Maximum Likelihood Receiver Research Articles

A Maximum Likelihood Combining Algorithm for Spatial Multiplexing MIMO Amplify-and-Forward Relaying Systems

Using a spatial multiplexing transmission scheme can improve the data rate in multiple-input–multiple-output (MIMO) relaying systems, while making signal detection more difficult at receivers. Aiming at lowering the computational complexity of the receiver, this paper proposes a maximum likelihood combining (MLC) algorithm for spatial multiplexing MIMO amplify-and-forward (AF) relaying systems in a Rayleigh flat-fading environment, which is implemented before maximum likelihood (ML) detection. The combining signal and equivalent channel are opportunely designed based on the ML rule in the MLC algorithm. We also formulate the diversity gain of the systems that employ the MLC algorithm mathematically, induced by the Chernoff bound of pairwise error probability (PEP). An upper bound on the symbol error probability (SEP) for the MLC algorithm with multiple modulations is also given, based on the derived bound of PEP. Moreover, the complexities of ML receivers adopting the MLC algorithm and the conventional vector combining (VC) algorithm are analyzed. Numerical simulations indicate that systems with the MLC algorithm achieve the same performance while consuming lower computational complexity compared to that with the VC algorithm.

Quantized Distributed Reception for MIMO Wireless Systems Using Spatial Multiplexing

We study a quantized distributed reception scenario in which a transmitter equipped with multiple antennas sends multiple streams via spatial multiplexing to a large number of geographically separated single antenna receive nodes. This approach is applicable to scenarios such as those enabled by the Internet of Things (IoT) which holds much commercial potential and could facilitate distributed multiple-input multiple-output (MIMO) communication in future systems. The receive nodes quantize their received signals and forward the quantized received signals to a receive fusion center. With global channel knowledge and forwarded quantized information from the receive nodes, the fusion center attempts to decode the transmitted symbols. We assume the transmit vector consists of arbitrary constellation points, and each receive node quantizes its received signal with one bit for each of the real and imaginary parts of the signal to minimize the transmission overhead between the receive nodes and the fusion center. Fusing this data is a nontrivial problem because the receive nodes cannot decode the transmitted symbols before quantization. We develop an optimal maximum likelihood (ML) receiver and a low-complexity zero-forcing (ZF)-type receiver at the fusion center. Despite its suboptimality, the ZF-type receiver is simple to implement and shows comparable performance with the ML receiver in the low signal-to-noise ratio (SNR) regime but experiences an error rate floor at high SNR. It is shown that this error floor can be overcome by increasing the number of receive nodes.

Diversity Transmission and Reception of DAPSK for OFDM

This paper studies the diversity-encoded differential amplitude and phase shift keying (DAPSK) for orthogonal frequency-division multiplexing (OFDM) systems with uniformly interleaved subcarrier grouping and multiple receive antennas over independent but not identically distributed (i.n.i.d.) frequency-selective Rayleigh fading channels. An asymptotic maximum-likelihood (AML) receiver is developed for differentially detecting the received diversity-encoded DAPSK OFDM signal. The bit error probability (BEP) upper bound for the AML receiver is analytically formulated by using the residue theorem. Particularly, an approximate BEP upper bound of the AML receiver is derived for large received signal-to-noise power ratios (SNRs). By virtue of this approximate bound, a design criterion is developed to determine the diversity encoding coefficients for the proposed DAPSK OFDM system. Performance results show that the AML receiver for diversity-encoded DAPSK OFDM can provide better error performance than conventional noncoherent OFDM systems under the same data throughput.

