4.2 VHT Model With Hidden Nodes: Vidden
4.2.2 Performance Evaluation and Results of Vidden
5.3.1.16 Timing Synchronization
The training symbols are used for Tx and Rx timing synchronization [109].
5.3.1.17
Channel Estimation
A VHT transmission has a preamble that contains VHT-LTF symbols, where the data tones of each VHT- LTF symbol are multiplied by the entries belonging to a matrix called PV HT LT F, to enable the channel estimation at the Rx [11].
5.3.1.18
Phase Tracking
The multiplication of the pilot tones in the VHT-LTF symbol by the RV HT LT F matrix instead of the PV HT LT F matrix allows Rx to track phase and frequency offset during a MIMO channel estimation using the VHT-LTF [11].
5.3.1.19
VHT Data Equalization
The data field in the VHT PPDU is recovered using Zero Forcing (ZF) equalizer which is a linear equal- ization algorithm that applies an inverse of the frequency response of the channel to the received signal [110].
5.3.2
Channel Model
We chose the TGn channel model B and D for the system so that the proposed system is applicable to the office environment as shown in Fig. 5.1. Further, we consider one GO and one client. The client communicates with the GO using a WD protocol over an 802.11ac PHY layer. Both the GO and the client have two antennas for transmission and reception. Thus, the channel is a 2x2 MIMO multipath fading TGn channel. As a general rule, this channel model can be extended to any number of clients, as well as, lower or higher order MIMOs. A set of WLAN channels was presented in [99] for different environments. There are profiles proposed for channel models, labelled as TGn A to F [99]. These represent six different scenarios namely: flat fading, residential, residential/small office, typical office, large office, and large space (indoors and outdoors). In addition, each channel in 802.11ac is characterized by a particular number of taps with respect to the first path delay where the overlapping subset of these tap delays makes a cluster.
5.3. SYSTEM MODEL
Table 5.1: Pathloss model of TGn channel B 802.11ac
Parameter
Value
Parameter
Value
Parameter
Value
K for LOS (dB)
0
Shadow fading before LOS (dB)
3
σ
RM S(ns)
15
K for NLOS (dB)
−∞
Shadow fading after NLOS (dB)
4
σ
M ax(ns)
80
Number of clusters
2
Number of taps
9
d
BP(m)
5
Table 5.2: Pathloss model of TGn channel D 802.11ac
Parameter
Value
Parameter
Value
Parameter
Value
K for LOS (dB)
3
Shadow fading before LOS (dB)
3
σ
RM S(ns)
50
K for NLOS (dB)
−∞
Shadow fading after NLOS (dB)
4
σ
M ax(ns)
390
Number of clusters
3
Number of taps
18
d
BP(m)
10
The system architecture is depicted in Fig.5.2, in which a client is working as a Txand a GO is a Rx. Furthermore, the client (Tx) has two transmit antennas (i.e., Tx1and Tx2), whereas the GO (Rx) has two receive antennas namely: Rx1and Rx2. Let the link between the transmit antenna i (Txi) and the receive antenna j (Rxj) is indicated by Txi− Rxj. We will use the same notations throughout this chapter.
The multipath fading 2x2 MIMO channel of a WD 802.11ac network for a TGn is derived from the transmit and receive correlation matrices [111]. The transmit and receive correlation matrices associated with each tap delay are determined from the mean AoA, mean AoD, AS at transmitter and AS at receiver. The LOS component can only be present on the 1st tap. If the distance between the Txand the Rxis greater than dBP then LOS component is not present. Note that dBP is the break-point distance or distance of the fist wall (i.e., the distance of the Txfrom the first reflector). The dBP for channel model B and D are listed in Table5.1and5.2, respectively. The path loss model considers the free space loss LF S (slope of 2) up to dBP and slope of 3.5 after dBP [101]. For each of the models, a different breakpoint distance dBP was chosen as shown in eq. (5.1).
