We consider the design of a modern uplink for supporting machine-type communication and the confluence of sensing, communication, and distributed learning. We demonstrate that grant-free multiple access is possible even in the presence of highly time-varying channels and high delay spread. Our approach is built on enhancing the 2 -step random access procedure of the 5GNR standard. This 2 -step procedure uses Zadoff-Chu (ZC) sequences as preambles that point to radio resources which are then used to upload data. ZC sequences are processed in the delay-Doppler (DD) domain rather than the time domain. We demonstrate that it is possible to detect multiple preambles in the presence of mobility and delay spread using a receiver with no knowledge of the channel other than the worst case delay and Doppler spreads. Our approach depends on the mathematical properties of ZC sequences in the DD domain. We derive a closed form expression for ZC pilots in the DD domain, we characterize the possible self-ambiguity functions, and we determine the magnitude of the possible cross-ambiguity functions. These mathematical properties combine with Zak-OTFS modulation to enable detection of multiple pilots through solution of a compressed sensing problem. The columns of the compressed sensing matrix are the translates of individual ZC pilots in delay and Doppler. We show that columns in the design matrix satisfy a coherence property that makes it possible to detect multiple preambles in a single Zak-OTFS subframe using One-Step Thresholding, which is an algorithm with low complexity.

Orthogonal Time Frequency Space (OTFS) is a framework for communications and active sensing that processes signals in the delay-Doppler (DD) domain. It is informed by 6G propagation environments, where Doppler spreads measured in$\text{kHz}$make it more and more difficult to estimate channels, and the standard model-dependent approach to wireless communication is starting to break down. We consider Zak-OTFS where inverse Zak transform converts information symbols mounted on DD domain pulses to the time domain for transmission. Zak-OTFS modulation is parameterized by a delay period$\tau_{p}$and a Doppler period$\nu_{p}$, where the product$\nu_{p}\nu_{p}=1$. When the channel spread is less than the delay period, and the Doppler spread is less than the Doppler period, the Zak-OTFS input-output relation can be predicted from the response to a single pilot symbol. The highly reliable channel estimates concentrate around the pilot location, and we configure low-density parity-check (LDPC) codes that take advantage of this prior information about reliability. It is advantageous to allocate information symbols to more reliable bins in the DD domain. We report simulation results for a Veh-A channel model where it is not possible to resolve all the paths, showing that LDPC coding extends the range of Doppler spreads for which reliable model-free communication is possible. We show that LDPC coding reduces sensitivity to the choice of transmit filter, making bandwidth expansion less necessary. Finally, we compare BER performance of Zak-OTFS to that of a multicarrier approximation (MC-OTFS), showing LDPC coding amplifies the gains previously reported for uncoded transmission.

In single-cell systems with high delay and Doppler spread channels, Orthogonal Time Frequency Space (OTFS) modulation is known to achieve significantly better throughput than OFDM. However, there is not much work reported on the throughput comparison between OTFS and OFDM for multi-cell systems. In this paper, we therefore study the spectral efficiency (SE) performance of OTFS based multi-cell communication systems where the time-frequency resource allocated to all cells is the same. Simulation studies reveal that the SE achieved with OTFS modulation is better than that achieved with OFDM. However, OTFS SE performance in multi-cell systems is limited by inter-cell interference (ICI). This emphasizes the need for delay-Doppler (DD) domain multi-cell resource allocation strategies in order to reduce the impact of ICI on the SE performance of OTFS based multi-cell systems.

In this paper we consider joint beamforming of data to scheduled terminals (STs) and broadcast of system information (SI) to idle terminals (ITs) on the same time-frequency resource in multi-cell multi-user massive MIMO systems. We propose two different multi-cell approaches to the broadcast of SI, i) synchronous broadcast of same SI symbols from all cells (SAME-SI), and ii) synchronous broadcast of statistically independent SI symbols from each cell (DIFF-SI). We also consider the traditional orthogonal access (OA) approach where a fraction of physical resource is reserved for broadcast of SI. Through analysis and simulations, it is observed that for both SAME-SI and DIFF-SI, joint beamforming and broadcasting (JBB) is more energy efficient than OA.

We consider a point-to-point mm-wave massive multiple-input multiple-output hybrid beamforming system where the transmitter is impaired with in-phase and quadrature-phase imbalance (IQI). We propose a novel channel estimation and IQI parameter estimation algorithm which first estimates the true sparse channel parameters using which it then estimates the IQI parameters. We show that the transmitter IQI limits the spectral efficiency of hybrid beamforming systems at high signal-to-noise ratio irrespective of the choice of hybrid precoder/combiner. We also propose a novel IQI symbol-level pre-compensation scheme at the transmitter which modifies the input symbol vector to the transmit radio frequency (RF) chains in such a way that the symbol vector received at the output of the RF chains is free from any IQI. Analysis and simulations confirm the effectiveness of the proposed IQI pre-compensation technique.

We consider the downlink communication of a point-to-point mm-wave massive multiple-input multiple-output hybrid beamforming (HB) system in which the transmitter is free from in-phase and quadrature-phase (IQ) imbalance whereas the receiver is IQ-impaired. We show that, irrespective of the design of the hybrid precoder/combiner, the receiver IQ imbalance (Rx-IQI) limits the spectral efficiency (SE) of HB systems at high signal-to-noise ratio. To solve this problem, we propose a novel Rx-IQI compensation scheme which completely mitigates the effects of Rx-IQI in HB systems. Analysis and simulations confirm the effectiveness of our Rx-IQI compensation scheme.

We consider joint beamforming of data to scheduled terminals (STs) and broadcast of system information (SI) to idle terminals (ITs) on the same time-frequency resource in multi-cell multi-user massive MIMO systems. We consider two different types of SI broadcast, i) synchronous broadcast of common (i.e., same) SI symbols from all cells, and ii) synchronous broadcast of cell-specific SI symbols from each cell. Through analysis we derive expressions for the achievable sum rate to STs in each cell and the rate of SI transmission to an IT for both these types of SI broadcast. We also derive expressions for the sum rate to STs and the rate to an IT for traditional orthogonal access (OA) where a fraction of physical resource is reserved for broadcast of SI. Simulations reveal that, just as in the single-cell scenario, for the multi-cell scenario also, joint beamforming and broadcasting (JBB) is more energy efficient than OA.