Analog Network Coding in the Multiple Access Relay Channel: Error Rate Analysis and Optimal Power Allocation

In this paper, we consider Analog Network Coding (ANC) in the Multiple Access Relay Channel (MARC) with multiple relays, and provide the following three-fold contribution: 1) we introduce a tractable mathematical framework for computing the Symbol Error Rate (SER) of Maximum-Likelihood (ML), Zero-Forcing (ZF), and Minimum Mean Square Error (MMSE) receivers; 2) by capitalizing on this tractable mathematical framework, we formulate a power allocation problem that is proved to be convex for ML, ZF and MMSE receivers; and 3) we provide closed-form expressions of the optimal power to be allocated to the sources and the relays for ZF and MMSE receivers. With the aid of Monte Carlo simulations, we validate the accuracy of the proposed mathematical framework for various network topologies and channel conditions, as well as study the effectiveness of optimal power allocation. It is shown, in particular, that power optimization is beneficial as the number of sources increases and if the quality of the source-relay links is better than the quality of the relay-destination links.

Error probability analysis of a novel adaptive beamforming receiver for large‐scale multiple‐input–multiple‐output communication system

A novel adaptive beamforming (BF) receiver is proposed for a multiple-input–multiple-output communication system over multipath fading channels. By dividing a large number of receive antennas into many adaptive beamformers (ABFs), the proposed system reduces the array dimension in order to simplify the signal detection process and enjoys the benefit of BF techniques to improve the symbol-error-rate (SER) performance. The effectiveness of the proposed system depends on the number of ABFs and the number of antennas per ABF. The statistical properties of complex Wishart matrices are applied to analyse the SER performance of the proposed system with both maximum-likelihood (ML) detection and zero-forcing detection. Furthermore, the authors have derived an upper bound for SER of the ML detection based on the smallest eigenvalue distribution. Through the authors analysis, it has been shown that the proposed system using ML detection provides comparable SER performance, but with a lower complexity as compared with that of a conventional ML receiver because of reduced array dimensions.

Adaptive Jamming Suppression in Coherent FFH System Using Weighted Equal Gain Combining Receiver over Fading Channels with Imperfect CSI

Fast frequency hopping (FFH) is commonly used as an antijamming communication method. In this paper, we propose efficient adaptive jamming suppression schemes for binary phase shift keying (BPSK) based coherent FFH system, namely, weighted equal gain combining (W-EGC) with the optimum and suboptimum weighting coefficient. We analyze the bit error ratio (BER) of EGC and W-EGC receivers with partial band noise jamming (PBNJ), frequency selective Rayleigh fading, and channel estimation errors. Particularly, closed-form BER expressions are presented with diversity order two. Our analysis is verified by simulations. It is shown that W-EGC receivers significantly outperform EGC. As compared to the maximum likelihood (ML) receiver in conventional noncoherent frequency shift keying (FSK) based FFH, coherent FFH/BPSK W-EGC receivers also show significant advantages in terms of BER. Moreover, W-EGC receivers greatly reduce the hostile jammers’ jamming efficiency.

Adaptive Non Orthogonal MFSK

M-ary frequency shift keying (MFSK) using one or more orthogonal tones per symbol has been in use in non-coherent systems for quite some time. We present an alternate system for non-coherent systems using non-orthogonal tones, spread non-uniformly throughout the bandwidth, which outperforms the equivalent orthogonal tone system. We demonstrate that from a theoretical capacity point of view, the same bit rate could be achieved by the proposed system with as much as 2.5 dB lower signal-to-noise ratio (SNR). For some practical configurations we demonstrate as much as 2 dB of gain. We present the performance with maximum-likelihood (ML) receivers as well as least-squares (LS) receivers as well as lower complexity receivers based on compressed sensing (CS). We also demonstrate that such a non-orthogonal system may be used to increase the spectral efficiency of the overall system by adapting the spectral efficiency in response to the link SNR. Such an adaptive non-orthogonal MFSK system requires estimation of the SNR (or $E_{s}/N_{0}$ ), and we present both the Cramer–Rao lower bound (CRLB) as well as maximum-likelihood (ML) estimators, which attain the CRLB for both data-aided (DA) SNR estimation as well as non-data-aided (NDA) SNR estimation.