L(d) = LF S(d) if d <= dBP LF S(dBP) + 35log10(d/dBP) if d > dBP (5.1)
where d indicates the distance between the Tx and the Rx, while χσ indicates a zero-mean, Gaussian random variable, with standard deviation, σ (in dB), added to the path loss. It is used to model the shadow fading, or log-normal shadowing. The values were found to be in the 3-14 dB range [102]. Similarly, the zero-mean Gaussian probability distribution is given by eq. (5.2).
p(x) = √1 2πσe
[x2
2σ2] (5.2)
The 2x2 MIMO channel matrix H for each tap, at one instance of time, under a channel B delay profile can be represented as a sum of two matrices namely: fixed (constant, LOS) matrix and a Rayleigh (variable, NLOS) matrix as illustrated in eq. (5.3).
H =√P ( r K K + 1HF+ 1 K + 1HV ! (5.3)
where P is the power of each tap obtained by summing all the power of LOS and NLOS powers, K is the Ricean K-factor. The HF and HV in eq. (5.3) can be extended for 2x2 MIMO as follows in eq. (5.4-5.5).
HF = ejφ11 ejφ12 ejφ21 ejφ22 (5.4) HV =XX11 X12 21 X22 (5.5) where eij indicates the constant elements of LOS matrix H
F, whereas Xijindicates the element of variable NLOS Rayleigh matrix HV between ithreceiving and jthtransmitting antenna. It is assumed that Xijis a complex Gaussian random variable with zero mean and unit variance. In order to correlate the Xijelements of the matrix HV, eq. (5.6) is used.
[X] = [Rrx] 1 2[H iid][Rtx] 1 2 (5.6)
where Rtxand Rrxare the receive and transmit correlation matrices, respectively, and Hiidis a complex Gaussian random variable. All these Gaussian random variables are supposed to be identically independent with zero mean, unit variance. In addition, the Rtxand Rrxare given in eq. (5.7) and eq. (5.8), respectively.
[Rtx] = [ρtxij] (5.7)
[Rrx] = [ρrxij] (5.8)
where ρtxij indicates the complex correlation coefficients between ithand jthtransmitting antennas, and ρrxij indicates the complex correlation coefficients between ithand jthreceiving antennas. Alternatively, we use another approach i.e., the Kronecker product of the transmit and receive correlation matrices eq. (5.9) to calculate X.
[X] = ([Rtx] ⊗ [Rrx]) 1 2[H
iid] (5.9)
It can be seen that Hiidis an array in this case instead of matrix. The Rtxand Rrxmatrices are given in eq. (5.10) and eq. (5.11), respectively.
Rtx= 1 ρtx12∗ ρtx21 1 (5.10) Rrx= 1 ρrx12∗ ρrx21 1 (5.11) The values of complex correlation coefficient ρ are calculated from Power Angular Spectrum (PAS), AS, mean AoA, mean AoD and individual tap powers [99],[104]. Consequently, for the Uniform Linear Array (ULA), the complex correlation coefficient at the linear antenna array is expressed as shown in eq. (5.12)
ρ = RXX(D) + jRXY(D) (5.12)
where D = 2πd/λ, RXX indicates cross-correlation functions between the real parts, and RXY indicates the cross-correlation between the real part and imaginary part. The expressions for RXX and RXY are given in eq. (5.13) and eq. (5.14), respectively.
RXX(D) = Z π
−π
cos(D sin φ)P AS(φ)dφ (5.13)
RXY(D) = Z π
−π
5.3. SYSTEM MODEL
Table 5.3: SNR values for different distances for a TGn channel B
d (m)
1
3
6
9
12
15
21
. . .
30
. . .
46
SNR (dB)
48
38.5
32.5
29
25
22
16
. . .
9
. . .
5
We calculate the correlation coefficients matrices using a uniform Gaussian PAS shape [99]. Once we have the channel matrix H, we calculate the output symbol matrix Y given the input symbol matrix, X in eq. (5.15).
