In this paper, we consider the minimum mean-squared error (MMSE) equalization for uplink multi-user multiple-input multiple-output communications. In particular, the transmitters adopt discrete-Fourier transform (DFT)-spread orthogonal frequency-division multiplexing (OFDM) to send$\pi /2$-PAM or square-QAM symbols, possibly with frequency-domain spectrum shaping (FDSS). It is well known that, in such cases with improper-complex symbols, widely-linear (WL) equalizers can improve performance over linear equalizers, but at the cost of sometimes drastically increased computational complexity. To overcome this, we exploit the spectral correlation in the received signal induced by the impropriety from$\pi /2$-PAM symbols and the cyclostationarity from the FDSS. The key differences from conventional high-complexity structures are to represent all the symbols as equivalent PAM symbols that are subsequently$\pi /2$-modulated, and to factor the effective channel into the$\pi /2$-modulator, the DFT-spreader, and a partial channel defined in the frequency domain. These representation and factoring enable us to design a low-complexity structure of the WL-MMSE equalizer that performs the signal processing mostly in the frequency domain and involves only sparse and structured matrices. Numerical results show that the proposed structure achieves significantly lower complexity than the conventional structures and that it greatly outperforms the linear MMSE equalizer with a similar complexity.

In this paper, the Nyquist criterion for ordinary linear modulation is generalized to the discrete-Fourier transform-spread (DFT-spread) orthogonal frequency-division multiplexing (OFDM). In particular, the DFT-spread OFDM of constellation-rotated PAM symbols is considered with frequency-domain spectrum shaping (FDSS). This includes the DFT-spread OFDM of π/2-BPSK symbols as a special case, which is supported by the 5th generation New Radio standard. Unlike the conventional Nyquist criterion with a linear receiver, the new criterion is to remove intersymbol interference in the output of a widely-linear receiver. It is shown that not only the folded spectrum but also the shifted and reverse-folded spectrum is crucial in the criterion, where the shift offset is determined by the rotation angle. As a design example, combinations of a constellation rotation angle and a square-root raised cosine pulse are proposed. It is shown that the proposed design can achieve better performance both in spectral efficiency and in peak-to-average power ratio than the conventional DFT-spread OFDM of π/2-BPSK symbols with FDSS.

In this paper, the Nyquist criteria for ordinary linear modulation are generalized to the discrete-Fourier transform-spread (DFT-spread) orthogonal frequency-division multiplexing (OFDM) of constellation-rotated PAM symbols. Unlike the conventional Nyquist criteria with a linear receiver, the new criteria are to remove intersymbol interference in the output of a widely-linear (WL) receiver. It is shown that not only the folded spectrum, but also the shifted and reverse-folded spectrum is crucial in the criteria, where the shift offset is determined by the rotation angle. As a design example, combinations of a constellation rotation angle and a square-root raised cosine pulse are proposed. It is shown that the proposed design can achieve better performance both in spectral efficiency and in peak-to-average power ratio than the conventional DFT-spread OFDM of π/2-BPSK symbols. The optimal one-tap frequency-domain equalizer is also derived under the WL zero-forcing (ZF) constraint. It is shown that, when the rotation angle is properly chosen, the proposed one-tap WL-ZF equalizer significantly outperforms the one-tap linear ZF equalizer in output signal-to-noise ratio. The proposed equalizer also outperforms the conventional equalizer in error vector magnitude measured at the output of a nonlinear power amplifier.

In this paper, a calibration of fully-switched multiple-input multiple-output (MIMO) channel sounders with internal crosstalk is considered. The objective is to reduce the number of back-to-back (B2B) connections needed to estimate the transmitter (Tx) and receiver (Rx) response matrices that convey the information about linear distortion and internal crosstalk. For the B2B measurements, a signal and system model is developed using only a few pairs of the Tx and Rx ports of the sounder among all pairs of ports. Using the measurement model, a least-square estimation problem is then formulated and converted in the frequency domain into weighted rank-one approximation problems. Some exemplary sets of B2B connections are proposed for which fewer B2B connections are required than before. Given a proposed set of B2B connections, the alternate convex search (ACS) algorithm with a proper initialization is also proposed to solve the weighted rank-one approximation problems. Numerical results show that the ACS algorithm with the proposed initialization achieves a calibration performance only after a couple of iterations comparable to the conventional method that requires the B2B connections of all port pairs.

In this paper, the problem of calibrating a fully switched MIMO channel sounder is considered that has internal crosstalk. A system model is proposed that takes into account the effect of the internal crosstalk in the transmitter and receiver response matrices. Then, a least-square system identification problem is formulated that utilizes to a set of back-to-back measurement data to find the estimates of the response matrices. It is shown that the solution can be found by making rank one approximations in the frequency domain. In addition, a channel estimation method for calibrating field measurement data is proposed by using the identified response matrices of the sounder. Experimental and simulation results show that the proposed approach outperforms the conventional approach that ignores the crosstalk.

In this paper, the problem of reducing the peak-to-average power ratio (PAPR) of a discrete Fourier transform-spread orthogonal frequency-division multiplexing signal is considered for the transmission of constellation-rotated QPSK symbols. In particular, a joint optimization of the constellation-rotation angle and the pulse-shaping vector is conducted, where the number of allocated subcarriers is larger than the number of QPSK symbols. To avoid the exponential complexity required to evaluate the exact PAPR, a computationally efficient upper bound on the worst-case PAPR is presented and adopted as the objective function. The signal-to-interference-plus-noise ratio (SINR) at the output of a constellation-derotating matched filter is also presented. Then, joint optimizations are conducted through numerical search for various target SINRs. Surprisingly, the optimal rotation angle is close to but not exactly equal to π/4. Numerical results show that the proposed technique is not only applicable to QPSK symbols but also to QAM symbols to significantly reduce the PAPR.

