System Modelling of WSN Systems Subject to Frequency-Selective Fading 

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Chapter 3 Cooperative Diversity Techniques in WSNs Subject to Frequency-Selective Fading

Introduction

Chapter 2 investigated the BER performance of a SISO (non-cooperative) WSN system sub-ject to AWGN channels affected by frequency-selective Rayleigh fading. In this chapter, the analysis will be extended to a WSN system with cooperative diversity techniques operating over frequency-selective Rayleigh fading channels.
Cooperative diversity techniques have been identified as a promising technique for re-ducing the energy consumption of wireless communications in energy-constrained WSNs The major cooperative diversity techniques described in the literature can be classified into two general categories with respect to the behaviour of the cooperating partner node, as demonstrated in Figure 1. In the first category, the cooperating partner node behaves as an analog amplifier and forwards an amplified version of the noisy information received from the source node. This kind of cooperation is aptly named Amplify-and-Forward (AF) cooperation [71–76].
In the second category, the cooperating partner node decodes and re-encodes the noisy information received from the source node and then forwards it to the receiver. The second category can be further classified according to how the cooperating pair (e.g. the source and partner nodes) communicate with the destination receiver, as follows:
Virtual-MISO (multiple input single output) [77–82]: The source and partner nodes form a virtual antenna array and simultaneously communicate with the destination receiver using space-time diversity codes.
Decode-and-Forward (DF) [71, 83–88]: The source and partner nodes transmit to the destination receiver on time-orthogonal channels. In DF cooperation, the partner node always forwards the overheard message signal to the destination receiver node.
Adaptive Decode-and-Forward (aDF) [88–92]: the source and partner nodes transmit to the destination receiver on time-orthogonal channels. However, the overheard mes-sage signal is not forwarded unless the partner node decodes it correctly. In aDF co-operation, the cooperating partner node makes its forwarding decision using a cyclic redundancy check (CRC) or by setting a SNR threshold for the overheard signal. These adaptive characteristics of the aDF scheme potentially mitigate the influence of error propagation, which is not avoidable in the DF scheme.
Importantly, there are several notable cooperative diversity techniques that are not shown in Figure 3.1, including the coded cooperative technique [31], the cooperative beamforming and the selection cooperative technique [94]. The coded cooperation technique has been proposed to avoid the repetition coding employed in DF and aDF cooperation. Us-ing the error correction coding in the coded cooperation, enables the cooperation to obtain a coding gain which can improve the BER performance of the cooperative system. Nev-ertheless, this design increases the transceiver and processing complexity and in practice is computationally expensive for resource-constrained wireless sensor nodes. Accordingly, coded cooperation is not considered in this thesis, and nor are cooperative beamforming and the selection cooperative scheme due to practical implementation concerns. In the coopera-tive beamforming scheme, it is vital that the cooperating nodes co-phase the transmissions precisely, so they can combine constructively at the receiver. However, it is challenging for a traditional physical antenna array to achieve the precise synchronisation. As a result, it would be very difficult to practically implement cooperative beamforming in a distributed WSN [95]. In the selection cooperative scheme, each candidate partner node competes to forward its overheard message based on the instantaneous channel quality. In other words, it is necessary for each partner node to obtain knowledge of the instantaneous condition of partner-source and partner-destination channels which results in substantial signalling overheard. Consequently, it is not practical in terms of energy efficiency to implement the selection cooperative scheme in energy-constrained WSNs. As the objective of this thesis is to evaluate cooperation as a practical energy saving tool for WSNs operating in indoor environments, only the second category consisting of the vMISO, DF and aDF cooperative schemes shown in Figure 1 is of interest, because these schemes are relatively straightfor-ward for practical implementation.
