Radio Resource Management

Abstract

This chapter is concerned with issues relating to link quality evaluation and handoff in cellular systems. The chapter begins by discussing several different types of signal strength based handoff algorithms. This is followed by a detailed treatment of temporal–spatial signal strength averaging. Guidelines are developed on the window length that is needed so that Ricean fading can be neglected in continuous- and discrete-time signal strength averaging. The need for velocity adaptive handoff algorithms is established and three different velocity estimators are presented. The velocity estimators are compared in terms of their sensitivity to the Rice factor, non-isotropic scattering, and additive white Gaussian noise. Afterwards, the velocity estimators are incorporated into a velocity adaptive handoff algorithm. Afterwards, an analytical treatment of conventional signal strength based hard handoff algorithms is undertaken, and the same is done for soft handoff algorithms. Finally, methods are discussed for carrier-to-interference plus noise ratio, C∕(I + N) measurements in TDMA cellular systems.

Appendices

Appendix 13A: Derivation of Equations (13.43) and (13.58)

The limit in (13.58) can be written as

$$\displaystyle{ \lim _{\tau \rightarrow 0}\frac{\frac{\lambda _{c}} {2\pi \tau }\sqrt{\frac{2\tilde{\lambda }_{rr } (0)-2\tilde{\lambda }_{rr } (\tau )} {\tilde{\lambda }_{rr}(0)}} } {\frac{\lambda _{c}} {2\pi \tau }\sqrt{\frac{2\lambda _{rr } (0)-2\lambda _{rr } (\tau )} {\lambda _{rr}(0)}} } = \frac{\lim _{\tau \rightarrow 0}\frac{\lambda _{c}} {2\pi \tau }\sqrt{\frac{2\tilde{\lambda }_{rr } (0)-2\tilde{\lambda }_{rr } (\tau )} {\tilde{\lambda }_{rr}(0)}} } {\lim _{\tau \rightarrow 0}\frac{\lambda _{c}} {2\pi \tau }\sqrt{\frac{2\lambda _{rr } (0)-2\lambda _{rr } (\tau )} {\lambda _{rr}(0)}} }. }$$

(13A.1)

Note that the limit of the denominator gives (13.43) and is a special case of the numerator limit with N _o  = 0. To find the numerator limit, the following property can be used [309]:

If a function f(τ) has a limit as τ approaches a, then

$$\displaystyle{ \lim _{\tau \rightarrow a}\root{n}\of{f(t)} = \root{n}\of{\lim _{\tau \rightarrow a}f(t)} }$$

(13A.2)

provided that either τ is an odd positive integer or n is an even positive integer and lim _τ → a f(τ) > 0.

Therefore, if the limit

$$\displaystyle{ \zeta =\lim _{\tau \rightarrow 0}f^{2}(\tau ) =\lim _{\tau \rightarrow 0} \frac{\lambda _{c}^{2}} {(2\pi \tau )^{2}} \frac{2\tilde{\lambda }_{rr}(0) - 2\tilde{\lambda }_{rr}(\tau )} {\tilde{\lambda }_{rr}(0)} }$$

(13A.3)

exists and is positive, the solution to (13A.1) can be determined. It is apparent that L’Hôpital’s Rule should be applied to determine the limit in (13A.3). After substituting $\tilde{\lambda }_{rr}(\tau )$ from (13.34) and applying L’Hôpital’s Rule four times, the limit is