In this paper, the problem of further reducing the peak-to-average power ratio (PAPR) of a discrete Fourier transform-spread orthogonal frequency-division multiplexing signal is considered for the transmission of π/2-BPSK symbols in the 5G New Radio specifications. In particular, a joint optimization of the constellation-rotation angle and the pulse-shaping vector is conducted. To avoid the exponential complexity required to evaluate the PAPR, a computationally efficient upper bound on the worst-case PAPR is presented and adopted as the objective function. The signal-to-interference-plus-noise ratio (SINR) at the output of a constellation-derotating matched filter is also presented. Then, joint optimizations are conducted through numerical search for various target SINRs. Surprisingly, the optimal rotation angle is close to but not exactly equal to π/2. It is shown that the proposed combinations significantly outperform the existing combinations of the rotation angle and the shaping vector when the signal is amplified by a nonlinear PA.

In this paper, single-carrier (SC) block transmission of improper-complex data symbols is considered over a multiple-input multiple-output (MIMO) frequency-selective channel with data-like cochannel interference (CCI). To exploit the cyclostationarity and impropriety of the desired and the interfering signals, an equalizer is designed that oversamples the received signal and then processes the sampled block by using widely-linear (WL) feedforward (FF) and noise-predicting feedback (NP-FB) filters. For the given equalizer structure, the minimum mean-squared error (MMSE)-optimal WL FF and NP-FB filters have high computational complexity due to the augmented correlation matrix of the data-like CCI in the received signal. Motivated by the asymptotic property of the correlation matrix, we approximate in the frequency domain the matrix by a block matrix with diagonal blocks. This leads to the low-complexity WL design of a frequency-domain FF filter and a causally noise-predicting FB filter. It is shown that this MIMO SC frequency-domain equalizer with noise prediction is asymptotically optimal in the sense that the average mean-squared error converges to that of the MMSE-optimal equalizer as the block length tends to infinity. Numerical results show that the proposed equalizer performs well even with a moderate block length.

In this paper, the design of a selfless overlay system is considered for a frequency-selective bandlimited linear time-invariant channel already occupied by a legacy system. It is assumed that the transmitted signal by the legacy system is well modeled by a zero-mean second-order cyclostationary (SOCS) Gaussian random process. It is also assumed that the legacy receiver employs a linear-conjugate linear (LCL) filter to capture possible impropriety of the signal. Our objective is to maximize the throughput of the overlay system under the constraint that no interfering signal component is observed at the output of the legacy LCL filter sampled at a uniform rate. A relevant problem of deriving the constrained capacity of a discrete-time vector Gaussian noise channel is first examined. Then, it is shown that the optimal input to the overlay channel must be a zero-mean SOCS Gaussian random process. Using these results, the optimization problem is formulated in the frequency domain, and the procedure named orthogonal cyclic water filling (O-CWF) is derived to find the optimal channel input distribution. Numerical results are provided to show that the proposed selfless overlay scheme enables reliable communication even over a channel fully occupied by a legacy system.

In this paper, a full-duplex (FD) amplify-and-forward (AF) relay is designed to compensate for the duplexing loss of the half-duplex (HD) AF relay. In particular, when there is no direct link between a source and a destination, joint analog domain self-interference suppression and digital domain residual self-interference cancellation is considered with an FD-AF relay having single receive antenna but multiple transmit antennas. Unlike previous approaches, a nonconvex quadratically constrained quadratic programming problem is formulated to find the optimal solution. The end-to-end spectral efficiency or, equivalently, the end-to-end signal-to-interference-plus-noise ratio from the source to the destination is chosen as the objective function to be maximized subject to the average transmit power constraint at the relay. In addition, an average power constraint is imposed on the output of the relay's receive antenna to avoid the nonlinear distortion in the low noise amplifier and the excessive quantization noise in the analog-to-digital converter. Through the systematic reduction and the partitioning of the constraint set, the optimal solution is derived in a closed algorithmic expression and shows how it allocates the transmission power not only in the direction of maximal performance improvement but also in the orthogonal direction in order to balance the system performance and the amount of self interference. It is shown that the optimal FD-AF relay significantly outperforms the optimal HD-AF relay even with the hardware limitations in the RF chain of the relay's receiver being well taken into account.

In this paper, the block processing of a discrete-time (DT) improper-complex second-order cyclostationary (SOCS) random process is considered. In particular, it is of interest to find a preprocessing operation that enables the adoption of conventional signal processing techniques and algorithms developed for the filtering of proper-complex signals and that leads to computationally efficient near-optimal postprocessing. An invertible linear-conjugate linear (LCL) operator named the DT frequency shift (FRESH) properizer is first proposed. It is shown that the DT FRESH properizer converts a DT improper-complex SOCS random process input to an equivalent DT proper-complex SOCS random process output by utilizing the information only about the cycle period of the input. An invertible LCL block processing operator named the asymptotic FRESH properizer is then proposed that mimics the operation of the DT FRESH properizer but processes a finite number of consecutive samples of a DT improper-complex SOCS random process. It is shown that the output of the asymptotic FRESH properizer is not proper but asymptotically proper and that its frequency-domain covariance matrix converges to a highly structured block matrix with diagonal blocks as the block size tends to infinity. Two representative estimation and detection problems are presented to demonstrate that asymptotically optimal low-complexity postprocessors can be easily designed by exploiting these asymptotic second-order properties of the output of the asymptotic FRESH properizer.