We derive an achievable rate region (ARR) of the zero-forcing precoder in a 2 × 2 multi-user multiple-input single-output broadcast intensity-modulation/direct-detection channel. A per-light emitting diode (LED) peak optical power constraint along with a per-LED average optical power constraint with inequality (Type-I constraint) generally considered in optical wireless communication systems is imposed for which we analytically characterize the boundary of the proposed ARR. Then, we compare this ARR with that under a per-LED peak optical power constraint along with a per-LED average power constraint with equality (Type-II constraint), which is considered in visible light communication systems for constant illumination requirement. Our analysis reveals that when the ratio (β) of the maximum allowed per-LED average optical transmit power to the per-LED peak power is less than or equal to half (β ≤1/2), the ARR under both the constraints is the same. However, Type-I constrained system is analytically shown to be more power efficient in terms of the required total average transmit optical power. When β > 1/2 , the ARR under the Type-I constraint remains constant with increasing β , whereas the ARR under the Type-II constraint shrinks.

Timing advance (TA) estimation at the base station (BS) and reliable decoding of random access response (RAR) at the users are important steps in the initial random access (RA) procedure. However, due to limited availability of physical resources dedicated for RA, successful completion of RA requests would become difficult in high user density scenarios, due to contention among users requesting RA. In this paper, we propose to use the large antenna array at the massive multiple input multiple output BS to jointly group RA requests from different users using the same RA preamble. We then beamform the common RAR of each detected user group onto the same frequency resource, in such a way that most users in the group can reliably decode the RAR. The proposed RAR beamforming therefore automatically resolves the problem of collision between multiple RA requests on the same preamble, which reduces the RA latency significantly as compared to LTE. Analysis and simulations also reveal that for a fixed desired signal-to-interference-and-noise ratio of the received RAR, both the required per-user preamble transmission power and the total RAR beamforming power can be decreased roughly by 1.5 dB with every doubling in the number of BS antennas.

In this paper, we consider the uplink of massive MIMO systems where the channel capacity is almost deterministic and varies slowly over time. We exploit this fact, by appropriately choosing the length of the codeword only once based on an initial estimate of the uplink channel capacity fed back by the base station (BS). The user terminal (UT) then transmits the codeword over consecutive coherence time intervals without waiting for any acknowledgement (ACK/NACK) from the BS. The BS sends only a single ACK/NACK after it completes decoding. Therefore, the proposed method has significantly less latency and signaling overhead when compared with stop-and-wait type hybrid automatic repeat request (HARQ) methods (as in LTE uplink) where a lot of delay is introduced as the UT needs to wait for the BS to signal the ACK/NACK for every retransmission. Analysis reveals that for sufficiently large number of antennas at the BS, the average codeword length of the proposed method (in number of coherence intervals) is the same as the average number of retransmissions (in number of coherence intervals) required by incremental redundancy (IR)-based HARQ and also that the energy efficiency of the proposed method and IR-HARQ is the same.

The authors consider a single‐channel power line communication (PLC) system in the presence of Middleton Class‐A impulsive noise employing multi‐level amplitude‐shift keying (ASK) modulation at the transmitter and non‐coherent detection at the receiver. An asymptotically optimal detector for the PLC system is obtained using a tight approximation of the noise statistics. The magnitude of the received symbol is obtained as the decision variable, whose statistics is utilised to derive a series expression for the symbol error rate (SER). An asymptotic expression for the SER at high signal‐to‐noise ratio (SNR) is also obtained which is further utilised to find the optimal ASK constellation minimising the SER. It is shown by numerical examples that the optimal solution is extremely close to the equally spaced ASK constellation set at high SNR. It is also observed that the SER variation of the system with the impulsive index of the noise validates the optimality of the proposed detector at high SNR.

In this paper, we study the information theoretic performance of the modified time-reversal maximum ratio combining (TR-MRC) receiver (presented in [9]) with the spatially averaged periodogram-based carrier frequency offset (CFO) estimator (proposed in [7]) in multi-user massive MIMO systems. √ Our analysis shows that an ( ) array gain is achieved with this periodogram-based CFO estimator, which is same as the array gain achieved in the ideal/zero CFO scenario (M is the number of base station antennas). Information theoretic performance comparison with the correlation-based CFO estimator for massive MIMO systems (proposed in [6]) reveals that this periodogram-based CFO estimator is more energy efficient in slowly time-varying channels.

In this paper we consider a constant envelope pilot signal based carrier frequency offset (CFO) estimation in massive multiple-input multiple-output (MIMO) systems. The proposed algorithm performs spatial averaging on the periodogram of the received pilots across the base station (BS) antennas. Our study reveals that the proposed algorithm has complexity only linear in (the number of BS antennas). Further our analysis and numerical simulations also reveal that with fixed number of users and a fixed pilot length, the minimum required transmit pilot power decreases as 1/√M with increasing , while maintaining a fixed desired mean squared error (MSE) of CFO estimation.

This paper proposes to use N-branch diversity reception for a power line communication (PLC) system with binary phase-shift keying to improve the reliability of data transmission. The PLC channel is subject to Rayleigh fading and additive Nakagami-m background noise with m <; 1, which is caused by multiple noise sources. The optimal detector for this system is derived by approximating the noise distribution by Hoyt distribution. A closed form expression and a series expression for the symbol error probability for even and odd N, respectively, are obtained. The advantage of using multiple receive branches in terms of achieving better error performance and its power efficiency are shown through numerical results. The effect of the shape parameter m of the background noise on the performance of the optimal receiver is also demonstrated.