$$\displaystyle\begin{array}{rcl} \zeta & =& \frac{\lambda _{c}^{2}\,\left (B_{w}^{4}\,\mathit{N}_{\mathit{o}}^{2}\,\pi ^{2} + 3\,B_{w}\,K\,\mathit{N}_{\mathit{o}}\,(2\pi f_{m})^{2}\,b_{0} + 2\,B_{w}^{3}\,K\,\mathit{N}_{\mathit{o}}\,\pi ^{2}\,b_{0} + 2\,B_{w}^{3}\,\mathit{N}_{\mathit{o}}\,\pi ^{2}\,a(0)\right )} {6\,\pi ^{2}\,\left (B_{w}\,\mathit{N}_{\mathit{o}} + 2\,a(0)\right )\,\left (B_{w}\,\mathit{N}_{\mathit{o}} + 4\,K\,b_{0} + 2\,a(0)\right )} \\ & & +\frac{\lambda _{c}^{2}\,\left (6\,K\,(2\pi f_{m})^{2}\,b_{0}\,a(0) + 3\,B_{w}\,K\,\mathit{N}_{\mathit{o}}\,(2\pi f_{m})^{2}\,b_{0}\,\cos (2\,\theta _{0})\right )} {6\,\pi ^{2}\,\left (B_{w}\,\mathit{N}_{\mathit{o}} + 2\,a(0)\right )\,\left (B_{w}\,\mathit{N}_{\mathit{o}} + 4\,K\,b_{0} + 2\,a(0)\right )} \\ & & + \frac{\lambda _{c}^{2}\,\left (6\,K\,(2\pi f_{m})^{2}\,b_{0}\,a(0)\,\cos (2\,\theta _{0})\right )} {6\,\pi ^{2}\,\left (B_{w}\,\mathit{N}_{\mathit{o}} + 2\,a(0)\right )\,\left (B_{w}\,\mathit{N}_{\mathit{o}} + 4\,K\,b_{0} + 2\,a(0)\right )} \\ & & +{\lambda _{c}^{2}\,\left (-12\,a'(0)^{2} - 12\,c'(0)^{2} - 6\,B_{w}\,\mathit{N}_{\mathit{o}}\,a''(0) - 12\,K\,b_{0}\,a''(0)\right ) \over 6\,\pi ^{2}\,\left (B_{w}\,\mathit{N}_{\mathit{o}} + 2\,a(0)\right )\,\left (B_{w}\,\mathit{N}_{\mathit{o}} + 4\,K\,b_{0} + 2\,a(0)\right )} \\ & & +{ \lambda _{c}^{2}\,\left (-12\,a(0)\,a''(0) - 12\,c(0)\,c''(0)\right ) \over 6\,\pi ^{2}\,\left (B_{w}\,\mathit{N}_{\mathit{o}} + 2\,a(0)\right )\,\left (B_{w}\,\mathit{N}_{\mathit{o}} + 4\,K\,b_{0} + 2\,a(0)\right )}, {}\end{array}$$

(13A.4)

where a(τ) and c(τ) are given by (13.35) and (13.36), respectively, and x′(0) denotes the derivative of x(t) evaluated at t = 0. Consequently, a(0) = b ₀, a′(0) = c(0) = 0, and

$$\displaystyle\begin{array}{rcl} a''(0)& =& b_{0}(2\pi f_{m})^{2}\int _{ 0}^{2\pi }\hat{p}(\theta )\cos ^{2}(\theta )\mathrm{d}\theta \\ c'(0)& =& b_{0}2\pi f_{m}\int _{0}^{2\pi }\hat{p}(\theta )\cos (\theta )\mathrm{d}\theta.{}\end{array}$$

(13A.5)

Using these, and the identity cos²(θ) = (1 + cos(2θ))∕2, it can be shown that (13A.4) is positive for all θ for the scattering distributions considered in Sect. 13.4.3.1. Consequently, applying the theorem in (13A.2), the limit of the numerator of (13A.1) is the square root of (13A.4), which if desired can be expressed in terms of the signal-to-noise ratio γ _S using

$$\displaystyle{ b_{0} = \frac{\gamma _{S}N_{o}B_{w}} {2(K + 1)} }$$

(13A.6)

from (13.53) with K = s ²∕2b ₀. The denominator of (13A.1), which is also (13.43), is obtained by assuming isotropic scattering and no noise, so that a(0) = b ₀, a′(0) = c(0) = c′(0) = c″(0) = 0, a″(0) = 2b ₀(π f _m )², and N _o  = 0 in (13A.4). After taking the square root, the result is

$$\displaystyle{ \lim _{\tau \rightarrow 0} \frac{\lambda _{c}} {2\pi \tau }\sqrt{\frac{2\lambda _{rr } (0) - 2\lambda _{rr } (\tau )} {\lambda _{rr}(0)}} = v\sqrt{\frac{\left (1 + 2\,K + K\,\cos (2\,\theta _{0 } ) \right ) } {\left (1 + 2\,K\right )}}. }$$