In this paper, the sum-rate optimal restricted FDMA system is investigated for asymmetric-power users, when they have individual upper limits on the bandwidths in addition to a constraint on total system bandwidth. A convex optimization problem is formulated to optimally allocate the system bandwidth to the users. First, the users are classified into oversized and non-oversized users, based on the strength of their minimal power spectral densities (PSDs). Then, the maximum sum rate and the unique optimal solution in a closed algorithmic expression are derived by using the Karush-Kuhn-Tucker optimality conditions. An iterative algorithm to construct the optimal solution is also presented that provides insights into the restricted FDMA system. Interestingly, the non-oversized users end up with an equal PSD among one another, which is always less than the PSDs of the oversized users, if they exist. It turns out that the sum-rate optimal restricted FDMA system achieves the sum capacity of the band-limited multiple-access channel if and only if there is no oversized user.

In this paper, a joint analog and digital domain self-interference cancellation is considered for the full-duplex (FD) amplify-and-forward (AF) relay with a single receive antenna but multiple transmit antennas. Under the assumption that there is no direct link between a source and a destination, the end-to-end spectral efficiency is maximized subject to the average transmit power constraint at the relay. Unlike previous approaches, an average power constraint is imposed also on the output of the relay's receive antenna to take into account the hardware limitations in the RF chain of the relay's receiver. A nonconvex quadratically constrained quadratic programming problem is formulated and the optimal beamforming vector is derived in a closed algorithmic expression through the systematic reduction and the partitioning of the constraint set. It is shown that the FD-AF relay significantly outperforms the half-duplex (HD) AF relay by properly compensating for the duplexing loss of the HD-AF relay.

In this paper, a low-complexity widely linear minimum mean-squared error (WLMMSE) estimator is proposed for a sampled improper-complex second-order cyclostationary (SOCS) random process. The conventional WLMMSE estimator that directly processes the sampled vector and its complex conjugate suffers from high computational complexity in matrix inversion and multiplication when the sample size is large. To overcome this shortcoming, the proposed estimator approximates the frequency-domain covariance and complementary covariance matrices by a block matrix with diagonal blocks and that with anti-diagonal blocks, respectively, which is motivated by the fact that both the two-dimensional (2-D) power spectral density (PSD) and the 2-D complementary PSD of an SOCS random process consist of equally spaced impulse fences. Moreover, unlike the conventional WLMMSE estimator, the proposed estimator processes the sampled vector and its complex conjugate after removing redundancies, which further reduces the complexity. It is shown that, for sufficiently large observation period, the redundancy-removing procedure results in a statistic that is approximately proper and sufficient. It is also shown that the proposed estimator is asymptotically optimal in the sense that the average mean-squared error converges to that of the WLMMSE estimator as the observation period tends to infinity.

In this paper, the sum rate of a multicode code-division multiple-access (CDMA) system with asymmetric-power users is maximized, given a processing gain and the power profile of users. Unlike the sum-rate maximization for a single-code CDMA system, the optimization requires the joint optimal distribution of each user's power to its multiple data streams as well as the optimal design of signature sequences. The crucial step is to establish an equivalence of the multicode CDMA system to restricted frequency-division multiple-access (FDMA) and time-division multiple-access (TDMA) systems. The CDMA system has upper limits on the numbers of multicodes of users, whereas the FDMA system has upper limits on the bandwidths, and the TDMA system has upper limits on the duty cycles of users. The equivalence facilitates the complete characterization of the maximum sum rate of the multicode CDMA system and also provides new insights into single- and multicode CDMA systems in terms of the parameters of the equivalent FDMA and TDMA systems.

In this paper, we derive the capacity of a continuous-time, single-input single-output (SISO), frequency-selective, band-limited, linear time-invariant (LTI) channel, whose output is corrupted by a second-order cyclostationary (SOCS) complex Gaussian noise. By using a pair of invertible, linear-conjugate linear time-varying operators called a properizing FREquency SHift (p-FRESH) vectorizer and a p-FRESH scalarizer, it is shown that, whether the complex noise is proper or improper, the SISO channel can always be converted to an equivalent multiple-input multiple-output (MIMO) LTI channel whose output is now corrupted by a proper-complex vector wide-sense stationary noise. A variational problem is then formulated in the frequency domain to find the optimal input distribution that maximizes the throughput of the equivalent MIMO channel. It turns out that the optimal input to the SISO channel, obtained through a procedure similar to the water filling, is an SOCS complex Gaussian random process with the same cycle period as the noise. It is shown that this procedure, named cyclic water filling, significantly outperforms ordinary water filling by effectively utilizing the spectral correlation of the cyclostationary noise.

In this paper, the design of a low-complexity linear equalizer is considered for single-carrier (SC) block transmission in the presence of inter-symbol interference (ISI) and data-like co-channel interference (CCI). Unlike the linear minimum mean-squared error (LMMSE) frequency-domain equalizer (FDE) designed to suppress ISI only, the LMMSE FDE suffers from high computational complexity due to the CCI component in the signal correlation matrix. Motivated by the fact that the double Fourier transform of the autocorrelation function of a wide-sense cyclostationary process consists of impulse fences with equal spacing, a low-complexity FDE is proposed that approximates the frequency-domain correlation matrix of the CCI plus noise by a block matrix with diagonal blocks. It is shown that the proposed FDE is asymptotically optimal in the sense that the average mean-squared error (MSE) converges to that of the LMMSE FDE as the block length tends to infinity. It is also shown that the proposed FDE is more numerically stable than the LMMSE FDE when the receive filter is matched to the transmit filter and its output is over-sampled to better capture the cyclostationarity of the CCI. Discussions and numerical results include SC block transmission systems with unique word instead of cyclic prefix, and systems with multiple receive antennas.