A noncoherent quadratic diversity reception system for multilevel amplitude-shift keying (ASK) signals in Rayleigh fading with different cases of the channel covariance matrix is considered. These include the important case of distributed antennas, which exhibit uncorrelated fading with distinct mean-squared channel gains (uncorrelated nonidentical fading) and weighted energy detectors, and the cases of exponentially correlated and uniformly correlated channels with equal mean-squared channel gains. For these cases, closed-form expressions for the symbol error probability (SEP) of the system are derived using the decision statistics obtained from the maximum likelihood receiver. The problem of determining the optimal amplitude levels that minimize the SEP under a total signal energy constraint is formulated and solved analytically for the high signal-to-noise ratio (SNR) configuration and numerically for the general configuration. For the high SNR configuration, it is shown that the optimal ASK levels should follow an approximately geometric progression. It is also observed that an equally spaced ASK constellation is not optimal in terms of achieving the minimum SEP. Numerical results are presented to highlight performance trends for channel gain imbalance and correlation.

We consider the multiple input single output (MISO) Gaussian broadcast channel with Ntantennas at the base station (BS) and Nusingle-antenna users in the downlink. We propose a novel user grouping precoder which improves the sum rate performance of the zero-forcing (ZF) precoder specially when the channel is ill-conditioned. The proposed precoder partitions all the users into small groups of equal size. Downlink beamforming is then done in such a way that, at each user's receiver, the interference from the signal intended for users not in its group is nulled out. Intragroup interference still remains, and is cancelled through successive interference presubtraction at the BS using dirty paper coding (DPC). The proposed user grouping method is different from user selection, since it is a method for precoding of information to the selected (scheduled) users, and not for selecting which users are to be scheduled. The proposed precoder is a generalization of two special cases, one where each group has only one user (ZF precoder) and another where all users are in a single group (ZF-DP precoder). A larger group size helps improve the sum rate performance but at the cost of greater complexity. The proposed generalization, therefore, allows for tradeoff between performance and complexity.

Low-complexity carrier frequency offset (CFO) estimation and compensation in multi-user massive multiple-input multiple-output (MIMO) systems is a challenging problem. The existing CFO estimation algorithms incur tremendous increase in complexity with increasing number of base station (BS) antennas, M and number of user terminals (UTs) K (i.e. massive MIMO regime). In this paper, we address this problem by proposing a novel low-complexity algorithm for CFO estimation which uses the pilot signal received at the BS during special uplink slots. The total per-channel use complexity of the proposed algorithm increases only linearly with increasing M and is independent of K. Analysis reveals that the CFO estimation accuracy can be considerably improved by increasing M and K (i.e. massive MIMO regime). For example, for a fixed K and a fixed training length, the required per-user radiated power during uplink training decreases as 1/√M with increasing M.

We consider a single user (SU) massive MIMO system with multiple antennas at the transmitter (base station) and a single antenna at the user terminal (UT). Taking transceiver power consumption into consideration, for a given spectral efficiency (SE) we maximize the energy efficiency (EE) as a function of the number of base station (BS) antennasM, resulting in a closed-form expression for the optimal SE-EE trade-off. It is observed that in contrast to the classical SE-EE trade-off (which considers only the radiated power), with transceiver power consumption taken into account, the EE increases with increasing SE when SE is sufficiently small. Further, for a fixed SE we analyze the impact of varying cell size (i.e., equivalently average channel gain Gc) on the optimal EE. We show the interesting result that for sufficiently small Gc, the optimal EE decreases as O(√Gc) with decreasing Gc. Our analysis also reveals that for sufficiently small SE (or large Gc), the EE is insensitive to the power amplifier efficiency.

Multiuser multiple-input-multiple-output (MIMO) cellular systems with an excess of base station (BS) antennas (Massive MIMO) offer unprecedented multiplexing gains and radiated energy efficiency. Oscillator phase noise is introduced in the transmitter and receiver radio frequency chains and severely degrades the performance of communication systems. We study the effect of oscillator phase noise in frequency-selective Massive MIMO systems with imperfect channel state information. In particular, we consider two distinct operation modes, namely, when the phase noise processes at the M BS antennas are identical (synchronous operation) and when they are independent (nonsynchronous operation) . We analyze a linear and low-complexity time-reversal maximum-ratio combining reception strategy. For both operation modes, we derive a lower bound on the sum-capacity, and we compare their performance. Based on the derived achievable sum-rates, we show that with the proposed receive processing, an O(√M) array gain is achievable. Due to the phase noise drift, the estimated effective channel becomes progressively outdated. Therefore, phase noise effectively limits the length of the interval used for data transmission and the number of scheduled users. The derived achievable rates provide insights into the optimum choice of the data interval length and the number of scheduled users.

We consider the impact of transceiver power consumption on the energy efficiency (EE) of the zero-forcing (ZF) detector in the uplink of massive MIMO systems, where a base station (BS) with M antennas communicates coherently with K single antenna user terminals (UTs). We consider the problem of maximizing the EE with respect to (M, K) for a fixed sum spectral efficiency. Through analysis, we study the impact of system parameters on the optimal EE. System parameters consists of the average channel gain to the users and the power consumption parameters (PCPs) (e.g., power consumed by each RF antenna/ receiver at BS). When the average user channel gain is high or else the BS/UT design is power inefficient, our analysis reveals that it is optimal to have a few BS antennas and a single user, i.e., nonmassive MIMO regime. Similarly, when the channel gain is small or else the BS/UT design is power efficient, it is optimal to have a larger (M, K), i.e., massive MIMO regime. Tight analytical bounds on the optimal EE are proposed for both these regimes. The impact of the system parameters on the optimal EE is studied, and several interesting insights are drawn.

We consider the multi-user MIMO broadcast channel with M single-antenna users and N transmit antennas under the constraint that each antenna emits signals having constant envelope (CE). The motivation for this is that CE signals facilitate the use of power-efficient RF power amplifiers. Analytical and numerical results show that, under certain mild conditions on the channel gains, for a fixed M, an array gain is achievable even under the stringent per-antenna CE constraint. Essentially, for a fixed M, at sufficiently large N the total transmitted power can be reduced with increasing N while maintaining a fixed information rate to each user. Simulations for the i.i.d. Rayleigh fading channel show that the total transmit power can be reduced linearly with increasing N (i.e., an O(N) array gain). We also propose a precoding scheme which finds near-optimal CE signals to be transmitted, and has O(MN) complexity. Also, in terms of the total transmit power required to achieve a fixed desired information sum-rate, despite the stringent per-antenna CE constraint, the proposed CE precoding scheme performs close to the sum-capacity achieving scheme for an average-only total transmit power constrained channel.