The energy efficiency of cooperative communications in WSNs subject to flat fading was first reported by Shuguang et al. [96]. They studied the energy efficiency of vMISO cooperation for a clustered WSN, whereby cooperation is established between the source node and its neighbouring sensor nodes to transmit information to the receiver. The energy model consisted of the total transmit energy consumption and the energy consumption of the transceiver circuit blocks. The findings confirmed that cooperative communications can significantly reduce the total energy consumption of a WSN system with a large source-destination separation [96]. A novel energy saving technique combining cooperative MIMO and data-aggregation was developed by Gao et al. [97] to reduce the energy consumption per bit in cluster-based WSNs. A new energy cost model was also proposed based on the correlation between data generated by sensor nodes and the transmission distance between them. Their analysis indicated that the proposed technique outperforms systems without data-aggregation in terms of energy efficiency for different cluster sizes [97].
The following two studies provided a comparison of the energy efficiency performance of the direct transmission and the cooperative transmission schemes in WSNs subject to narrowband Rayleigh fading. Sadek et al. [98] optimised energy efficiency under a given QoS constraint, and Wang and Nie [99] obtained maximum enregy efficiency for coopera-tion by jointly optimising both the packet size and modulation level. The results from both studies demonstrate that for a short source-destination separation, the overhead of cooper-ation degrades its gains and direct transmission is more energy efficient, while above the separation threshold, cooperative gains can be obtained (i.e. the cooperative scheme is more energy efficient) [98, 99]. Brante et al. [100] compared the energy efficiency of single-hop, multi-hop and cooperative transmissions in a WSN system. The destination receiver in the system was assumed to be constrained to both a target packet loss rate and a target end-to-end throughput. Their results show that if a feedback channel is available, cooperative transmission is more energy efficient even with a short transmission distance. In a subse-quent study, Brante et al. compared the energy efficiency of incremental DF cooperation in multiple-input-multiple-output (MIMO) systems subject to flat Rayleigh fading [101]. They defined energy efficiency as the effective spectral efficiency seen at the receiver normalised by the total energy consumption, given in bits/J/Hz [101]. Qing et al. [102] investigated the energy efficiency of fixed AF and selective DF cooperative networks subject to Rayleigh fading. The proposed energy cost model consists of the circuit, transmission and retrans-mission energies. The M-ary quadrature amplitude modulation (MQAM) constellation size is optimised in this study to reduce the energy expenditure subject to a given BER constraint The results demonstrate that direct transmission is more energy efficient with small constellation sizes, while the cooperative system can achieve significant cooperative gains with large constellation sizes and a long transmission distance.
It is important to note that all the studies discussed [96–102] have analysed the energy efficiency of cooperation in WSNs subject to flat Rayleigh fading. Cooperation in WSNs operating over frequency-selective Rayleigh fading channels has not been addressed. Moti-vated by this gap in the literature, the energy efficiency of cooperative transmission schemes in WSNs subject to frequency-selective Rayleigh fading is a particular focus in this the-sis. As described previously, two studies have investigated a special case of cooperation in cluster-based WSNs, whereby the neighbouring source and partner nodes (separated by a distance of 1 m) cooperatively transmit message signals to the destination receiver [96, 97]. Instead, this thesis considers a more general case of randomly deployed WSNs, whereby a source node can choose a cooperating partner node located anywhere within the network region.
Accordingly, this chapter investigates the BER performance of vMISO, DF and aDF cooperation in WSNs operating over frequency-selective Rayleigh fading channels. In ad-dition, the energy consumption models of vMISO, DF and aDF cooperation are presented as well. The following are the particular achievements of this study:
A propagation model of a cooperative WSN system operating over frequency-selective Rayleigh fading channels is introduced.
BER expressions of vMISO, DF and aDF cooperation in WSNs operating over frequency-selective Rayleigh fading channels are derived. Theoretical BER curves are plotted using MATLAB.
Energy consumption models of vMISO, DF and aDF cooperation are presented by con-sidering the energy expenditure of transceiver circuit blocks.
Figure 3.2 demonstrates the route map for Chapter 3. Section 3.2 presents a block schematic of a cooperative WSN system operating over frequency-selective Rayleigh fad-ing channels. Further, the error expressions of vMISO, DF and aDF cooperative schemes are developed for wireless systems subject to frequency-selective Rayleigh fading. The en-ergy consumption models of these three cooperative schemes are provided in Section 3.3. Next, the energy efficiency is defined as a metric to evaluate the energy saving capability of vMISO, DF and aDF cooperation. Finally, the whole investigation is summarised in Section 3.4.