In this paper, the design of an overlay system is considered that operates on a channel already occupied by a legacy system. It is assumed that the legacy transmitter generates a cyclostationary signal, and that the legacy receiver is equipped with a linear filter followed by a uniform sampler. Under a zero-interference constraint at the legacy receiver, the meansquared error at the overlay receiver is minimized to find the optimal overlay system that employs linear modulation and demodulation. For the trade-off between performance and rate of the overlay system, the problem is formulated to allow a transmission rate that is a fraction of the fundamental cycle frequency of the legacy signal. The notion of a virtual legacy receiver is devised to incorporate cases with non-identical frequency bands for the transmission and reception of the overlay signal. Using the vectorized Fourier transform technique, the problem is reformulated, the solution is derived, and a necessary and sufficient condition for the existence of the optimal solution is found, all in the frequency domain. Numerical results show that the proposed scheme significantly improves the spectral efficiency by effectively exploiting the cyclostationarity of the legacy signal.

Spectrum sensing is an activity of a cognitive radio to detect the presence of a primary user in the frequency band of interest. In this paper, we consider under the Neyman-Pearson criterion the detection of a primary-user signal that linearly modulates codeword symbols from a Gaussian codebook. To reduce the complexity in computing the likelihood ratio, a simple method based on the approximation of signal covariance matrices is presented. By invoking the Central Limit Theorem, the approximate probability distribution of the decision statistic, the threshold for decision, and the performance of the proposed detector are computed and parameterized only by the overall pulse shape and noise variance. Numerical results show that the proposed detector with much lower computational complexity performs almost the same as the optimal detector. The signal-to-noise ratio wall of the proposed detector is also investigated to quantify the performance limit under uncertainty in the noise variance.

In this paper, a full-duplex amplify-and-forward (AF) relay is considered that suffers from self-interference in a MIMO wireless channel. We derive the optimal transformation matrix that maximizes the mutual information under average power constraint at the relay output. The capacity of the channel without a direct path is derived and it is shown that the relay maximizes the throughput as if there is no interference from the relay itself. A comparison is made to the channel with a half-duplex relay having the same average transmission power. In particular, a necessary and sufficient condition is derived in terms only of the signal-to-noise ratios (SNRs) for a full-duplex relay to perform better than a half-duplex relay in SISO cases. A simple rule of thumb shows that a full-duplex relay outperforms a half-duplex relay if the sum of the SNR in dB at the relay input and that at the destination input is greater than 0.75. Numerical results show that this result also holds for MIMO channels approximately.

In this paper, we consider overlaying a secondary-user signal over a satellite communication channel occupied by a primary user. The objective is to find the jointly optimal transmitter and receiver pair of a secondary system to minimize the mean squared error (MSE) at the output of the secondary receiver, subject to zero interference induced at the output samples of the primary receiver. It is assumed that both the primary and the secondary transmitters employ linear modulation and the receivers employ linear filter front-ends. Unlike prior work, the secondary user is allowed to transmit data symbols at a fraction of the primary user's symbol rate. This rate reduction technique enables the secondary user to achieve the additive white Gaussian noise (AWGN) bound or the performance close to the AWGN bound even when the excess bandwidth of the primary user is very small but positive. Numerical results show that the proposed scheme significantly improves the spectral efficiency by exploiting the cyclostationarity of the primary-user signal.

In this paper, linear minimum mean-squared error (LMMSE) frequency domain equalizers (FDEs) are considered for single-carrier (SC) block transmission over additive wide- sense cyclostationary (WSCS) noise. Using the theory of asymptotically equivalent sequences of matrices, it is shown that the mean-squared error (MSE) of cyclic prefix (CP) appended SC- FDE and that of the unique word (UW) appended SC-FDE converge to the same limit as the block length tends to infinity. The closed-form expression of the limit is also derived. Unlike SC-FDEs in additive white Gaussian noise, the computational complexity of the FDEs are as high as that of the time domain equalizers in the presence of the WSCS noise. So, suboptimal SC- FDEs with much lower computational complexity are proposed that achieve the asymptotic MSE of the LMMSE SC-FDEs as the block length tends to infinity. Numerical results are also provided.

In this paper, a frequency-domain joint maximum- likelihood (ML) estimation of channel and radio frequency (RF) chain responses is considered when noisy side information is available. The channel includes only transmit and receive antennas and radio propagation medium, while the RF chain includes transmitter (Tx) and receiver (Rx) RF chains. A side information vector of the same length as an observation vector is obtained by directly connecting the Tx and the Rx RF chains after removing the antennas. Since the Rx RF chain is a part of the RF chain whose response is unknown, the problem appears ill-posed because the covariance matrices of Gaussian noise components in the observation and the side information vectors are unknown. However, it is shown, by using asymptotically equivalent sequences of matrices, that the simple entry-by-entry division of the discrete Fourier transform (DFT) of the observation vector by the DFT of the side information vector leads to the jointly optimal channel estimate if the length of the vectors is sufficiently large. A typical experimental result that is obtained using wideband channel sounders is also provided.

