This is to prove that the thesis entitled "MODELING AND ANALYSIS OF ASIN-TIMED INTERFERENCE IN WIRE NETWORKS" presented by Sam Darshi, a research scholar in the Department of Electronics and Electrical Engineering, Indian Institute of Technology Guwahati. degree of Doctor of Philosophy, was completed by him under my supervision and direction. This bit error rate analysis takes into account the intervening frame bit.
Glossary
List of Publications
Introduction
- Spectrum Reuse from an Interference Perspective
- Asynchronous Co-channel Interference in Wireless Networks
- Various Available Models for Interference Analysis
- Status of Existing Models in Dealing with Asynchronous Sce- narios
- Issues Related to Modeling and Analysis of Asynchronous In- terference
- Motivation of the Present Work
- Thesis Contribution
- Thesis Organization
One of the main problems to be included arises from the lack of coordination between nodes. A short presentation of the problem of asynchronous interference in infrastructure-free and infrastructure wireless networks is also presented.
Literature Survey: Review of Related Work
Interference Modeling
As mentioned earlier, the main difference between networks with infrastructure and networks without infrastructure is the absence of a central entity in the later class of networks. The presence of a central entity in infrastructure-based networks makes it easy to achieve and maintain synchronization/coordination between user nodes of (different) networks.
TxRx
Mi−Mj| ≤RC, protocol model gives the condition for a transmission, originating from node Mi to another (receiver) node Mj, j ∈ k, to be successful in the frequency reuse scenario as. Mk−Mj| ≥(1 + ∆)|Mi−Mj| (2.1) where Mk, k∈k can be any other node of the network transmitting on the same frequency and RC denotes the reception range.
Interferer
Graph Based Approaches for Interference Modeling
There are several key elements of interference analysis that can be efficiently depicted by graphs [44] in wireless networks. Typical problems such as scheduling [45], frequency assignment problems [46] and topology control [47] can be efficiently handled by graphs which is another important form of describing interference effects.
Asynchronous Interference Modeling and Analysis
- Modeling Issues
- Issues Related to Performance Metrics
- Performance Evaluation Using Outage Probability
- Performance Evaluation Using Bit Error Rate
The number of interferers is not a deterministic quantity in a (non-centralized) wireless network due to the uncertainty of the wireless medium and the availability of the data to be sent (e.g. in event-driven scenarios), so the total interference power also becomes a random quantity. A probabilistic treatment of bluetooth piconet performance under CCI from other bluetooth piconets is presented in [28].
Interference Analysis and Management in Heterogeneous/
Overlaid Wireless Network
- Interference Scenarios
- Issues Related to Interference Management
- Spectrum Allocation Methods : Contribution to Interference
- Access Methods : Effects on Interference
- Interference Management : Comparison with Cellular Network
- Interference Management Strategies
- Appropriate Strategies for Interference mitigation
- Motivation for Our Work
- Interference management by optimum Subband Allocation : A Practical ViewView
- Some More Issues to Address
- Summary
In the case of the OFDMA-based femtocell network, cross-layer interference occurs between the elements of the femtocell level and the macrocell level. A proper subband allocation can be an efficient way to mitigate co-layer interference in OFDMA-based femtocell networks. For example, in the case of the macrocell-femtocell two-level network based on OFDMA, the spectrum can be allocated to the femtocells in two ways.
An optimal subband allocation in the two-tier femtocell network can be crucial from the following considerations.
![Figure 2.7: Cross-tier interference between neighbouring femtocells in a two-tier network [3].](https://thumb-ap.123doks.com/thumbv2/azpdfnet/10510888.0/48.892.146.825.150.612/figure-cross-tier-interference-neighbouring-femtocells-tier-network.webp)
Outage Analysis of Asynchronous Interference Limited Wireless
Introduction
Finally, as a performance evaluation metric, we analyze the outage performance of the network using the proposed interference model. Some simulation results are presented to show the effects of antenna height on network performance. To date, the physical interference model is considered an efficient and accurate model for analyzing interference due to its additive nature [1, 7, 21].
A two-slope model [10] is used to calculate the distance-dependent path loss and antenna height effects are also considered.