Cooperative System over Frequency-Selective Fading

The cooperative scheme applied in WSNs is comprised of a source node (S), a cooperating partner node (P) and a destination receiver (D). Additionally, it is assumed that the wire-less channels of source-partner, partner-destination and source-destination are independent frequency-selective Rayleigh fading channels.
A block schematic of the cooperative wireless communication system is shown in Figure 3.3. The subsequent analysis will demonstrate the operation of vMISO, DF and aDF diver-sity techniques, and study the BER expressions of WSNs (subject to frequency-selective Rayleigh fading channels) adopting cooperative diversity techniques. Uncoded BPSK mod-ulation is applied in the communication system, and BPSK signals are transmitted in half-duplex over two time phases. As shown in Figure 3.3, each wireless channel is represented by (M+1) fading coefficients, which are realisations of the Rayleigh independent random variables (α₀₀, α₀₁, …, α_0M), and (M+1) time delays, which are realisations of the inde-pendent exponentially distributed random variables (τ₀, τ₁, …, τ_M). The channel are also affected by AWGN, i.e., n(k).

Error Expression of Virtual-MISO Cooperation

In a vMISO cooperative diversity scheme, the source and partner nodes act as elements of a virtual antenna array and cooperate by simultaneously transmitting the source’s message signal to the destination receiver using space-time diversity. The operation shown in Figure 3.4 can be described as: (A) in the first phase, the source node sends the message signal to the partner node; (B) in the second phase, the source and the partner nodes transmit the original signal to the destination receiver at the same time. Eventually, the receiver node combines the received signals and decodes them.
In the vMISO scheme, the partner node consistently forwards the overheard message signal, even if it has not decoded the signal correctly. In this thesis, the partner node for-wards an erroneous signal to the destination receiver with the error probability BER_sp, which is defined as the BER of the source-partner transmission. In addition, this error propaga-tion would cause a very high BER at the receiver, which can be roughly approximated as BER_e ≈ 1/2 [103]. Accordingly, that the end to end BER of the vMISO cooperative WSNs, BER_vMISO, is expressed as.
where BER _f is the BER of the (full second order) cooperative communication of the source and partner nodes to the receiver.
In order to avoid significant error transmission at the partner node, it is important to ensure the BER_sp in (3.1) is low enough to make the second term in the equation negligible. Accordingly, it is assumed in this thesis that the targeted source-partner BER (P_esp) is one order of magnitude lower than the targeted end to end BER of the total communication system P_e (i.e. P_esp = P_e ×10⁻¹). Eventually, the overall end to end BER of the cooperative network BER_vMISO, can be approximated

.Error Expression of Decode and Forward Cooperation

A DF cooperative diversity scheme takes advantage of the broadcast characteristics of wire-less channels, whereby the cooperating partner node overhears and forwards the received signal to the receiver. By avoiding a distinct transmission from source to partner, DF co-operation may potentially achieve greater energy savings compared to vMISO cooperation. Moreover, the DF scheme is particularly advantageous in a distributed WSN, as strict syn-chronisation of the cooperating nodes is not essential because the source and partner nodes communicate with the receiver over time-orthogonal channels. As shown in Figure 3.5, the
operation of a DF scheme goes as follows: in the first phase, the source node sends its mes-sage to the receiver and the partner node; and in the second phase, the partner node forwards the received signal to the receiver. The destination receiver combines the independently fad-ed signals received from the source and partner nodes and then decodes the original message signal.
The end-to-end BER of a DF cooperative scheme, BER_DF , which is identical to that for vMISO cooperation, can be expressed as [103]
Importantly, the partner node in DF cooperation always forwards the message signal it over-hears from the source to the destination, regardless of whether it decodes the signal correctly.
The partner node will forward erroneous information to the destination with the probability BER_sp. Accordingly, the transmission power of the source should be large enough for the partner to overhear it reliably. A constraint of BER_sp ≤ P_esp is therefore also imposed, i.e., P_esp = P_e ×10⁻¹. Finally, BER_DF can be approximated as.