In this paper, a frequency-division counterpart of joint power control and sequence design problem for code- division multiple-access (CDMA) systems is solved. Total transmit and receive power minimizations are considered for frequency- division multiplexing (FDM) and frequency-division multiple- access (FDMA) communications over overloaded channels. After the definition of channel overloading for CDMA systems is extended to the frequency-division systems, the user admissibility is characterized by a necessary and sufficient condition for the existence of the optimal solution under unequal signal-to- interference-plus-noise ratio constraints at the output of linear receivers and asymmetric data transmission rate constraints among users. The optimal signal power, bandwidth, transmit waveform, and receive waveform are derived for each user as the decision parameters of the optimization problem. It is shown that, if this solution is applied for the uplink users to minimize the total receive power, the optimal FDMA system performs the same as the optimal CDMA system. It is also shown that, if this solution is applied for the downlink users to minimize the total transmit power, the optimal FDM system always outperforms the code-division system that minimizes the extended total squared correlation. Numerical results suggest that the optimal FDM system and the optimal downlink code-division system achieve the same performance when the total transmit power is minimized.

In this paper, signature waveforms and signal powers are jointly optimized for multiuser communications over strictly bandlimited, continuous-time, overloaded channels corrupted by additive white Gaussian noise (AWGN). The total signal power is minimized subject to general asymmetric signal-to-interference-plus-noise ratio (SINR) constraints at the output of linear minimum mean-squared error (LMMSE) receivers. Using vectorized Fourier transform (VFT) technique, the optimal solutions as well as a necessary and sufficient condition for the existence of a feasible solution are derived in the frequency domain. It turns out that every optimal solution performs the same as the optimal frequency-division multiple-access (FDMA) system. A geometric procedure called multiuser constrained water-pouring is developed to construct every possible optimal solution, of which profiles of signal power and equivalent bandwidth are, respectively, the same as those of signal power and physical bandwidth of the optimal FDMA system. It is shown that orthogonal signature waveforms are assigned to oversized users and continuous-time equivalents of generalized Welch bound equality (CTE-GWBE) sequences are assigned to non-oversized users.

In this paper, the jointly optimal transmitter and receiver pair of an overlay system is derived to minimize the mean squared error (MSE) at the output of the linear receiver, subject to zero interference induced to legacy systems already existing in the frequency band of interest. It is assumed that the overlay and the legacy systems all employ linear modulation with the same symbol transmission rate but they are not necessarily symbol- synchronized. The symbol sequences are modeled as wide-sense stationary (WSS) colored random processes and the channels are modeled as strictly band-limited linear time-invariant systems with frequency selective impulse responses. Using the vectorized Fourier transform (VFT) technique, the optimal transmit and receive waveforms are derived in the frequency domain. Numerical results show that the proposed system significantly improves the bit error rate (BER) performance over the systems with receiver-only optimization and the systems with no transmitter and receiver optimization.

Under general asymmetric signal-to-interference- plus-noise ratio (SINR) constraints at the output of linear minimum mean-squared error (LMMSE) receivers, the joint transmitter and receiver optimization is performed to achieve the minimum total signal power for overloaded multiuser communications in additive white Gaussian noise (AWGN). Unlike previous works that find the optimal signaturesequences, the signal powers, and despreadingsequences, the problem is solved to find strictly band-limited, continuous-time signaturewaveforms, signal powers, and receivewaveforms. A necessary and sufficient condition for user admissibility is derived, and the optimal solutions are obtained in the frequency domain through vectorized Fourier transform (VFT) technique. A geometric procedure called multi-user constrained water-pouring is proposed to construct optimal solutions. It turns out that the optimal FDMA system is among the optimal multiple-access schemes given the optimality criterion.

In this paper, it is shown that single-carrier (SC) linear minimum mean-squared error (LMMSE) frequency domain equalizer (FDE) is asymptotically equivalent to continuous-time (CT) LMMSE equalizer in the limit of a very large block length. The equivalence is established in the sense that the mean-squared error (MSE) of the SC LMMSE-FDE converges to that of the CT LMMSE equalizer. First, the asymptotic MSE of the SC LMMSE-FDE is derived. Then, the necessary and sufficient condition for the asymptotic equivalence is obtained. It is shown that if the received signal is sampled slower than the Nyquist rate then no fixed receive filter followed by a symbol-rate sampler can achieve the MSE of the CT LMMSE equalizer, given an arbitrary channel response. On the contrary, if the received signal is sampled faster than the Nyquist rate then the MSE of the CT LMMSE receiver can be asymptotically achieved by any square-root Nyquist receive filter, of which energy spectral density is flat over transmitted signal's frequency band. Representative numerical results are provided and discussions on convergence rate are also provided.

In this paper, the peak-to-average power ratio (PAPR) is evaluated for the uncoded orthogonal frequency division multiplexing (OFDM) signals generated by using the IDFT procedure. The power spectral density of the transmitted OFDM signal is derived, taking into account the effects of cyclic prefix, windowing, digital-to-analog converter, null-subcarriers, and analog transmit filter. The PAPR distribution is then analyzed based on the extreme value theory. It is shown that the PAPR distribution is parameterized only by the length of the observation interval and the root mean square bandwidth of the signal, whose computation requires the PSD of the transmitted signal. Numerical results confirm that the proposed analysis accurately predicts the PAPR distribution of practical OFDM signals.

