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**Chapter 7OFDM-to-OFDM Interference —Analytical Treatment**

**Introduction**

OFDM-based wireless systems, like any other wireless system, can be detrimentally affected by interference.

Interference can come from a variety of sources, especially if the system operates in licenseexempt bands (e.g. ISM band). The focus of this chapter (and Chapters 8 & 9) is to study the effects of interference from same-type systems, e.g. two or more 802.11g networks, or two or more WiMAX systems. These same-type interference situations could occur in places where the receiver can detect two or more networks but the networks cannot detect each other, and are therefore unable to mitigate the effects of interference via MAC layer protocols. These kinds of situations often take place in cluttered environments where there is large path loss, such as indoor environments. The ability to estimate the error rate performance precisely without relying on time-consuming Monte Carlo numerical methods is crucial if error rate calculations are required intensively in the system planning process.

Interference analyses for OFDM systems have traditionally considered the interference to be narrowband, e.g. [45, 66, 120]. Although an OFDM interferer can be modelled as a superposition of narrowband carriers [66], the models and expressions presented in [45,66,120] do not consider the modulation of the interfering system. The authors of [47] have considered the interference effects ofWiMAX on multiband (MB)-OFDM systems (see Table 2.2); modulation of the interfering WiMAX system was considered and analytical expressions for the BER derived. However, the analysis in [47] considers only BPSK and QPSK modulation for the desired and interfering systems and just a single interferer. The authors of [67] have considered the reverse problem studied in [47], where coded and uncoded WiMAX systems are impaired by a single MB-OFDM. The study in [67] produced a closed form analytical BER expression that is obtained by computing the MB-OFDM characteristic function without using numerical integration methods.Section §7.2 exact analytical error expressions of a generic M-ary QAM OFDM system in the presence of multiple generic Z-ary QAM OFDMIs of the same system type as the desired system are derived. Approximations to the exact analytical expressions that are more computationally efficient are presented in Section §7.3. Finally, an algorithm for rapid error rate estimation is proposed in Section §7.4. 7.2 Error Rate Calculations Similar to Chapter 6, the error rate calculations are performed on the received signal after it passes through the DFT at the receiver. Thus, the analysis begins by formulating the post-DFT received signal.

**Post-DFT Signal**

Using the same system assumptions described in Section §6.2.1, a received, sampled, baseband OFDM symbol, rn, in the presence of J OFDMIs is represented as The ith OFDM interferer has Gi subcarriers each with i;g , i;g , and i, respectively, as the amplitude, normalised frequency, and constant phase offset relative to the desired OFDM transmission. D(`) i;g is the ith OFDMI’s modulated data for the gth subcarrier of the `th time-domain symbol. Throughout this thesis, all OFDM systems (both desired and interfering) are assumed to be of the same type (e.g. all WiMAX) since those scenarios result in maximum frequency band alignment which causes maximum

interference levels. This assumption results in the following: Gi = N 8i, and a maximum of two interfering time-domain symbols per OFDMI are present in the DFT window at the receiver as illustrated by Fig. 7.1. Therefore,are the complex spectral leakage terms for ?(1)n;i and ?(2) n;i, respectively. Derivations of (1) i;g (; ; ) and(2) i;g (; ; ) are presented in Appendix C. D(1) i;g and D(2) i;g are random variables and in this thesis, it is assumed, without loss of generality, that both have the same QAM level, Zi, of the ith OFDMI1. This means that Ik is a sum of 2 N J random variables and is thus a random variable itself with a pdf given by the convolution of the individual pdfs of its terms [121, p. 47]. As discussed in Section §6.2.1, the post-DFT received signal at the kth bin, Rk, is given by that has a pdf given by the convolution of the pdfs of Ik and Hk

2. The error rate expressions are derived using the pdf of Rk.

**Probability Density Function of Rk**

The pdf of Rk, PRk (r), in the I- and Q-channels are considered independent of each other and are derived separately. Hk has a Gaussian pdf (given by Equation (4.12)) in both the I- and Q-channels, which are assumed to be independent of each other. The original locations of the interfering message points, L(`) i;g (x; y), in signal space (where ` can be either 1 or 2) with bipolar symmetric ASK signals are given by The expressions in (7.18) and (7.19) are used to derive the probabilities of symbol and bit error for an M-ary QAM OFDM system in the presence of multiple Z-ary QAM OFDMIs.

**Probability of Symbol Error, Ps**

The relationship between Ps, PI s and PQ s is given by (6.9). Since (7.18) is symmetrical around zero, PI s can be derived as where ku is a vector of size v containing the indicies of the frequencies occupied by the uth user.

**1 Introduction **

**2 Wireless Communication Systems and Interference**

2.1 Introduction

2.2 Spectrum Sharing

2.3 Contemporary WCSs and their Modes of Operation

2.4 Development History of OFDM and Multi-Carrier Transmission Systems

2.5 Thesis Contributions

2.6 Summary

**3 OFDM Fundamentals**

3.1 Introduction

3.2 What is OFDM?

3.3 Implementation of OFDM in Modern Communication Systems

3.4 Summary

**4 Channel Characterisation**

4.1 Introduction

4.2 Fundamentals of Radio Wave Propagation

4.3 Radio Channel Characterisation

4.4 Channel Models in Thesis

4.5 Summary

**5 OFDM and Indoor Environments— Investigation Overview**

5.1 Introduction

5.2 Environmental Considerations

5.3 Investigation Plan

5.4 Summary

**6 OFDM in the Presence of Single-Carrier Narrowband Interference**

6.1 Introduction

6.2 Error Rate Calculations

6.3 Analytical Models’ Validity

6.4 Error Rate Performance Assessment

6.5 OFDM Interference as a Superposition of Single-Carrier NBIs

6.6 Summary

**7 OFDM-to-OFDM Interference —Analytical Treatment**

7.1 Introduction

7.2 Error Rate Calculations

7.3 Approximations to the Exact Error Rate Expressions

7.4 Proposed Algorithm for Rapid Error Rate Estimation

7.5 Application to OFDMA

7.6 Forward Error Correction Coding and Interleaving

7.7 Summary

**8 OFDM-to-OFDM Interference Performance Assessment—Indoor Environments**

8.1 Introduction

8.2 General Performance Trends

8.3 Case Studies

8.4 Comparison with DS-SS Systems

8.5 Summary

**9 OFDM-to-OFDM Interference Performance Assessment—Indoor/Outdoor Environments**

9.1 Introduction

9.2 Case Studies

9.3 Comparison with DS-SS Systems

9.4 Summary

**10 Context and Future Developments**

10.1 Introduction

10.2 Wireless Systems Design and Optimisation

10.3 Recommendations for Future Work

10.4 Summary

**11 Conclusions**

**A Derivation of the Separation Distance Between** **Adjacent Signal Levels, , in Signal Space**

**B Monte Carlo Numerical Model**

**C Derivation of Equations (7.7) and (7.8)**

**D Derivation of Equation (7.17) 151**

**E Derivation of Equation (7.30) 153**

**F Error Rate Patterns When There is No Spectral Leakage**

F.1 Effect of Changes in J

F.2 Effect of Changes in

**G Measured RF Path Loss Values in Test Environments A and B **

**H Additional Error Rate Performance Results for Test Environments A & B**

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