Error Expression of Adaptive Decode and Forward Cooperation

The adaptive DF cooperation and its basic operations are demonstrated in Figure 3.6 [103]. In the first phase, the transmission from the source node to the receiver node is also received and decoded by the partner node. If the partner node can decode the received message cor-rectly (case 1), it then forwards it to the destination node in the second phase. Alternatively, if the partner node does not decode the message correctly (case 2), the message will not be forwarded to the receiver. In the first case, the receiver combines the independently faded signals received from the source and partner nodes and decodes the original message signal. In the second case, the receiver will only decode the signal received from the source node.
The probability of the partner node not forwarding is given by BLER_sp (the block error rate on the source-partner channel). The end to end BER of an aDF cooperative scheme BER_aDF can be expressed as [90]
where BER_n is the BER of the non-cooperative transmission.
It is evident from (3.5) that the error performance of aDF cooperation with a blocked source-partner channel (i.e. BLER_sp = 1) is equivalent to that for non-cooperative commu-nication, i.e., BER_n. In contrast, the full second order cooperative diversity can be achieved at the destination by assuming an ideal source-partner channel (i.e. BLER_sp = 0), with BER_aDF = BER _f , as given by (3.5).

BER Curves and Discussions

In this thesis, wireless channels between sensor nodes are assumed to be AWGN channels affected by frequency-selective Rayleigh fading. The BER expression of a non-cooperative communication subject to frequency-selective Rayleigh fading is given by (2.25)
where SNR_sd is the average received SNR on the non-cooperative source-destination chan-nel.
The BER expression of a full second order cooperative communication can be expressed as (refer to Appendix A.5) where SNR_sd and SNR_pd are the average received SNRs on the source-destination and partner-destination channels, respectively.
To obtain a better understanding of these BER expressions, theoretical BER curves are plotted in MATLAB using the reference channel parameters listed in Table 3.1.
In Figure 3.7, the theoretical BER curve of a vMISO (or DF) cooperative system (BER_vMISO or BER_DF ) is presented, alongside that of a non-cooperative system (BER_n) and a full sec-ond order cooperative system (BER _f ). It is evident from Figure 3.7 that when BER_sp is low enough, the difference between BER _f and BER_vMISO (or BER_DF ) curves is nearly neg-ligible for a high SNR value, which confirms the preciseness of the approximation made in (3.2) and (3.4). For example, if the targeted BER is set as P_e = 10⁻³ (corresponding to BER_sp ≤ 10⁻⁴), the difference is approximately 5.0 × 10⁻⁵ for SNR = 30 dB; if P_e = 10⁻⁴ (corresponding to BER_sp ≤ 10⁻⁵), the difference is just about 5.0 × 10⁻⁶ for SNR = 30 dB. It is clear that the system’s BER performance can be greatly improved by employing cooperative diversity techniques. Thus, the wireless system’s energy expenditure can be significantly reduced.
The theoretical BER curves of aDF cooperation are presented in Figure 3.8 in terms of different kinds of source-partner channels. It is evident from Figure 3.8 that BER_aD is equivalent to BER _f if BLER_sp = 0 is assumed (corresponding to an ideal source-partner channel). Conversely, BER_aDF is equivalent to BER_n if BLER_sp = 1 is assumed (corre-sponding to a blocked source-partner channel). Assuming BLER_sp = 0.25, the BER curve of an aDF cooperative system is demonstrated as a weighted combination of BER _f and BER_n, as given by (3.5). Importantly, Figure 3.8 clearly indicates that considerable reduc-tion in the total transmit energy expenditure can be achieved from an aDF scheme even with a non-ideal source-partner channel (i.e. BLER_sp = 0.25). Accordingly, the aDF cooperative diversity technique is shown to be a powerful energy saving tool for WSNs, and capable of establishing energy efficient cooperation with various candidate partners (including poten-tially non-ideal candidate partner nodes).