A new asymptotic analysis is presented to establish whether or not commonly used techniques to approximate the performance of direct-sequence spread-spectrum multiple-access (DS/SSMA) systems still apply when the systems are strictly band limited. The results apply to any linear data modulation and spreading scheme. The interference components, including the interchip interference (ICI) of a linear receiver output, are shown to be asymptotically jointly Gaussian random variables conditioned on the phases and delays of the interfering signals. Expressions for the error probabilities of band-limited systems are also developed from this result.

In this paper, the optimal design of a wideband overlay system is considered for communications over a white Gaussian noise channel corrupted by the signal from an existing system. Under the assumptions that the symbol transmission rate of the new system is an integer multiple of that of the existing system and that the transmit filter is time invariant, the optimum transmitter and receiver waveforms are derived that jointly minimize the average mean-squared error (MSE) at the output of the linear receiver of the new system. It is shown that this joint optimization technique leads to significant performance improvement through complete interference avoidance over the overlay systems with receiver-only optimization, and over those with no transmitter and receiver optimization. It is also shown that, if the existing system does not induce any self interference, the derived solution reduces to the generalized Nyquist condition for no mutual as well as self interference. The case where the symbol transmission rate of the existing system is an integer multiple of that of the new system is also briefly discussed.

In this paper, Welch's lower bound on the total squared correlation (TSC) for a set of vectors is extended to a set of band-limited waveforms. First, a continuous-time equivalent of total squared correlation (CTE-TSC) is derived by examining the definition of the TSC for a set of vectors in multiple access communication system. The multiple-access system is assumed to employ these vectors as spreading sequences and matched filters as receivers. Then, a lower bound on the CTE-TSC is derived using a frequency domain approach. It is shown that the lower bound on the CTE-TSC has the same form as the Welch's lower bound except that the dimensionality of the vectors is replaced by the average degrees of freedom of the vectorized Fourier transform of the band-limited waveforms. Unlike the dimensionality of a vector, this average degrees of freedom of a band-limited signal used as a transmit waveform for a linear modulation is not restricted only to positive integers. Interestingly, it turns out that the set of waveforms that achieves the lower bound on the CTE-TSC is also the set of the optimum transmit waveforms for overloaded multiple access communication system employing linear minimum mean-squared error (LMMSE) receivers. This extends to continuous cases the discrete counterpart that the Welch bound equality sequences are optimal sequences for overloaded synchronous code-division multiple-access system employing LMMSE receivers

In this paper, a linear receiver is proposed and its performance is analyzed for direct-sequence spread-spectrum communications with wideband data-like interference. Two groups of communicators employing generalized random spreading are considered, and the signals are assumed to have harmonically related cyclostationarity periods. First, the output signal-to-interference ratio (SIR) of a general correlation receiver is derived in the frequency domain, and the key system parameters that affect the structure of the interference are identified. Then, a linear interference suppression scheme based on the maximum SIR (MSIR) criterion is proposed, and a receiver structure similar to the cyclic Wiener filter is derived. Numerical results show that the proposed linear MSIR receiver significantly outperforms the conventional correlation receiver by effectively suppressing the wideband data-like interference.

Performance bounds on chip-matched-filter (CMF) receivers for bandlimited direct-sequence spread-spectrum multiple-access (BL-DS/SSMA) systems with aperiodic random spreading sequences are obtained. First, the optimum transmit-receive chip waveform pairs that maximize the conditional signal-to-interference ratio are derived. This leads to performance bounds on CMF receivers when the conditional Gaussian approximation for cyclostationary multiple-access interference (MAI) is exploited. The bounds are used to examine the dependence of the MAI suppression capability of the CMF receivers on the excess bandwidth of the system and the delay profile of multiple-access users. The system employing the flat-spectrum chip waveform pair is shown to have near-optimum average bit-error rate performance among the fixed CMF (FCMF) receiver systems. Numerical results are provided for an adaptive CMF receiver and for FCMF receivers employing several different fixed chip waveforms.

The theory developed on the sequence optimization for equal-power code-division multiple-access (CDMA) systems is generalized in this paper. Unlike previous works, where discrete-time or vector channel models are predominantly employed, the overloaded channels are modeled as strictly band-limited, continuous-time multiple-access channels corrupted by additive white Gaussian noise (AWGN). After being posed as a multiple-input/single-output (MISO) joint transmitter and receiver optimization problem with the total mean-squared error (MSE) as the objective functional to be minimized, the variational problem is solved by using a frequency-domain approach. It is shown that there exist continuous-time equivalents of Welch bound equality (CTE-WBE) sequences as the jointly optimum transmit waveforms and that the matched filters are the jointly optimum receivers. The user capacity of the band-limited channels is characterized by a necessary and sufficient condition for the admissibility of users into the system in terms of the channel load, the received signal-to-noise ratio, and the signal-to-interference-plus-noise ratio (SINR) requirement. It is also shown that CTE-WBE sequences achieve the lower bound on the continuous-time equivalent of total squared correlation (CTE-TSC).

An optimal power and bandwidth allocation problem is considered for multi-rate frequency-division multiplexing (FDM) and frequency-division multiple-access (FDMA) over overloaded channels. We have derived the optimum frequency-division system that minimizes the total transmitted power subject to the QoS of users defined in terms of the transmission rates and the SINR requirements. The necessary and sufficient condition is found for the admissibility of the users, and the optimum power, bandwidth, transmit waveform, and receive waveform are found for each user. It is shown that the optimum frequency-division system performs exactly the same as the optimum CDMA system when all the users have the same transmission rate and channel gain. It is also shown that the optimum frequency-division system always outperforms the ETSC-minimizing code-division system when all the overloading users have the same transmission rate.