(13A.7)

Problems

13.1. Suppose that a MS is traveling along a straight line from BS₁ to BS₂, as shown in Fig. 13.35. The BSs are separated by distance D, and the MS is at distance r from BS₁ and distance D − r from BS₂. Ignore the effects of fading and assume that the signals from the two BSs experience independent log-normal shadowing. The received signal power (in decibels) at the MS from each BS is given by (1.4).

Fig. 13.35

MS traversing from BS₀ to BS₁ along a handoff route

• A handoff from BS₁ to BS₂, or vice versa, can never occur if | Ω _{1 (dB)} −Ω _{2 (dB)} | < H but may or may not occur otherwise.

• A handoff from BS₁ to BS₂ will occur if the MS is currently assigned to BS₁ and Ω _{2 (dB)} ≥ Ω _{1 (dB)} + H.

• (a) Find an expression for the probability that a handoff can never occur from BS₁ to BS₂, or vice versa.

• (b) Given that the MS is currently assigned to BS₁ what is the probability that a handoff will occur from BS₁ to BS₂.

13.2. A freeway with a speed limit of 120 km/h passes through a metropolitan area. If the average call duration is 120 s:

• (a) What will be the average number of handoffs in a cellular system that uses omnidirectional cells having a 10 km radius.

• (b) Repeat part (a) for a cellular system that uses 120^∘ sectored cells having a 1 km radius.

13.3. A MS is moving with speed 100 km/h along a straight line between two base stations, BS₁ and BS₂. For simplicity ignore envelope fading and shadowing, and consider only the path loss. The received power (in dBm) follows the characteristic

$$\displaystyle{\mu _{\varOmega _{p\ \mathrm{(dBm)}}}(d_{i}) =\mu _{\varOmega _{p\ \mathrm{(dBm)}}}(d_{o}) - 10\beta \log _{10}(d_{i}/d_{o})\ \ (\mathrm{dBm}),}$$

where d _i is distance from BS _i in meters. Assume μ _o  = 0 dBm at d _o  = 1 m, and let the path loss exponent be β = 3. 0.

Assume that the minimum usable signal quality at the receiver (at either link end) is μ _min = −88 dBm. The mobile station is connected to BS₁ and signal level at/from BS₁ is measured. The measured signal level is compared to a threshold μ _HO; if it drops below the threshold a handoff is initiated. Once the handoff is initiated it takes 0.5 s to complete.

• (a) Determine the minimum margin Δ = μ _HO −μ _min so that calls are not lost due to weak signal strength during a handoff.

• (b) What is the maximum allowable distance between BS₁ and BS₂?

• (c) Describe the effects of the margin on the link quality performance and capacity of a cellular system.

13.4. Derive Eq. (13.19).

13.5. Derive Eq. (13.21).

13.6. Derive Eq. (13.34).

13.7. Derive Eq. (13.52).

13.8. Consider a communication link operating over a channel with propagation path loss exponent β = 3. 5 and a shadow standard deviation σ _Ω  = 8 dB.

• (a) Consider the case of two adjacent cells. A mobile station is transmitting at its maximum power and is located exactly on the cell boundary between the two base stations. In the absence of shadowing, the received power level would be equal to the receiver sensitivity, S _RX, i.e., the mobile station is located at distance d _max from each base station.

  Now assume that shadowing is present and a soft handoff algorithm is used, such that the least attenuation link is always selected. The shadows experienced on the two possible links are independent. If an outage probability of 10% is desired for the given mobile station location (averaged over a large ensemble of realizations), what is the required margin (M _shad − G _HO), where M _shad is the required shadow margin for a single isolated cell and G _HO is the soft handoff gain?

• (b) What is the value of G _HO?

• (c) Repeat parts (a) and (b) assuming that the mobile is located on the boundaries of and equidistant from three base stations, i.e., the mobile station is located at distance d _max from three base stations.