On the bit error probability of QAM modulation

Fitz, M.P.; Seymour, James P.

doi:10.1007/bf02106515

Cited by 57 publications

(15 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where erfc(x)= 2 √ π ∞ x e −t 2 dt is the complementary error function and rank(S k ) ≤ 1 [73,189]. This error measure should be minimized, thus it is equivalent to maximizing g k (SINR k )=0.5 − P k,16-QAM .…”

Section: User Performancementioning

confidence: 99%

Optimal Resource Allocation in Coordinated Multi-Cell Systems

Björnson

2013

FNT in Communications and Information Theory

309

317

View full text Add to dashboard Cite

The use of multiple antennas at base stations is a key component in the design of cellular communication systems that can meet high-capacity demands in the downlink. Under ideal conditions, the gain of employing multiple antennas is well-recognized: the data throughput increases linearly with the number of transmit antennas if the spatial dimension is utilized to serve many users in parallel. The practical performance of multi-cell systems is, however, limited by a variety of nonidealities, such as insufficient channel knowledge, high computational complexity, heterogeneous user conditions, limited backhaul capacity, transceiver impairments, and the constrained level of coordination between base stations. This tutorial presents a general framework for modeling different multi-cell scenarios, including clustered joint transmission, coordinated beamforming, interference channels, cognitive radio, and spectrum sharing between operators. The framework enables joint analysis and insights that are both scenario independent and dependent.The performance of multi-cell systems depends on the resource allocation; that is, how the time, power, frequency, and spatial resources are divided among users. A comprehensive characterization of resource allocation problem categories is provided, along with the signal processing algorithms that solve them. The inherent difficulties are revealed: (a) the overwhelming spatial degrees-of-freedom created by the multitude of transmit antennas; and (b) the fundamental tradeoff between maximizing aggregate system throughput and maintaining user fairness. The tutorial provides a pragmatic foundation for resource allocation where the system utility metric can be selected to achieve practical feasibility. The structure of optimal resource allocation is also derived, in terms of beamforming parameterizations and optimal operating points.This tutorial provides a solid ground and understanding for optimization of practical multi-cell systems, including the impact of the nonidealities mentioned above. The Matlab code is available online for some of the examples and algorithms in this tutorial. IntroductionThis section describes a general framework for modeling different types of multi-cell systems and measuring their performance -both in terms of system utility and individual user performance. The framework is based on the concept of dynamic cooperation clusters, which enables unified analysis of everything from interference channels and cognitive radio to cellular networks with global joint transmission. The concept of resource allocation is defined as allocating transmit power among users and spatial directions, while satisfying a set of power constraints that have physical, regulatory, and economic implications. A major complication in resource allocation is the inter-user interference that arises and limits the performance when multiple users are served in parallel. Resource allocation is particularly complex when multiple antennas are employed at each base station. However, the throu...

show abstract

Section: User Performancementioning

confidence: 99%

Optimal Resource Allocation in Coordinated Multi-Cell Systems

Björnson

2013

FNT in Communications and Information Theory

309

317

View full text Add to dashboard Cite

show abstract

“…In order to meet the constraint, the BER for a QAM in AWGN channels can be used. Although the exact BER expressions for M-QAM are shown in [14], they are not easily inverted with respect to the SNR, so that a numerical method is necessary. Instead, in the adaptive modulation literature [5][6][7][8], an exponential function form is used, which is given by…”

Section: Snr Thresholds For Instantaneous Ber Constraintmentioning

confidence: 99%

Dynamic rate-adaptive MIMO mode switching between spatial multiplexing and diversity

Kim

Lee

2012

J Wireless Com Network

View full text Add to dashboard Cite

In this article, we propose a dynamic multiple-input multiple-output (MIMO) mode switching scheme between spatial multiplexing and diversity modes, which also includes adaptive modulation. At each transmission, we select the modulation level and the MIMO mode that maximize the spectral efficiency while satisfying a given target bit error rate. The dynamic MIMO mode scheme considers instantaneous spectral efficiency whereas the conventional static scheme considers only the average SNR. As for adaptive modulation, a new method is proposed to compute the SNR thresholds for adaptive modulation in each MIMO mode, and it can avoid the computational difficulty of the conventional Lagrangian (optimal) method at high average SNR. To deal with the case where the rates of the two MIMO modes are the same, we also propose a new measure based on the BER exponent, which has lower computational complexity than a conventional measure. Numerical results show that the proposed dynamic mode switching improves over the conventional static mode switching in terms of average spectral efficiency.

show abstract

“…The BER performance of M-ary QAM has been investigated by several authors. The exact BER expressions for QAM is presented in [3]. An extension of BER expressions considering of an arbitrary constellation size is discussed in [4].…”

Section: Introductionmentioning

confidence: 99%

Performance Analysis of an Optimal Circular 16-QAM for Wavelet Based OFDM Systems

Abdullah

Mahmoud²,

Hussain³

2009

IJCNS

View full text Add to dashboard Cite

The BER performance for an optimal circular 16-QAM constellation is theoretically derived and applied in wavelet based OFDM system in additive white Gaussian noise channel. Signal point constellations have been discussed in much literature. An optimal circular 16-QAM is developed. The calculation of the BER is based on the four types of the decision boundaries. Each decision boundary is determined based on the space distance d following the pdf Gaussian distribution with respect to the in-phase and quadrature components nI and nQ with the assumption that they are statistically independent to each other. The BER analysis for other circular M-ary QAM is also analyzed. The system is then applied to wavelet based OFDM. The wavelet transform is considered because it offers a better spectral containment feature compared to conventional OFDM using Fourier transform. The circular schemes are slightly better than the square schemes in most SNR values. All simulation results have met the theoretical calculations. When applying to wavelet based OFDM, the circular modulation scheme has also performed slightly less errors as compared to the square modulation scheme.

show abstract

On the bit error probability of QAM modulation

Cited by 57 publications

References 9 publications

Optimal Resource Allocation in Coordinated Multi-Cell Systems

Optimal Resource Allocation in Coordinated Multi-Cell Systems

Dynamic rate-adaptive MIMO mode switching between spatial multiplexing and diversity

Performance Analysis of an Optimal Circular 16-QAM for Wavelet Based OFDM Systems

Contact Info

Product

Resources

About