In this paper, the optimal signaling problem for multiple-access communications over Gaussian overloaded channels is considered with equal-power users having linear minimum mean-squared error (LMMSE) receivers. Unlike previous similar work on the sequence design for code-division multiple-access (CDMA) communications where discrete-time or vector channel models are predominantly employed, the overloaded channel is modeled as a strictly band-limited, continuous-time multiple-access channel corrupted by an additive white Gaussian noise. After being posed as a multi-input/single-output (MISO) joint transmitter and receiver optimization problem with the total mean-squared error as the objective functional, the variational problem is solved by using a frequency-domain approach. It is shown that the matched filters are the optimal receivers and that there exist continuous-time equivalents of Welch bound equality (CTE-WBE) sequences as the optimal transmit waveforms. The user capacity of the band-limited channel in terms of the admissibility of users into the system is also characterized by a necessary and sufficient condition on the channel load, the received signal-to-noise ratio, and the maximum signal-to-interference ratio.

In this paper, we have proposed a novel concept called Hitch-hiking in order to reduce the energy consumption of broadcast application for wireless networks. Hitch-hiking takes advantage of the physical layer design that facilitates the combining of partial signals to obtain the complete information. The concept of combining partial signals using maximal ratio combiner [J.G. Proakis, 2001] has been used to improve the reliability of the communication channel but has never been exploited to reduce energy consumption. We propose a centralized heuristic algorithm called wireless multicast with Hitch-hiking (WMH) to construct an energy efficient tree using Hitch-hiking and also present a distributed version of the heuristic. We also evaluate the proposed heuristics through simulation. Simulation results show that Hitch-hiking can reduce the transmission cost of broadcast by as much as 50%. Further, we propose and evaluate a protocol called PSBT that reduces energy consumption of broadcast by eliminating redundancy in receive operation. Finally, we propose an algorithm that takes advantage of both Hitch-hiking and PSBT in conserving energy

This paper presents the basic CDMA model with jointly optimal signature sequences and power allotment for overloaded multiuser communications. The linear minimum mean-squared-error (LMMSE) receivers are being employed. It is shown that the Welch bound equality (WBE) sequences are optimal sequences for equal SINR requirements. It is also shown that users are admissible if and only if the summation of effective bandwidths is less than the processing gain. However, the notion of the Welch bound equality sequences are extended to the continuous-time waveforms.

Gaussian approximations to the overall interference at the output of linear receivers are commonly used to analyze the performance of asynchronous DS/SSMA communication systems. In this paper, a new asymptotic analysis is presented to establish the validity of Gaussian approximations for the systems employing more general chip waveforms of interest, which include strictly band-limited waveforms. The transmit and receive chip waveforms, can be either time-limited or band-limited with their energy normalized to unity.

It is often claimed that frequency-division multiple-access (FDMA) und time-division multiple-access (TDMA) are inferior to code-division multiple-access (CDMA) in the sense that they have hard limits on the user capacity while the performance of CDMA systems degrade gradually as the number of users increases. In this paper, it is shown that FDMA and TDMA systems with flat spectrum pulses are equivalent to optimum CDMA systems for multiple-access communications over Gaussian overloaded channels. Optimal transmit and receive waveforms are employed to minimize the output mean-squared errors of linear receivers, and equal-power users are assumed with strictly hand-limited continuous-time channels. Using a frequency domain approach, a necessary and sufficient condition is derived for the optimally of a multiple-access scheme. The continuous-time equivalents of Welch bound equality (CTE- WBE) sequences are defined and, as transmit waveforms, shown to comprise the optimal systems together with the matched filter receivers. The equivalence is verified by showing that FDMA and TDMA signals with flat spectrum pulses are CTE-WBE sequences.

A joint optimization of transmitter and receiver is considered for strictly band-limited linear modulations in additive cyclostationary noise. Under the assumptions that the period of the cyclostationarity of the noise is the same as the inverse of the symbol transmission rate and that the noise has a positive-definite autocorrelation function, the optimum transmitter and receiver waveforms that jointly minimize the mean-squared error at the output of the linear receiver are derived with the data sequence modeled as a wide-sense stationary (WSS) colored random process and the channel modeled as a linear time-invariant system with a general frequency-selective impulse response. Numerical results show that this joint optimization technique leads to a significant performance improvement over the systems with receiver-only optimization and the systems with no transmitter and receiver optimizations.

Direct-sequence spread-spectrum multiple-access (DS/SSMA) communications, strictly band-limited transmitter chip waveforms with excess bandwidth in the interval between zero and one, pseudo-random spreading sequences, an additive white Gaussian noise channel, and matched filter receivers are considered. First, a new expression for the average bit error rate (BER) is derived for systems with quaternary phase-shift keying (QPSK) spreading, the conventional matched filter receiver, a coherent detector for binary phase-shift keying (BPSK) data symbols, and chip waveforms that result in no interchip interference. The expression consists of a well known BER expression based on the standard Gaussian approximation to multiple-access interference and a few correction terms. It enables accurate BER evaluations without any numerical integration for various choices of system parameters of interest. The accuracy of the expression is guaranteed as long as the conditional Gaussian approximation to the cross-correlation coefficients between the desired user's spreading sequence and the interfering users' spreading sequences is valid. The expression well reflects the effect of filtering on the system performance. Extensions of the expression are discussed for systems with QPSK spreading and different detection schemes, systems with BPSK spreading, and systems with different transmit and receive filters. Monte Carlo simulation results are also provided to verify the accuracy.