We consider downlink cellular multi-user communication between a base station (BS) having N antennas and M single-antenna users, i.e., an N × M Gaussian Broadcast Channel (GBC). Under an average only total transmit power constraint (APC), large antenna arrays at the BS (having tens to a few hundred antennas) have been recently shown to achieve remarkable multi-user interference (MUI) suppression with simple precoding techniques. However, building large arrays in practice, would require cheap/power-efficient Radio-Frequency (RF) electronic components. The type of transmitted signal that facilitates the use of most power-efficient RF components is a constant envelope (CE) signal (i.e., the amplitude of the signal transmitted from each antenna is constant for every channel use and every channel realization). Under certain mild channel conditions (including i.i.d. fading), we analytically show that, even under the stringent per-antenna CE transmission constraint (compared to APC), MUI suppression can still be achieved with large antenna arrays. Our analysis also reveals that, with a fixed M and increasing N, the total transmitted power can be reduced while maintaining a constant signal-to-interference-noise-ratio (SINR) level at each user. We also propose a novel low-complexity CE precoding scheme, using which, we confirm our analytical observations for the i.i.d. Rayleigh fading channel, through Monte-Carlo simulations. Simulation of the information sum-rate under the per-antenna CE constraint, shows that, for a fixed M and a fixed desired sum-rate, the required total transmit power decreases linearly with increasing N, i.e., an O(N) array power gain. Also, in terms of the total transmit power required to achieve a fixed desired information sum-rate, despite the stringent per-antenna CE constraint, the proposed CE precoding scheme performs close to the GBC sum-capacity (under APC) achieving scheme.

Large antenna arrays at the base station can facilitate power efficient single user downlink communication due to the inherent array power gain, i.e., under an average only total transmit power constraint, for a fixed desired information rate, the required total transmit power can be reduced by increasing the number of base station antennas (e.g. with i.i.d. fading, the required total transmit power can be reduced by roughly 3 dB with every doubling in the number of base station antennas, i.e., an O(N) array power gain can be achieved with N antennas). However, in practice, building power efficient large antenna arrays would require power efficient amplifiers/analog RF components. With current technology, highly linear power amplifiers generally have low power efficiency, and therefore linearity constraints on power amplifiers must be relaxed. Under such relaxed linearity constraints, the transmit signal that suffers the least distortion is a signal with constant envelope (CE). In this paper, we consider a single user Gaussian multiple-input single-output (MISO) downlink channel where the signal transmitted from each antenna is constrained to have a constant envelope (i.e., for every channel-use the amplitude of the signal transmitted from each antenna is constant, irrespective of the channel realization). We show that under such a per-antenna CE constraint, the complex noise-free received signal lies in the interior of a “doughnut” shaped region in the complex plane. The per-antenna CE constrained MISO channel is therefore equivalent to a doughnut channel, i.e., a single-input single-output (SISO) AWGN channel where the channel input is constrained to lie inside a “doughnut” shaped region. Using this equivalence, we analytically compute a closed-form expression for an achievable information rate under the per-antenna CE constraint. We then show that, for a broad class of fading channels (i.i.d. and direct-line-of-sight (DLOS)), even under the more stringent per-antenna CE constraint (compared to the average only total power constraint), an O(N) array power gain can still be achieved with N base station antennas. We also show that with N ≫1, compared to the average only total transmit power constrained channel, the extra total transmit power required under the per-antenna CE constraint, to achieve a desired information rate is small and bounded for a broad class of fading channels (i.i.d. and DLOS). We also propose novel CE precoding algorithms. The analysis and algorithms presented are general and therefore applicable to conventional systems with a small number of antennas. Analytical results are supported with numerical results for the i.i.d. Rayleigh fading channel.

Large antenna arrays at the transmitter (TX) have recently been shown to achieve remarkable intra-cell interference suppression at low complexity. However, building large arrays in practice, would require the use of power-efficient RF amplifiers, which generally have poor linearity characteristics and hence would require the use of input signals with a very small peak-to-average power ratio (PAPR). In this paper, we consider the single-user Multiple-Input Single-Output (MISO) channel for the case where the TX antennas are constrained to transmit signals having constant envelope (CE). We show that, with per-antenna CE transmission the effective channel seen by the receiver is a SISO AWGN channel with its input constrained to lie in a doughnut-shaped region. For a broad class of fading channels, analysis of the effective doughnut channel shows that under a per-antenna CE input constraint, i) compared to an average-only total TX power constrained MISO channel, the extra total TX power required to achieve a desired information rate is small and bounded, ii) with N TX antennas an O(N) array power gain is achievable, and iii) for a desired information rate, using power-efficient amplifiers with CE inputs would require significantly less total TX power when compared to using highly linear (power-inefficient) amplifiers with high PAPR inputs.

In this paper, we address the design of codes which achieve modulation diversity in block fading single-input single-output (SISO) channels with signal quantization at the receiver. With an unquantized receiver, coding based on algebraic rotations is known to achieve maximum modulation coding diversity. On the other hand, with a quantized receiver, algebraic rotations may not guarantee gains in diversity. Through analysis, we propose specific rotations which result in the codewords having equidistant component-wise projections. We show that the proposed coding scheme achieves maximum modulation diversity with a low-complexity minimum distance decoder and perfect channel knowledge. Relaxing the perfect channel knowledge assumption we propose a novel channel training/estimation technique to estimate the channel. We show that our coding/training/estimation scheme and minimum distance decoding achieves an error probability performance similar to that achieved with perfect channel knowledge.

We consider low complexity precoding for the Multiple Input Single Output (MISO) Gaussian Broadcast channel with Ntantennas at the base station and Nusingle antenna users in the downlink. Theoretical studies have suggested high throughput communication with increasing spatial dimensions i.e., min(Nt,Nu). Nevertheless, most modern communication standards are unable to exploit the spatial dimension fully, since they are restricted to orthogonal communication techniques like TDMA/FDMA (Time/Frequency Division Multiplexed Access) which are known to be sub-optimal. This restriction is mostly due to the prohibitive complexity of optimal/near-optimal precoding schemes. On the other hand low complexity techniques like Zero Forcing (ZF) and MMSE have poor sum rate performance. In this paper, we propose a novel low-complexity user grouping based precoding scheme which schedules all users on the same time-frequency resource (i.e., optimal utilization of resources). The proposed precoder is analytically shown to achieve a sum rate performance significantly better than the ZF precoder at similar complexity. Through simulations, it is also observed to achieve a significant fraction of the sum rate achieved by the optimal schemes.