Differential Amplitude/Phase Modulation for Correlated Rayleigh Fading Channels: Performance Analysis and Labeling Design

In this paper, we investigate differential amplitude/ phase modulation (APM) schemes for correlated Rayleigh fading channels. Considering the noncoherent maximum-likelihood receiver, a theoretical pairwise error probability (PEP) formula for differential signal vectors with arbitrary power values is derived. The design criterion for the signal set of differential vectors is then proposed based on the asymptotic analysis of the PEP. For both uncoded and coded APM schemes, the design criteria and optimization procedures for bit labeling rules are investigated. The designed differential APM schemes are shown to provide significant improvement in bit-error-rate performance, particularly in the error-floor regions.

PLC Performance Analysis Assuming BPSK Modulation Over Nakagami- <inline-formula> <tex-math notation="TeX">$m$</tex-math></inline-formula> Additive Noise

In this letter, we derive a maximum likelihood receiver of binary phase shift keying signals over Nakagami- $m$ distributed additive noise in power line communication system. The decision variable is characterized by using copula approach. The analytical average bit error rate of the considered scheme is numerically evaluated by using the cumulative distribution function of the decision variable. It is shown by simulations that the proposed receiver performs significantly better than an existing suboptimal receiver.

Differential Space-Time Modulation Using DAPSK Over Rician Fading Channels

This paper studies differential space-time modulation using diversity-encoded differential amplitude and phase shift keying (DAPSK) for the multiple-input multiple-output (MIMO) system over independent but not identically distributed (inid) time-correlated Rician fading channels. An asymptotic maximum likelihood (AML) receiver is developed for differentially detecting diversity-encoded DAPSK symbol signals by operating on two consecutive received symbol blocks sequentially. Based on Beaulieu's convergent series, the bit error probability (BEP) upper bound is analyzed for the AML receiver over inid time-correlated Rician fading channels. Particularly, an approximate BEP upper bound of the AML receiver is also derived for inid time-invariant Rayleigh fading channels with large received signal-to-noise power ratios. By virtue of this approximate bound, a design criterion is developed to determine the appropriate diversity encoding coefficients for the proposed DAPSK MIMO system. Numerical and simulation results show that the AML receiver for diversity-encoded DAPSK is nearly optimum when the average received signal-to-noise power ratios are high and the channel is heavily correlated fading and can provide better error performance than conventional noncoherent MIMO systems when the effect of non-ideal transmit power amplification is taken into account.

Phase Noise Jitter Synchronization for Coherent Optical OFDM via Pilot-Data-Aided and Wiener Filter

modulation (M-QAM) coherent optical orthogonal frequency division multiplexing (CO-OFDM) signal employing a unique pilot’s system design, Feed forward maximum likelihood phase estimator as well as Wiener filter-type Minimum Mean square error (MMSE) interpolator. The wiener filter relies upon Kolmogorov type to interpolate the estimated phase noise with M taps. A 20 Gb/s CO-OFDM via 4-QAM, 16-QAM, 64-QAM then 256-QAM modulation is applied as simulation model in Optisystem. System efficiency is evaluated throughout phase root mean square error (RMSE) calculated in degree. A comparative investigation of four different modulation techniques found that 4-QAM performs with good RMSE versus the rest of square M-QAM. A free-noise receiver, a pilot aided feed forward maximum likelihood (PA-FF-ML) receiver and a PA-FF-ML with MMSE (PA-FF-ML-MMSE) are compared. PA-FF-ML-MMSE exhibited superior performance rather than receiver using just PA-FF-ML.

Throughput Modeling and Measurement in an Isotropic-Scattering Reverberation Chamber

This paper presents simple throughput models for multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems with hybrid automatic repeat request (HARQ). In particular, we consider the long term evolution (LTE) systems. Antenna correlations and power imbalances are implicitly included in the models. In order to explicitly characterize the antenna effects on throughput, we resort to the spatial multiplexing (SM) efficiency. The SM efficiencies of a MIMO antenna with zero forcing (ZF), minimum mean square error (MMSE), and maximum likelihood (ML) receivers are studied via numerical simulations using the throughput models. To verify the throughput models, the throughputs of two LTE terminals (including antenna correlations and power imbalances) are measured in a reverberation chamber (RC). Good agreements between the measured and modeled throughputs are observed.