An optimal signal design for band-limited, asynchronous, direct-sequence code-division multiple-access (DS-CDMA) communications with aperiodic random spreading sequences and a conventional matched filter receiver is considered in an additive white Gaussian noise (AWGN) channel. With bandwidth defined in the strict sense, two optimization problems are solved under finite bandwidth and zero interchip interference constraints. First, a chip waveform optimization is performed given the system bandwidth, the data symbol transmission rate, and the processing gain. A technique to characterize a band-limited chip waveform with a finite number of parameters is developed, and it is used to derive optimum chip waveforms which minimize the effect of multiple-access interference (MAI) for any energy and delay profile of users. Next, a joint optimization of the processing gain and the chip waveform is performed, given the system bandwidth and the data symbol transmission rate. A sufficient condition for a system to have lower average probability of bit error for any energy profile is found, and it is used to derive some design strategies. It is shown that the flat spectrum pulse with the processing gain leading to zero excess bandwidth results in the minimum average probability of bit error. Design examples and numerical results are also provided.

The dependence of the error performance and spectral efficiency of direct-sequence spread-spectrum multiple-access (DS/SSMA) systems with matched filter receivers on the chip waveform is examined. The actual shape of the chip waveform, as well as its energy, is found to influence the statistical properties of the multiple-access interference (MAI). An approach to design waveforms that may result in interchip interference (ICI) is proposed and a criterion for design based on the conditional Gaussian approximation of the MAI for systems with aperiodic random spreading sequences is derived. For a simplified system, a closed-form solution for optimal band-limited waveforms is obtained for excess bandwidth less than or equal to one by using a performance metric that includes the effect of ICI. Numerical results, based on an analytical method, as well as Monte Carlo simulations, are provided to evaluate the performance of the proposed waveforms in general systems with conventional matched filter receivers.

A new spreading scheme and an accompanying blind adaptive receiver structure are proposed for direct-sequence spread-spectrum multiple-access communications in a slowly-varying, frequency-selective fading channel. Each user's spreading sequence is given by the Kronecker product of a long-period pseudonoise (PN) sequence, which is accurately modeled by a random sequence, and a short-length deterministic signature code. This spreading scheme bridges the gap between pure PN spreading and pure short-code spreading schemes. It is shown that with this spreading scheme, the channel response to the desired signal component is easily estimated without relying on the spectral decomposition of the signal correlation matrix. With the estimate of the channel response, the receiver suppresses interference based on the maximum signal-to-interference ratio criterion. The blind adaptive receiver requires only coarse timing information and a priori knowledge of the desired user's PN sequence for adaptation. Numerical results show that the adaptive receiver significantly suppresses interference by successfully estimating the channel response and the interference statistics with a low computational complexity. An extension to spatio-temporal processing using an array antenna is also discussed.

The problem of selecting the processing gain and the chip waveform of a band-limited, direct-sequence spread-spectrum multiple-access communication system with aperiodic random spreading sequences and conventional matched filter receiver is considered when given the system bandwidth and the symbol transmission rate. The average probability of bit error is used as the objective function of the optimization. The signals are constrained to be strictly band-limited and to produce zero interchip interference. With a technique to characterize a band-limited chip waveform with a finite number of parameters, a sufficient condition for a system to have lower average probability of bit error is found. Some design strategies are derived that are based on the sufficient condition. Design examples are also provided using analytical methods and Monte-Carlo simulations.

A spatio-temporal matched filter receiver for direct-sequence spread-spectrum multiple-access (DS/SSMA) communications with aperiodic random quadriphase spreading sequences is derived, and the system performance is analyzed. It is shown with the method of characteristic functions that the cross-correlation coefficients between the desired user's and the interfering users' spreading sequences tend, in distribution, to independently and identically distributed circularly symmetric complex Gaussian random variables as the processing gain goes to infinity. Based on this Gaussian approximation, the structure of the spatio-temporal matched filter receiver is derived and a bit error rate formula is obtained. Using Monte-Carlo simulations, as well as analytical methods, it is shown that the spatio-temporal matched filter receiver achieves a significant performance improvement over the conventional, temporal, and spatial matched filter receivers by effectively suppressing the multiple access interference.

In this paper, we consider the transmitter optimization problem in direct-sequence spread-spectrum multiple-access (DS/SSMA) communications with random spreading sequences and a matched filter receiver. A chip waveform optimization is performed under strict-sense bandwidth and zero interchip interference (ICI) conditions. Optimum chip waveforms are found for the excess bandwidth 0/spl les//spl beta//spl les/1, and are shown to achieve the minimum average bit error probability (BEP) for any distribution of the power and delay profiles of users. A simple efficiency measure is derived to assess how efficiently a chip waveform utilizes the excess bandwidth, and it is shown that the square-root raised cosine chip waveforms have only 50% efficiency. Numerical examples including BEP performance of the optimum chip waveforms are also provided.

In this paper, we consider the problem of fitting two users into a channel normally occupied by one user. The users share the same physical channel, but crosstalk is controlled. A linear receiver, which maximizes the signal-to-noise ratio (SNR) is employed, and several well known time-limited symbol waveforms are tested. Performance analysis shows that two users can be easily accommodated in a single-user channel with slight degradation of bit error rate (BER), and furthermore, near single-user performance is achievable by properly selecting the symbol waveform. A simple LMS-type algorithm is also discussed for adaptive implementation.