In this paper, we investigate the achievable rate region of Gaussian multiple access channels (MAC) with finite input alphabet and quantized output. With finite input alphabet and an unquantized receiver, the two-user Gaussian MAC rate region was studied. In most high throughput communication systems based on digital signal processing, the analog received signal is quantized using a low precision quantizer. In this paper, we first derive the expressions for the achievable rate region of a two-user Gaussian MAC with finite input alphabet and quantized output. We show that, with finite input alphabet, the achievable rate region with the commonly used uniform receiver quantizer has a significant loss in the rate region compared. It is observed that this degradation is due to the fact that the received analog signal is densely distributed around the origin, and is therefore not efficiently quantized with a uniform quantizer which has equally spaced quantization intervals. It is also observed that the density of the received analog signal around the origin increases with increasing number of users. Hence, the loss in the achievable rate region due to uniform receiver quantization is expected to increase with increasing number of users. We, therefore, propose a novel non-uniform quantizer with finely spaced quantization intervals near the origin. For a two-user Gaussian MAC with a given finite input alphabet and low precision receiver quantization, we show that the proposed non-uniform quantizer has a significantly larger rate region compared to what is achieved with a uniform quantizer.

In this paper, we address the design of codes which achieve modulation diversity in block fading single-input single-output (SISO) channels with signal quantization at receiver and low-complexity decoding. With an unquantized receiver, coding based on algebraic rotations is known to achieve modulation coding diversity. On the other hand, with a quantized receiver, algebraic rotations may not guarantee diversity. Through analysis, we propose specific rotations which result in the codewords having equidistant component-wise projections. We show that the proposed coding scheme achieves maximum modulation diversity with a low-complexity minimum distance decoder.

Abstract—We consider a slow fading multiple-input multiple-output (MIMO) system with channel state information at both the transmitter and receiver. A well-known precoding scheme is based upon the singular value decomposition (SVD) of the channel matrix, which transforms the MIMO channel into parallel subchannels. Despite having low maximum likelihood decoding (MLD) complexity, this SVD precoding scheme provides a diversity gain which is limited by the diversity gain of the weakest subchannel. We therefore propose X- and Y-Codes, which improve the diversity gain of the SVD precoding scheme but maintain the low MLD complexity, by jointly coding information across a pair of subchannels. In particular, subchannels with high diversity gain are paired with those having low diversity gain. A pair of subchannels is jointly encoded using a 2 2 real matrix, which is fixed a priori and does not change with each channel realization. For X-Codes, these rotation matrices are parameterized by a single angle, while for Y-Codes, these matrices are left triangular matrices. Moreover, we propose X-, Y-Precoders with the same structure as X-, Y-Codes, but with encoding matrices adapted to each channel realization. We observed that X-Codes/Precoders are good for well-conditioned channels, while Y-Codes/Precoders are good for ill-conditioned channels. Index Terms—Condition number, diversity, error probability, MIMO, precoding, singular value decomposition. I.

We consider Gaussian multiple-input multiple-output (MIMO) channels with discrete input alphabets. We propose a non diagonal precoder based on the X-Codes in to increase the mutual information. The MIMO channel is transformed into a set of parallel subchannels using singular value decomposition (SVD) and X-Codes are then used to pair the subchannels. X-Codes are fully characterized by the pairings and a 2 × 2 real rotation matrix for each pair (parameterized with a single angle). This precoding structure enables us to express the total mutual information as a sum of the mutual information of all the pairs. The problem of finding the optimal precoder with the above structure, which maximizes the total mutual information, is solved by: i) optimizing the rotation angle and the power allocation within each pair and ii) finding the optimal pairing and power allocation among the pairs. It is shown that the mutual information achieved with the proposed pairing scheme is very close to that achieved with the optimal pre coder by Cruz et al., and is significantly better than Mercury/waterfllling strategy by Lozano et al. Our approach greatly simplifies both the precoder optimization and the detection complexity, making it suitable for practical applications.

We consider a time division duplex multiple-input multiple-output (nt× nrMIMO). Using channel state information (CSI) at the transmitter, singular value decomposition (SVD) of the channel matrix is performed. This transforms the MIMO channel into parallel subchannels, but has a low overall diversity order. Hence, we propose X-Codes which achieve a higher diversity order by pairing the subchannels, prior to SVD preceding. In particular, each pair of information symbols is encoded by a fixed 2 × 2 real rotation matrix. X-Codes can be decoded using nrvery low complexity two-dimensional real sphere decoders. Error probability analysis for X-Codes enables us to choose the optimal pairing and the optimal rotation angle for each pair. Finally, we show that our new scheme outperforms other low complexity precoding schemes.

In this paper, we shed light on the cross-layer interactions between the PHY, link and routing layers in networks with MIMO links operating in the diversity mode. Many previous studies assume an overly simplistic PHY layer model that does not sufficiently capture these interactions. We show that the use of simplistic models can in fact lead to misleading conclusions with regards to the higher layer performance with MIMO diversity. Towards understanding the impact of various PHY layer features on MIMO diversity, we begin with a simple but widely-used model and progressively incorporate these features to create new models. We examine the goodness of these models by comparing the simulated performance results with each, with measurements on an indoor 802.11 n testbed. Our work reveals several interesting cross-layer dependencies that affect the gains due to MIMO diversity. In particular, we observe that relative to SISO links: (a) PHY layer gains due to MIMO diversity do not always carry over to the higher layers, (b) the use of other PHY layer features such as FEC codes significantly influence the gains due to MIMO diversity, and (c) the choice of the routing metric can impact the gains possible with MIMO.

