Channel Environments

The simulation is done with AWGN and SUI-3 channels with mobile speed being 60 km/hr.

More detailed channel environments are described in the following, which are taken from

Table 3.1: System Parameters Used in Our Study

Parameter Value

System Channel Bandwidth (MHz) 10 Sampling Frequency (MHz) 11.2

FFT Size 1024

Subcarrier Spacing (kHz) 10.94 Useful Symbol Time (µsec) 91.4

Guard Time (µsec) 11.4

OFDMA Symbol Time (µsec) 102.9 G (Ratio of CP Time to “Useful” Time) 1/8

n (Sampling Factor) 28/25

[10] and [11].

Typical models of the wireless communication channel include additive noise and mul-tipath fading. For channel simulation, noise and mulmul-tipath fading are described as random processes, so they can be algorithmically generated as well as mathematically analyzed.

Gaussian Noise

The simplest kind of channel is AWGN channel, where the received signal is only subject to added noise. A major source of this noise is the thermal noise in the amplifiers which may be modeled as Gaussian with zero mean and constant variance. In computer simulations, random number generators may be used to generate Gaussian noise of given power to obtain a particular SNR.

Slow Fading Channel

In slow fading, multipath propagation may exist, but the channel coefficients do not change significantly over a relatively long transmission period. The channel impulse response over

a short time period can be modeled as

h(τ ) =

N −1X

i=0

αie^jθiδ(τ − τi) (3.41)

where N is the number of multipaths, α_i and τ_i are respectively the amplitude and the delay of the ith multipath, and θ_i represents the phase shift associated with path i. These parameters are time-invariant in a short enough time period.

Fast Fading Channel

With sufficiently fast motion of either the transmitter or the receiver, the coefficient of each propagation path becomes time varying. The equivalent baseband channel impulse response can then be better modeled as

h(τ, t) =

N −1X

i=0

α_i(t)e^jθi(t)δ(τ − τ_i). (3.42)

Note that α_i and θ_i are now functions of time. But τ_i is still time-invariant, because the path delays usually change at a much slower rate than the path coefficients. The channel coefficients are often modeled as complex independent stochastic processes. If there is no LOS path between the transmitter and the receiver, then each path may be made of the superposition of many reflected paths, yielding a Rayleigh fading characteristic. A commonly used method to simulate Rayleigh fading is Jakes’ fading model, which is a deterministic method for simulating time-correlated Rayleigh fading waveforms. An improvement to Jakes’

model is proposed in [12].

Power-Delay Profile Model

For simplicity in analysis and simulation, the delay τ_i in the above two models can be discretized to have a certain easily manageable granularity. This results in a tapped-delay-line model for the channel impulse response, where the spacing between any two taps is

Table 3.2: SUI-3 Channel Model

Relative delay (µs and sample number) Average power

Tap (µs) (4×oversampling) (normal) (dB) (normal scale) (normalized)

1 0 0 0 0 1 0.7061

2 0.4 17 4 -5 0.3162 0.2233

3 0.9 40 10 -10 0.1 0.0706

an integer multiple of the chosen granularity. For convenience, one may excise the initial delay and make τ0 = 0. Often, it is convenient to normalize the path powers relative to the strongest path. And, often, the first path has the highest average power.

The channel model used here is a modification of the Stanford University Interim (SUI) channel models proposed in [13]. A set of 6 typical channels was selected for the three most common terrain categories that are typical of the continental United States. The scenario of SUI channels are:

• Cell size: 7 km.

• Base station antenna height: 30 m.

• Receiver antenna height: 6 m.

• Base station antenna beamwidth: 120^◦.

• Receiver antenna beamwidth: omnidirectional (360^◦) and 30^◦.

• Vertical polarization only.

We list the SUI-3 channel model in Tables 3.2, which is the one used in our simulation.

3.3.3 Missed Detection and False Alarm Penalty of Ranging Sig-nal Detection

Missed detection means that a ranging code has been transmitted by a certain MS but the BS does not detect it. In this case, the BS will send a RNG-RSP with continue status but without corrections [1], [2]. Then the MS will need to retransmit a ranging signal. It will do some random backoff and adjust the power level of ranging signal up to PT x IR M AX. The MS will send ranging signal at next ranging opportunity, that is, at the next UL-subframe which is 5 ms later according to our simulation parameters.

The false alarm means that the BS detects a ranging code that has not been transmitted by any MS. In this case, the BS will redundantly estimate wrong transmission parameters (time, power and possibly frequency offset). Then the BS will broadcast a RNG-RSP with corrections, but this message is redundant and will not be used by any MS.

We compare the effect of missed detection and false alarm. The effect of missed detection is retransmission of ranging signal. The main penalties are retransmission efforts for the MS and more latency to complete the ranging process because next ranging opportunity will be 5 ms later. On the other hand, the effect of false alarm is needless parameter estimation and RNG-RSP transmission. The main penalties are redundant efforts for the BS and the wasted downlink bandwidth for RNG-RSP transmission.

The rates of missed detection and false alarm are affected by the choice of the detection threshold (h4). Since it is difficult to decide which one costs more, we only set the cost of them to be a certain ratio. We calculate the weighted costs and use them to help us determining the detection threshold. In the following, we provide some examples of weighted costs in the one ranging user case under single-path Rayleigh fading channel. Note that the weighted cost is obtained by missed detection rate × r_md+ f alse alarm rate × r_{f a}, where we set the ratio of the cost of missed detection to that of false alarm as r_md : r_{f a}. Figures 3.6 to 3.10

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

Weighted cost with cost of md:fa=3:1, single user single−path fading, method−2

Figure 3.6: Weighted cost for r_md: r_{f a} = 3 : 1.

shows the results for rmd : rf a being 3:1, 2:1, 1:1, 1:2 and 1:3, respectively. We can choose the best threshold as the one that leads to a minimum weighted cost. Note that the weighted costs do not have large sensitivity to h₄.