Diversity analysis of distributed linear convolutive space‐time codes for time–frequency asynchronous cooperative networks

This study analyses the achievable cooperative diversity order of the distributed linear convolutional space-time coding (DLC-STC) scheme for time–frequency asynchronous cooperative networks. The authors first prove that perfect time or frequency synchronisation is impractical for cooperative networks with multiple relays serving multiple destinations even when the relays know all accurate time delays and frequency offsets. Then the DLC-STC scheme, in which the exact time synchronisation at the relay nodes is unnecessary, is introduced into this type of cooperative networks. This study proves that the achievable time–frequency asynchronous cooperative diversity order of the DLC-STC scheme with maximum-likelihood receivers is equal to the number of relays. Simulation results verify the analysis.

Design of Simplified Maximum-Likelihood Receivers for Multiuser CPM Systems

A class of simplified maximum-likelihood receivers designed for continuous phase modulation based multiuser systems is proposed. The presented receiver is built upon a front end employing mismatched filters and a maximum-likelihood detector defined in a low-dimensional signal space. The performance of the proposed receivers is analyzed and compared to some existing receivers. Some schemes are designed to implement the proposed receivers and to reveal the roles of different system parameters. Analysis and numerical results show that the proposed receivers can approach the optimum multiuser receivers with significantly (even exponentially in some cases) reduced complexity and marginal performance degradation.

Jamming Rejection Using FFH/MFSK ML Receiver Over Fading Channels With the Presence of Timing and Frequency Offsets

The composite effect of hostile multitone jamming and partial-band noise jamming on bit-error rate (BER) performance of a fast frequency-hopped M-ary frequency-shift-keying system is studied over Rayleigh fading channels in the presence of timing and frequency offsets. The maximum-likelihood (ML) diversity-combining method is employed to improve BER performance of the system. Analytical BER expression of the proposed ML receiver is derived. The analytical results, validated by computer simulation, show that the proposed ML receiver can suppress the composite hostile jamming more effectively than some existing conventional diversity-combining receivers. The ML receiver is also found to be robust against inaccurate estimation of the required side information.

Space–time–frequency coding over quasi-static frequency-selective channels with linear complexity for the ML receiver

The achievement of our previously proposed space–time coding algorithm entitled full-rate linear-receiver space–time block code (FRLR STBC) has motivated us to propose, in this paper, a new class of high-rate space–time–frequency block codes (STFBCs) over frequency-selective Rayleigh fading channels. We have called these codes FRLR STFBCs with interleaving (FRLR STFBCs-I). FRLR STFBCs-I could achieve a full-diversity property over quasi-static channels. Simulation results also verify that the proposed schemes exhibit proper performances in comparison with the recently proposed STFBCs. The most outstanding characteristic of the newly introduced high-rate codes is the linear complexity of the maximum likelihood (ML) receiver which makes possible a fast and economical decoding process.

Diversity Analysis of Randomized Linear Dispersion Codes in a Half-Duplex Amplify-and-Forward Multiple-Relay System

A point-to-point multiple-relay communication system with half-duplex constraints is considered. The relays operate under the amplify-and-forward paradigm and implement a linear dispersion distributed space-time code with randomized dispersion matrices of independent and identically distributed entries. The large-signal-to-noise-ratio behavior of the asymptotically large deterministic system is studied for both the optimum (maximum likelihood) receiver and the linear minimum mean squared error (LMMSE) receiver. The diversity order of the system is shown to have a strong dependence on the aspect ratio of the linear dispersion matrices. More specifically, when the linear dispersion matrices are sufficiently tall, both receivers achieve the maximum diversity order, i.e., the total number of relays plus one. Conversely, when the linear dispersion matrices are fat (in the sense that relays linearly compress the information received from the source), the optimum receiver is shown to achieve an asymptotic diversity order of two, whereas the LMMSE receiver is totally unable to exploit the available spatial diversity.