We consider a time division duplex (TDD) nt× nrmultiple-input multiple-output (MIMO) system with known channel state information (CSI) at both transmitter and receiver. Using singular value decomposition (SVD) precoding at the transmitter, the MIMO channels are transformed into parallel subchannels. To improve the low diversity order, we propose X- and Y-Codes, prior to SVD precoding, to pair subchannels having different diversity orders. Specifically, a pair of channels is jointly encoded using a 2 × 2 real matrix, which is fixed a priori and does not change with each channel realization. Moreover, we propose X-, Y-Precoders with the same encoding matrices as X-, Y-Codes, which adapt to each channel realization. The optimal encoding matrices for X- and Y-Codes/Precoders are derived analytically to minimize the average error probability. Finally, we see that X-, Y-Codes/Precoders indeed achieve higher diversity gains at very low encoding/decoding complexity for both well- and ill-conditioned channels, respectively, when compared to other precoding schemes in the literature. We also observe that for the Rayleigh fading channel model X- and Y-Codes/Precoders exhibit the best average error performance.

We consider Gaussian multiple-input multiple-output (MIMO) channels with discrete input alphabets. We propose a non-diagonal precoder based on X-Codes in to increase the mutual information. The MIMO channel is transformed into a set of parallel subchannels using Singular Value Decomposition (SVD) and X-codes are then used to pair the subchannels. X-Codes are fully characterized by the pairings and the 2 × 2 real rotation matrices for each pair (parameterized with a single angle). This precoding structure enables to express the total mutual information as a sum of the mutual information of all the pairs. The problem of finding the optimal precoder with the above structure, which maximizes the total mutual information, is equivalent to i) optimizing the rotation angle and the power allocation within each pair and ii) finding the optimal pairing and power allocation among the pairs. It is shown that the mutual information achieved with the proposed pairing scheme is very close to that achieved with the optimal precoder by Cruz et al., and significantly better than mercury/waterfilling strategy by Lozano et al.. Our approach greatly simplifies both the precoder optimization and the detection complexity, making it suitable for practical applications.

Consider L independent and identically distributed exponential random variables (r.vs) X1, X2,...,XLand positive scalars b1, b2,...,bL. In this letter, we present the probability density function (pdf), cumulative distribution function and the Laplace transform of the pdf of the composite r.v Z = (Σ(j=1)LXj)2/(Σ(j=1}LbjXj). We show that the r.v Z appears in various communication systems such as i) maximal ratio combining of signals received over multiple channels with mismatched noise variances, ii) M-ary phase-shift keying with spatial diversity and imperfect channel estimation, and iii) coded multi-carrier code-division multiple access reception affected by an unknown narrow-band interference, and the statistics of the r.v Z derived here enable us to carry out the performance analysis of such systems in closed-form.

We propose a novel equalizer for ultra wideband (UWB) multiple-input multiple-output (MIMO) channels characterized by severe delay spreads. The proposed equalizer is based on reactive tabu search (RTS), which is a heuristic originally designed to obtain approximate solutions to combinatorial optimization problems. The proposed RTS equalizer is shown to perform increasingly better for increasing number of multipath components (MPC), and achieve near maximum likelihood (ML) performance for large number of MPCs at a much less complexity than that of the ML detector. The proposed RTS equalizer is shown to perform close to within 0.4 dB of single-input multiple-output AWGN performance at 10-3uncoded BER on a severely delay-spread UWB MIMO channel with 48 equal-energy MPCs.

In this paper, we propose a training-based channel estimation scheme for large non-orthogonal space-time block coded (STBC) MIMO systems. The proposed scheme employs a block transmission strategy where an Nttimes Ntpilot matrix is sent (for training purposes) followed by several Nttimes Ntsquare data STBC matrices, where Ntis the number of transmit antennas. At the receiver, we iterate between channel estimation (using an MMSE estimator) and detection (using a low-complexity likelihood ascent search (LAS) detector) till convergence or for a fixed number of iterations. Our simulation results show that excellent bit error rate and nearness-to-capacity performance are achieved by the proposed scheme at low complexities. The fact that we could show such good results for large STBCs (e.g., 16times16 STBC from cyclic division algebras) operating at spectral efficiencies in excess of 20 bps/Hz (even after accounting for the overheads meant for pilot-based channel estimation and turbo coding) establishes the effectiveness of the proposed scheme.

Non-orthogonal space-time block codes (STBC) from cyclic division algebras (CDA) are attractive because they can simultaneously achieve both high spectral efficiencies (same spectral efficiency as in V-BLAST for a given number of transmit antennas) as well as full transmit diversity. Decoding of non-orthogonal STBCs with hundreds of dimensions has been a challenge. In this paper, we present a probabilistic data association (PDA) based algorithm for decoding non-orthogonal STBCs with large dimensions. Our simulation results show that the proposed PDA-based algorithm achieves near SISO AWGN uncoded BER as well as near-capacity coded BER (within 5 dB of the theoretical capacity) for large non-orthogonal STBCs from CDA.We study the effect of spatial correlation on the BER, and show that the performance loss due to spatial correlation can be alleviated by providing more receive spatial dimensions. We report good BER performance when a training-based iterative decoding/channel estimation is used (instead of assuming perfect channel knowledge) in channels with large coherence times. A comparison of the performances of the PDA algorithm and the likelihood ascent search (LAS) algorithm (reported in our recent work) is also presented.

Non-orthogonal space-time block codes (STBC) with large dimensions are attractive because they can simultaneously achieve both high spectral efficiencies (same spectral efficiency as in V-BLAST for a given number of transmit antennas) as well as full transmit diversity. Decoding of non-orthogonal STBCs with large dimensions has been a challenge. In this paper, we present a reactive tabu search (RTS) based algorithm for decoding non-orthogonal STBCs from cyclic division algebras (CDA) having large dimensions. Under i.i.d fading and perfect channel state information at the receiver (CSIR), our simulation results show that RTS based decoding of 12 × 12 STBC from CDA and 4-QAM with 288 real dimensions achieves i) 10−3uncoded BER at an SNR of just 0.5 dB away from SISO AWGN performance, and ii) a coded BER performance close to within about 5 dB of the theoretical MIMO capacity, using rate-3/4 turbo code at a spectral efficiency of 18 bps/Hz. RTS is shown to achieve near SISO AWGN performance with less number of dimensions than with LAS algorithm (which we reported recently) at some extra complexity than LAS.We also report good BER performance of RTS when i.i.d fading and perfect CSIR assumptions are relaxed by considering a spatially correlatedMIMO channelmodel, and by using a training based iterative RTS decoding/channel estimation scheme.

