve simultaneous downconversion of the received signals. The technique requires simpler bandpass filters and the ADC has a baseband input as compared to bandpass sampling, which imposes strict requirements on bandpass filters and requires an ADC which can handle RF inputs. The performance of the method has been evaluated by simulating a BPSK receiver employing this technique.

Average symbol error rate (ASER) of an equal gain combining (EGC) receiver with an arbitrary number of branches in exponentially correlated, Nakagami-m fading channels has been derived for binary, differential phase-shift keying (DPSK) and noncoherent frequency-shift keying (NCFSK) modulations. A Parseval's theorem based approach has been used. Numerical and simulation results have been found to be in close agreement. Results show that for a given ASER, as expected, exponentially correlated fading requires a higher SNR with respect to independent fading. For a given number of branches L, increase in SNR required (SNR penalty) with respect to independent fading is less for higher values of fading parameter m while for a given m, SNR penalty is more for higher L

For a given blocklength we determine the number of interleavers which have spread equal to two. Using this, we find out the probability that a randomly chosen interleaver has spread two. We show that as blocklength increases, this probability increases but very quickly converges to the value 1 - e-2ap 0.8647. Subsequently, we determine a lower bound on the probability of an interleaver having spread at least s. We show that this lower bound converges to the value e-2(s-2)2, as the blocklength increases

Using a Gil-Palaez lemma-based approach, we derive a general expression for the bit-error rate of a predetection equal gain combining receiver for coherent binary phase-shift keying modulation in exponentially correlated, Nakagami-m fading channel for an arbitrary number of branches. The obtained expressions are different for even and odd numbers of branches. Numerical results have been corroborated with simulations.

In code-division multiple-access (CDMA) systems, it is interesting to study the optimal bandwidth allocation to coding and spreading in order to maximize the number of users that the system can accommodate. This optimal bandwidth allocation is referred to as the optimal allocation point (OAP). In this brief, a practical CDMA system with a fixed total-bandwidth expansion factor that employs convolutional codes and random spreading is considered. The receiver consists of a multiuser linear-minimum-mean-square-error (lmmse) detector front end followed by autonomous single-user decoders. Intuitive reasoning is applied for the existence of an OAP in such a system. Also, we present a theoretical formulation to estimate the OAP in the aforementioned system. Simulations confirm the correctness of results obtained. Further, the paper investigates system behavior at different values of information-bit signal-to-noise ratio (SNR). At high values of SNR, within the range considered, the system favors spreading only. However, at relatively lower SNRs, channel coding is required to improve the system performance, and it is important that we operate at the OAP obtained.

Geolocation using received signal strength (RSS) has large errors due to multipath fading, since fading results in high variations in RSS. We show how and when spatial diversity combined with channel knowledge at the receiver can be used to combat fading effects to increase accuracy in location estimation. We then propose a simple scheme for distance estimation, characterize the channels for which improvement in distance estimates can be thus obtained and prove that the mean square error of the distance estimate converges to zero with increasing diversity order. It is observed that the improvement can always be obtained for the Rayleigh channel, and for the Nakagami-m channel if the parameter m remains the same regardless of the distance.

Recently, there has been work in use of LDPC codes over channels with memory, in particular, over Gilbert-Elliott (GE) channels. In this paper, we derive expressions for upper bounds on the rate of LDPC codes for reliable communication over a large class (non-oscillatory and non-inverting) of GE channels using the methods for memoryless channels.

We consider here the problem of allocating variable length orthogonal codes in an ad hoc network based on CDMA. We consider a snapshot version of the problem at some instant. It had been proved earlier than even for a static set of communications and topology the problem is intractable. A greedy algorithm is stated to provide a bounded approximation to the throughput maximizing optimal allocation. We present a simple distributed code allocation protocol based on the greedy approximation. Simulation experiments show the enhanced throughput obtained by our protocol as compared to other code allocation schemes.