Energy Consumption Models

The total average power consumption P_total of a short range communication system (e.g. WSNs) can be expressed as the sum of the total power consumption of the radio frequency (RF) power amplifiers P_A and the total power consumption of the whole transceiver circuit The power consumption of the amplifiers is proportional to the transmit power P_o, ex-pressed as
P_A = (ξ  η)P_o,               (3.9)
where ξ is the peak to average ratio and η is the drain efficiency of the RF power amplifier, which is determined by the modulation scheme [104]. The transmit power is defined .
where E_b is the energy per bit required at the destination receiver to achieve a targeted BER (P_e), R_b specifies the bit rate, and L is the channel path loss which can be calculated using the log-distance path loss model, giving where L_{re f} is the reference path loss at a reference distance (i.e. 1 m) [105], k represents the value of the channel path loss exponent and D_sd is the source-destination separation. It is important to note that E_b is obtained from the average received SNR required at the receiver to achieve the targeted BER (P_e), where N₀ is the noise power spectral density.
For the sake of simplicity, the total power consumption of all transceiver circuit blocks is intentionally grouped into two parameters, i.e, P_Ct and P_Cr. P_C can be expressed as
where P_Ct represents the power consumption of the transmitter circuit blocks and P_Cr repre-sents the power consumption of the receiver circuit blocks.

Table of Contents
Table of Contents 
List of figures 
List of tables 
Nomenclature 
1 Thesis Introduction 
1.1 Wireless Sensor Networks
1.2 Fading Channels in Wireless Communication Systems
1.3 Thesis Motivation and Objectives
1.4 Thesis Contributions
1.5 Thesis Framework
2 System Modelling of WSN Systems Subject to Frequency-Selective Fading 
2.1 Introduction
2.2 System Structure
2.3 DSSS Transceiver Models
2.4 DSSS Transceiver Models with Chip-Interleaving Signal Processing
2.5 Simulation Results and Discussion
2.6 Summary
3 Cooperative Diversity Techniques in WSNs Subject to Frequency-Selective Fading
3.1 Introduction
3.2 Cooperative System over Frequency-Selective Fading
3.3 Energy Consumption Models
3.4 Summary
4 Power Allocation for Energy Efficient Cooperation in WSNs Subject to Frequency- Selective Fading 
4.1 Introduction
4.2 Non-Cooperative Communication
4.3 Virtual-MISO Cooperation
4.4 Decode and Forward Cooperation
4.5 Numerical Results and Discussion
4.6 Summary
5 Partner Selection Region of Energy Efficient Cooperation in WSNs Subject to Frequency-Selective Fading 
5.1 Introduction
5.2 Partner Selection Region of Energy Efficient Cooperation in WSNs
5.3 Effects of Varying Parameters in Energy Efficient Cooperative Communication
5.4 Summary
6 Energy Efficient Cooperation with Chip-Interleaving Signal Processing 
6.1 Introduction
6.2 Non-cooperative Communication with Chip-Interleaving
6.3 Energy Efficient Cooperation with Chip-Interleaving
6.4 Practical Partner Selection for Energy Efficient Cooperation
6.5 Evaluation of the Practical Partner Selection Heuristics
6.6 Summary
7 Conclusions and Future Work 
7.1 Summary of Important Findings
7.2 Suggestions for Future Work
References
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Energy Efficient Cooperative Communication in Wireless Sensor Networks Subject to Frequency-Selective Fading