In this paper, we present novel precoder designs for V-BLAST systems which achieve full-rate. We first present a precoding scheme based on algebraic lattices over real number fields. We prove that this full-rate scheme achieves full-diversity, assuming availability of full channel state information at the transmitter. We then propose a precoding scheme which achieves full-rate and high orders of diversity with limited feedback. The proposed scheme involves a precoder codebook design consisting of unitary matrices parametrized by a single angular parameter, thereby requiring less feedback overhead. Our simulation results show that the proposed limited feedback precoding scheme provides a performance improvement of 1.5 dB and 2.5 dB at a bit error rate of 10-3over existing schemes for 2×2 and 4×4 V-BLAST systems, respectively, using 4-QAM.

Large MIMO systems with tens of antennas in each communication terminal using full-rate non-orthogonal space- time block codes (STBC) from cyclic division algebras (CDA) can achieve the benefits of both transmit diversity as well as high spectral efficiencies. Maximum-likelihood (ML) or near-ML decoding of these large-sized STBCs at low complexities, however, has been a challenge. In this paper, we establish that near-ML decoding of these large STBCs is possible at practically affordable low complexities. We show that the likelihood ascent search (LAS) detector, reported earlier by us for V-BLAST, is able to achieve near-ML uncoded BER performance in decoding a 32 times 32 STBC from CDA, which employs 32 transmit antennas and sends 322= 1024 complex data symbols in 32 time slots in one STBC matrix (i.e., 32 data symbols sent per channel use). In terms of coded BER, with a 16 times 16 STBC, rate-3/4 turbo code and 4-QAM (i.e., 24 bps/Hz), the LAS detector performs close to within just about 4 dB from the theoretical MIMO capacity. Our results further show that, with LAS detection, information lossless (ILL) STBCs perform almost as good as full-diversity ILL (FD-ILL) STBCs. Such low-complexity detectors can potentially enable implementation of high spectral efficiency large MIMO systems that could be considered in wireless standards.

We consider large MIMO systems, where by 'large' we mean number of transmit and receive antennas of the order of tens to hundreds. Such large MIMO systems will be of immense interest because of the very high spectral efficiencies possible in such systems. We present a low-complexity detector which achieves uncoded near-exponential diversity performance for hundreds of antennas in V-BLAST (i.e., achieves near SISO AWGN performance in a large MIMO fading environment) with an average per-bit complexity of just 0(NtNr), where Ntand Nrdenote the number of transmit and receive antennas, respectively. With an outer turbo code, the proposed detector achieves good coded bit error performance as well. For example, in a 600 transmit and 600 receive antennas V-BLAST system with a high spectral efficiency of 200 bps/Hz (using BPSK and rate-1/3 turbo code), our simulation results show that the proposed detector performs close to within about 4.6 dB of the theoretical capacity. We also adopt the proposed detector for the low-complexity decoding of high-rate non-orthogonal space- time block codes (STBC) from division algebras (DA). We have decoded the 16x16 full-rate STBC from DA using the proposed detector and show that it performs close to within about 5.5 dB of the capacity using 4-QAM and rate-3/4 turbo code at a spectral efficiency of 24 bps/Hz. The practical feasibility of the proposed high-performance low-complexity detector could trigger wide interest in the implementation of large MIMO systems.

In this paper, we present a low-complexity, near maximum-likelihood (ML) performance achieving detector for large MIMO systems having tens of transmit and receive antennas. Such large MIMO systems are of interest because of the high spectral efficiencies possible in such systems. The proposed detection algorithm, termed as multistage likelihood-ascent search (M-LAS) algorithm, is rooted in Hopfield neural networks, and is shown to possess excellent performance as well as complexity attributes. In terms of performance, in a 64 × 64 V-BLAST system with 4-QAM, the proposed algorithm achieves an uncoded BER of 10−3at an SNR of just about 1 dB away from AWGN-only SISO performance given by Q(√SNR). In terms of coded BER, with a rate-3/4 turbo code at a spectral efficiency of 96 bps/Hz the algorithm performs close to within about 4.5 dB from theoretical capacity, which is remarkable in terms of both high spectral efficiency as well as nearness to theoretical capacity. Our simulation results show that the above performance is achieved with a complexity of just O(NtNr) per symbol, where Ntand Nrdenote the number of transmit and receive antennas.

Recently, we reported a low-complexity likelihood ascent search (LAS) detection algorithm for large MIMO systems with several tens of antennas that can achieve high spectral efficiencies of the order of tens to hundreds of bps/Hz. Through simulations, we showed that this algorithm achieves increasingly near SISO AWGN performance for increasing number of antennas in i.i.d. Rayleigh fading. However, no bit error performance analysis of the algorithm was reported. In this paper, we extend our work on this low-complexity large MIMO detector in two directions: i)We report an asymptotic bit error probability analysis of the LAS algorithm in the large system limit, where Nt, Nr→ ∞ keeping Nt= Nr, where Ntand Nrare the number of transmit and receive antennas, respectively. Specifically, we prove that the error performance of the LAS detector for V-BLAST with 4-QAM in i.i.d. Rayleigh fading converges to that of the maximum-likelihood (ML) detector as Nt,Nr→ ∞ keeping Nt= Nr. ii)We present simulated BER and nearness to capacity results for V-BLAST as well as high-rate non-orthogonal STBC from Division Algebras (DA), in a more realistic spatially correlated MIMO channel model. Our simulation results show that a) at an uncoded BER of 10−3, the performance of the LAS detector in decoding 16×16 STBC from DA with Nt=Nr=16 and 16-QAM degrades in spatially correlated fading by about 7 dB compared to that in i.i.d. fading, and b) with a rate-3/4 outer turbo code and 48 bps/Hz spectral efficiency, the performance degrades by about 6 dB at a coded BER of 10−4. Our results further show that providing asymmetry in number of antennas such thatNr≫Ntkeeping the total receiver array length same as that for Nr=Nt, the detector is able to pick up the extra receive diversity thereby significantly improving the BER performance.