System Model
- Network Organization
- Proposed Model for Representing Interference
- Expected Numbers of Type-1 and Type-2 Interferers
- Exposed Node Phenomenon : A different View
- Path loss Model
- Received Signal Model
- Link Probability Based Range and Guard Zone
- Channel Model
Two important parameters of interest in the proposed model are the average overlap of the i-th bit of the desired frame and the expected number of effective type 1 and type 2 interferences. At any moment, the actual number of interferers in the network is all transmitters except those that are banned MAC protocol (they are inside rz), i.e. Now the number of (interfering) emitters within rz Rxo can be written as T xrzRxo = (Ks −1)PrizRxo.
Here we assume that the number of such receivers in rz Rxo can be given by.
Performance Analysis
- Analysis Under Approximation
- Outage Probability Calculation
Υij eλ(εj−ε) = eλ~i =Ne (3.41) where ~ is a Gaussian RV whose mean and variance can be calculated using the GMM method (details are given in Appendix A.3) and Ne is the combination of (Ief f + 1) RVs with random and independent weights. In the absence of closed form expression for (3.46), standard numerical techniques [105] can be used to obtain outcome probabilities. With the outcome probability calculated above, the probability of success can also be estimated as.
The probability of packet (frame) interruption can be easily obtained where transmission of bits can be assumed to be independent.
Numerical Results
- Effect of Number of Interferers
- Effect of Antenna Height
It can be observed that as the number of simultaneous transmissions increases, the probability of interruptions approaches a limiting value. Intuitive explanation comes from the interference averaging effect which states that when the number of users is very large, variance decreases markedly due to law of large numbers [104]. In interference-free environment, where performance becomes independent of the number of simultaneous transmissions, the PLP model is found to underestimate the performance due to distance-independent path loss exponent.
The reduction of the variance in the interference energy for the case of a large number of interferers under the high interference regime can be observed in the form of saturation in figure 3.6.
Comparison with Existing works
Conclusion
For this example, the accumulated perturbation can be assumed to be Gaussian (as an approximation), but for the mathematical analysis we followed a more general approach (GMM method) that can also handle non-Gaussian cases. Furthermore, in the case of compound fading, the Gaussian assumption is reported to be incorrect. Therefore, an important result of this investigation is the formulation of an analytical framework for the analysis of an asynchronous wireless network in a limited interference environment.
The investigation reported in this chapter can be useful in the analysis of large wireless networks where synchronization is not possible centrally between (groups of) user nodes.
BER Analysis of Asynchronous Interference Limited Wireless
Introduction
By considering the fractional bit overlap, the pdf of the effective signed fractional overlap variable is derived. The pdf of the resultant amplitude of the asynchronous interfering signal is calculated using an amplitude metric-based approach. The effect of the number of simultaneous transmissions (active users), the interference factor and the size of the deployment area on the network performance is investigated.
The effect of the guard zone on various network parameters is discussed in detail in section 4.4.
System Model
- Statistics of the Proposed Model
- Statistics of Effective Signed Fractional Overlap Variable
Assuming that α1j (α2j) represents the relative position of the first bit of the desired frame with respect to the last bit of the jth type -1 (type - 2) interfering frame, the position (index) of the interfering bit(s) and the corresponding overlap(s) of the j. unwanted frame for the ith† bit of the desired frame due to the type-1 interferers can be written as (omission of the subscript {j,1} on α). The unfaded weighted amplitude (weighted by √ . Tb ) of the desired bit after matched filtering can be written as [112]. Therefore, the effective amplitude of the interference experienced by bits of the desired frame can be expressed after matched filtering.
Using (4.7), the effective amplitude of the interfering signal can further be written as (leave the subscripts I and α1j).
Error Analysis
- PDF of Interference Variable
- BER Expression
- BER Expression : with Noise Considered
To evaluate the BER expression, we invoke the CLT for the interfering signal terms. It can be mentioned that although the CLT is generally applicable for the large number of picking. To apply the CLT to the second term of (4.22), we use a Gaussian RVGI for the sum of the interfering terms, whose mean (mGI) and variance (σG2I) are given as follows.