Y = HX + W (5.15)
The expression for a 2x2 MIMO system can be formulated as illustrated in eq. (5.16) [112]. y1 y2 =hh11 h12 21 h22 x1 x2 +ww1 2 (5.16)
where y1 and y2 are the output symbols received at antennas Rx1 and Rx2respectively. Similarly, w1 and w2 are the noise components at antennas Rx1and Rx2respectively, whereas x1and x2are the input symbols transmitted from antennas Tx1and Tx2respectively. In the same way, hijis the channel coefficient for link Txi− Rxj.
We calculate the expected average SNR at the GO based on the pathloss model defined in eq. (5.1) for TGn Channel B. We assume that the client transmits with a transmit power of 5 dBm, and the receive sensitivity (or signal detection threshold) at the GO is −90 dBm. Furthermore, we ignore the presence of any other external interference. Thereafter, the SNR values for different distance values d between the GO and client are calculated as illustrated in Table5.3.
5.3.3
Quality of Experience
The Quality of Experience (QoE) is defined as the overall acceptability of an application or service, as perceived subjectively by the end-user [113]. The QoE is a subjective measurement, which includes the complete end-to-end system effects, such as a client, a terminal, a network, and services infrastructure. In order to assess the QoE, a Mean Opinion Score (MOS) is used. The MOS test specified by International Telegraph Union-Telecommunication (ITU-T) is shown in Table5.4. We consider five types of applications (i.e., A5, A4, A3, A2, A1) running on our system, each with a different level of QoE requirements. While QoE is a subjective measurement that is highly dependent on a complex assortment of network, application and human factors, in this chapter as a first order approximation, we use PER in the ranges shown in Table 5.4as a rough indicator of QoE [114]. Fixing the design parameters for the given system, so that the only parameters that can be chosen to adapt the performance of the system in accordance with the given QoE include MCS, SNR, and distance of transmitter and receiver. It permits the relationship between SNR and distance d be calculated from eq.5.1and the Table5.4as shown in eq. (5.17) .
d = fdist(SN R) (5.17)
We formulate the adaptive optimized function fAi(.) to calculate the parameters, which achieves the opti- mal QoE for a targeted application Ai as shown in eq. (5.17). These parameters include minimum SNR (SN Rmin), maximum SNR (SN Rmax), minimum distance between GO and client (dmin), maximum
distance between GO and client (dmax), and MCS as illustrated in eq. (5.18).
OptimalP aramters = fAi(SN Rmin, SN Rmax, dmin, dmax, M CS) ∀ Ai and M CSj (5.18)
where i = 1, 2, 3, 4, 5 and j = 0, 1, 2, ..., 8 and M CSj indicates one of the nine MCS defined for a 2x2 MIMO-OFDM WD system under a 20MHz bandwidth TGn B channel. In order to calculate the optimal values, we define a matrix R ∈ Rm×nthat represents the range of SNR values for a where m and n indicate the number of applications and number of MCS, respectively. The element Rij indicates SNR range for application Aiand M CSj. We have calculated the values of Rijfor application Aiand MCS M CSjfrom our simulation setup as illustrated in Table.5.4. The optimized values are calculated in eq. (5.19-5.23). A5:
SN Rmin= 0, SN Rmax= Rij− 1, M CS = M CSj
dmin = fdist(SN Rmin), dmax= fdist(SN Rmax) (5.19) A4:
SN Rmin= Rij, SN Rmax= R1j+ R2j− 1, M CS = M CSj
dmin = fdist(SN Rmin), dmax= fdist(SN Rmax) (5.20) A3:
SN Rmin= R1j+ R2j, SN Rmax= R1j+ R2j+ R3j− 1
M CS = M CSj, dmin= fdist(SN Rmin), dmax= fdist(SN Rmax) (5.21) A2:
SN Rmin= R1j+ R2j+ R3j SN Rmax= R1j+ R2j+ R3j+ R4j− 1
M CS = M CSj, dmin= fdist(SN Rmin), dmax= fdist(SN Rmax)
(5.22) A1:
SN Rmin= R1j+ R2j+ R3j+ R4j
SN Rmax= R1j+ R2j+ R3j+ R4j+ R5j− 1, M CS = M CSj dmin = fdist(SN Rmin), dmax= fdist(SN Rmax)
(5.23)