In this paper, we consider the problem of preceding in large multiuser MISO systems, where by 'large' we mean (i) large number of transmit antennas (Nt) at the base station of the order of tens to hundreds of transmit antennas, and (ii) large number of downlink users (Nu) of the order of tens to hundreds of users where each user has one receive antenna. Such large MISO systems will be of immense interest because of the high capacities (sum-rates) of the order of hundreds of bits/channel use possible in such systems. We propose a vector perturbation based low-complexity precoder, termed as norm descent search (NDS) precoder, which has a complexity of just O(NuNt) per information symbol. This low complexity attribute of the precoder is achieved by searching for the perturbation vector over a reduced search space. Interestingly, in terms of BER performance, the proposed precoder achieves increasingly better BER for increasing Nt, Nu, such that for large Nt, Nuit achieves near-exponential diversity with some SNR loss, thus making it suited for large MISO systems both in terms of complexity as well as performance. The results of uncoded/turbo-coded simulations without and with channel estimation errors are presented.

We consider large MIMO systems, where by 'large' we mean number of transmit and receive antennas of the order of tens to hundreds. Such large MIMO systems will be of immense interest because of the very high spectral efficiencies possible in such systems. We present a low-complexity detector which achieves uncoded near-exponential diversity performance for hundreds of antennas (i.e., achieves near SISO AWGN performance in a large MIMO fading environment) with an average per-bit complexity of just O(NtNr), where Ntand Nrdenote the number of transmit and receive antennas, respectively. With an outer turbo code, the proposed detector achieves good coded bit error performance as well. For example, in a 600 transmit and 600 receive antennas V-BLAST system with a high spectral efficiency of 450 bps/Hz (using BPSK and rate-3/4 turbo code), our simulation results show that the proposed detector performs to within about 7 dB from capacity. This practical feasibility of the proposed high-performance, low-complexity detector could potentially trigger wide interest in the theory and implementation of large MIMO systems. We also illustrate the applicability of the proposed detector in the low-complexity detection of high-rate, non-orthogonal space-time block codes and large multicarrier CDMA (MC-CDMA) systems. In large MC-CDMA systems with hundreds of users, the proposed detector is shown to achieve near single-user performance at an average per-bit complexity linear in number of users, which is quite appealing for its use in practical CDMA systems.

Multicode operation in space-time block coded (STBC) multiple input multiple output (MIMO) systems can provide additional degrees of freedom in code domain to achieve high data rates. In such multicode STBC systems, the receiver experiences code domain interference (CDI) in frequency selective fading. In this paper, we propose a linear parallel interference cancellation (LPIC) approach to cancel the CDI in multicode STBC signals in frequency selective fading. The proposed detector first performs LPIC followed by STBC decoding. We present an SINK for the proposed detector. We evaluate the bit error rate (BER) performance of the system, and show that the proposed detector effectively cancels the CDI and achieves improved error performance. Our BER results further illustrate how the combined effect of interference cancellation, transmit diversity, and RAKE diversity affects the performance of the system.

A linear processing complex orthogonal design (LPCOD) is a ptimesn matrix epsiv, (pgesn) in k complex indeterminates x1,x2,...,xksuch that (i) the entries of epsiv are complex linear combinations of 0, plusmnxi, i=1,...,k and their conjugates, (ii) epsivHepsiv=D, where epsivHis the Hermitian (conjugate transpose) of epsiv and D is a diagonal matrix with the (i,i)-th diagonal element of the form l1(i)|x1|2+l2(i)|x2|2+...+lk(i)|xk|2where lj(i),i=1,2,...,n, j=1,2,...,k are strictly positive real numbers and the condition l1(i)=l2(i)=...=lk(i), called the equal- weights condition, holds for all values of i. For square designs it is known that whenever a LPCOD exists without the equal-weights condition satisfied then there exists another LPCOD with identical parameters with l1(i)=l2(i)=...=lk(i)=1. This implies that the maximum possible rate for square LPCODs without the equal-weights condition is the same as that of square LPCODs with equal-weights condition. In this paper, this result is extended to a subclass of non-square LPCODs. It is shown that, a set of sufficient conditions is identified such that whenever a non- square (p>n) LPCOD satisfies these sufficient conditions and do not satisfy the equal-weights condition, then there exists another LPCOD with the same parameters n, k and p in the same complex indeterminates with l1(i)=l2(i)=...=lk(i)=1.

In this paper, we propose and analyze a novel idea of performing interference cancellation (IC) in a distributed/cooperative manner, with a motivation to provide multiuser detection (MUD) benefit to nodes that have only a single user detection capability. In the proposed distributed interference cancellation (DIC) scheme, during phase-1 of transmission, an MUD capable cooperating relay node estimates all the sender nodes' bits through multistage interference cancellation. These estimated bits are then sent by the relay node on orthogonal tones in phase-2 of transmission. The destination nodes receive these bit estimates and use them for interference estimation/cancellation, thus achieving IC benefit in a distributed manner. For this DIC scheme, we analytically derive an exact expression for the bit error rate (BER) in a basic five-node network (two source-destination node pairs and a cooperating relay node) on AWGN channels. Analytical BER results are shown to match with simulation results. For more general system scenarios, including more than two source-destination pairs and fading channels without and with space-time coding, we present simulation results to establish the potential for improved performance in the proposed distributed approach to interference cancellation. We also present a linear version of the proposed DIC.

Multicode operation in space-time block coded (STBC) multiple input multiple output (MIMO) systems can provide additional degrees of freedom in code domain to achieve high data rates. In such multicode STBC systems, the receiver experiences code domain interference (CDI) in frequency selective fading. In this paper, we propose a linear parallel interference cancellation (LPIC) approach to cancel the CDI in multicode STBC in frequency selective fading. The proposed detector first performs LPIC followed by STBC decoding. We evaluate the bit error performance of the detector and show that it effectively cancels the CDI and achieves improved error performance. Our results further illustrate how the combined effect of interference cancellation, transmit diversity, and RAKE diversity affect the bit error performance of the system.