After removing the condition and using simple adjustments, the expression is found to be for the BER.
Results
- Effect of the Number of Interferers
- Effect of the Interference Range
- Performance With Noise Included
The variation of the AIVS for different deployment areas and path loss environments is shown in Figure 4.6. A larger number of interfering nodes, which are otherwise user nodes in the network, will be excluded from the transmission due to the higher value of the IRF and therefore the overall network throughput is degraded. Including the noise degrades ABER performance as the number of simultaneous transmissions increases.
However, the difference in performance between ABERN and ABER slowly disappears as the number of simultaneous transmissions increases, because the higher values of the simultaneous transmissions continue to make the effective interfering signal significantly stronger.
Conclusion
Interference Management in Heterogeneous Wireless Network
- Introduction
- System Description
- Frequency Subband Selection Strategy
- Interference Analysis and Modeling
- Statistics of Aggregated Interference Signal
- Analysis Under Approximation
- Results and Discussions
- Results : Second Approach
- Some More Observations
- Conclusion
The second approach suggests a suitable approximation to the pdf of the individual interfering signal in order to obtain a closed-form solution for optimal subband selection. The term Uj indicates the number of uplink interferers in the second macrocell in the analysis of the interference effect due to uplink transmissions. Since this work deals with downlink interferers, therefore Uj = 1 for the remainder of the analysis.
Selection of the appropriate subband for communication purposes can be performed by solving the following equations.
Discussion and Future Work
Summary of Contributions and Discussions
In this thesis, we address issues regarding modeling and analysis of interference in an asynchronous environment. This chapter presents the summary of the thesis and also discusses some of the possible future directions of expansion of the research works reported in this thesis. The main contributions of this thesis are summarized in Section 6.1 and possible future extension of the work is outlined in Section 6.2.
We also introduced a metric EINR to quantify the ratio of the desired energy to the interference energy plus noise spectral density ratio.
Suggestions for Future Work
Some other powerful methods like Schwartz and Yeh's, Cumulants matching method can be used to get better accuracy. Investigations of BER and subband selection can be extended to include shadowing effects for a better characterization of the fading environment. Users with unequal frame lengths and ACI effects can be considered for modeling a relatively general scenario.
We foresee that analyzing interference-constrained networks using game theory can be an efficient and interesting way to model complex scenarios.
Outage Performance
It can be observed that the accuracy of the assumptions made decreases as r gets closer to g. A.2) Now, with some calculations using the above assumptions, PrizRx for this case can be written as.
Comment on Replacement in Equation 3.38
GMM method : Mean and Variance Calculation of ~
BER Performance
ABER Analysis with Phase Considered
To observe the effects of the phase term on ABER values, we consider an individual interfering signal as follows. The result shows that including the phase term does not significantly affect the overall system performance in terms of ABER. By considering the phase term (cos(θ)) for each interfering signal component, the randomness of the total signal is further increased, which may be the possible reason of a higher BER for a small number of interfering substances.
Therefore, the phase term loses its effect in terms of added randomness, which decreases in the presence of a large number of interfering substances and thus ABER.
For ξj ∈ [0, Amj ], w must be greater than zero to make the argument of the channel fading parameter pdf positive.
Bibliography
Hamdi, “Precise interference analysis of ofdma time-asynchronous wireless ad-hoc networks,” Wireless Communications, IEEE Transactions on, vol. Andrews, “Analytical evaluation of fractional frequency reuse for ofdma cellular networks,” Wireless Communications, IEEE Transactions on, vol. Jeong, “Downlink radio resource partitioning with fractional frequency reuse in femtocell networks,” Vehicle Technology, IEEE Transactions on, vol.
Fourestie, "Performance evaluation of frequency planning schemes in ofdma-based networks," Wireless Communications, IEEE Transactions on, vol.
![Figure 2.8: Co-tier interference between neighbouring femtocells in a two-tier network [3].](https://thumb-ap.123doks.com/thumbv2/azpdfnet/10510888.0/49.892.131.816.144.655/figure-2-tier-interference-neighbouring-femtocells-tier-network.webp)