Diversity Analysis of Non-Coherent Wireless Network Coding

Network coding has been widely used in the wireless uplink. To do coherent detection at the receiver, channel estimation is performed to collect the channel state information (CSI). For multi-user channels, the channel estimation overhead is sometimes formidable and may even outweigh the network coding gain. To address this issue, we study the non-coherent network coding in this work. Both the analog network coding (ANC) and digital network coding (DNC) are studied. Depending on the available CSI, we first develop the coherent and non-coherent maximum likelihood receivers. For ANC, as the non-coherent receivers have no closed form, we develop two suboptimum receivers according to the average link qualities. Next we study the error rates, and show that full diversity can always be achieved at extremely high signal-to-noise ratios (SNR) regardless of the CSI assumptions. However, the lack of perfect CSI would incur some diversity loss at modest SNRs. Besides, the performance loss of ANC is more serious due to the incapability to efficiently suppress multi-user interferences at the receivers. Extensive simulations are performed to verify our analytical results.

Improving the DMT Performance for MIMO Communication With Linear Receivers

Multiple-input-multiple-output (MIMO) linear receivers are often of more practical interest than maximum-likelihood (ML) receivers due to their low decoding complexity but at the cost of worse diversity gain performance. Such a statement on performance loss is due to the assumption of using an independent identically distributed complex Gaussian vector as channel input. By removing this assumption, we find that the diversity performance of MIMO linear receivers can be significantly improved. In an extreme case, it can be the same as that of ML receivers. Specifically, in this paper, we investigate the diversity-multiplexing tradeoff (DMT) performance of MIMO linear receivers with colored and possibly degenerate Gaussian channel inputs. By varying the rank of the covariance matrix of the channel input vector and by allowing temporal coding across multiple channel uses, we show that the MIMO linear receiver can achieve a much better DMT performance than the currently known one. Explicit optimal code constructions are provided, along with simulation results, to justify the above findings. For the case of (2 × 2) and (3 × 3) MIMO linear receivers, simulation results show that the newly proposed codes provide significant gains of 10 and 12.08 dB in E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> /N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> at bit error rate 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> compared to the conventional schemes, respectively.

Energy-Efficient Full Diversity Collaborative Unitary Space-Time Block Code Designs via Unique Factorization of Signals

In this paper, a novel concept called a uniquely factorable constellation pair (UFCP) is proposed for the systematic design of a noncoherent full diversity collaborative unitary space-time block code by normalizing two Alamouti codes for a wireless communication system having two transmitter antennas and a single receiver antenna. It is proved that such a unitary UFCP code assures the unique identification of both channel coefficients and transmitted signals in a noise-free case as well as full diversity for the noncoherent maximum likelihood receiver in a noise case. To further improve error performance, an optimal unitary UFCP code is designed by appropriately and uniquely factorizing a pair of energy-efficient cross quadrature amplitude modulation (QAM) constellations to maximize the coding gain subject to a transmission bit rate constraint. After a deep investigation of the fractional coding gain function, a technical approach developed in this paper to maximizing the coding gain is to carefully design an energy scale to compress the first three largest energy points in the corner of the QAM constellations in the denominator of the objective as well as carefully design a constellation triple forming two UFCPs, with one collaborating with the other two so as to make the accumulated minimum Euclidean distance along the two transmitter antennas in the numerator of the objective as large as possible, and at the same time, to avoid as many corner points of the QAM constellations with the largest energy as possible to achieve the minimum of the numerator. In other words, the optimal coding gain is attained by intelligent constellations collaboration and efficient energy compression. Computer simulations demonstrate that error performance of the optimal unitary UFCP code presented in this paper outperforms those of the differential code and the signal-to-noise-ratio-efficient training code.