Channel Sounding Measurement Analysis Tool · The goal of the project is to implement a channel sounding measurement analysis tool for the wireless test bed utilized by the Communications

Digital Communications Project Work Channel Sounding

Measurement Analysis Tool

Performed by: Ibrahim Asghar Shah

Matriculation Number: 28247777 Supervised by: Thomas Edlich Submitted on

15 December 2009 At

Communications Laboratory, FB 16 (Elektrotechnik/Informatik), Universität

Kassel

2 Channel Sounding Measurement Analysis Tool

3 0BDeclaration

Declaration

With this I declare that the present Project Report was made by myself. Prohibited means were not used and only the aids specified in the Project Report were applied. All parts which are taken over word-to-word or analogous from literature and other publications are quoted and identified.

Kassel, 15-12-2009

Ibrahim Asghar Shah


Abstract

The goal of the project is to implement a channel sounding measurement analysis tool for the wireless test bed utilized by the Communications Laboratory (ComLab) at the University of Kassel.

The analysis tool is implemented based on the mobile radio channel theory by Bello [1], which is further explored by Molisch [2] and Kattenbach [3].

The tool gives the user the option to plot either of the deterministic system functions, stochastic system correlation functions or special correlation functions & condensed parameters corresponding to [1], [2] and [3].

Since the wireless test bed can be configured in up to a 4X4 MIMO mode, the user is also allowed to select which of the up to 16 MIMO channels he intends to characterize. Noisy channel components can be reduced by applying averaging filter methods with variable filter length. Furthermore, to avoid errors affecting the Fast Fourier Transform (FFT) due to non-periodic signals, an option to window the data is also given to the user.

Since this is the first version of the tool for the wireless test bed, efforts have been made to execute an implementation that can be easily modified and extended for future versions. Some areas where future work can be done have also been identified.

5 2BAbbreviations Used

Abbreviations Used

ACF Auto Correlation Function DDSF Delay Doppler Spread Function DpCSD Doppler Cross Spectral Density DSD Doppler Spectral Density DyCSD Delay Cross Spectral Density FCF Frequency Correlation Function FFT Fast Fourier Transform IDSF Input Delay Spread Function MIMO Multiple Input Multiple Output ODSF Output Doppler Spread Function OFDM Orthogonal Frequency Division Multiplexing PDP Power Delay Profile RX Receiver SF Scattering Function TCF Time Correlation Function TDMA Time Division Multiple Access TFCF Time Frequency Correlation Function TVTF Time Variant Transfer Function TX Transmitter US Uncorrelated Scattering WSS Wide Sense Stationary WSSUS Wide Sense Stationary Uncorrelated Scattering


Table of Contents

Declaration .................................................................................................................................................. 3 Abstract ....................................................................................................................................................... 4 Abbreviations Used ..................................................................................................................................... 5 Table of Contents ........................................................................................................................................ 6 Chapter 1 ..................................................................................................................................................... 7 System-Theoretic Description of the Mobile Radio Channel ...................................................................... 7

1.1 Characterization of Deterministic Linear Time-Variant Systems ...................................................... 7 1.2 Stochastic System Functions ............................................................................................................. 8 1.3 The WSSUS Model ............................................................................................................................. 8 1.4 Special Correlation Functions and Condensed Parameters .............................................................. 9

1.4.1 Special Correlation Functions .................................................................................................... 9 1.4.2 Moments of the PDP ............................................................................................................... 10 1.4.3 Moments of the DSD ............................................................................................................... 10 1.4.4 Coherence Bandwidth and Coherence Time ........................................................................... 11

Chapter 2 ................................................................................................................................................... 12 A Brief Guide to the Keithley Channel Sounder ........................................................................................ 12

2.1 Introduction .................................................................................................................................... 12 2.2 Channel Sounding Algorithm .......................................................................................................... 13 2.3 Configuration File ............................................................................................................................ 13 2.4 Header Format ................................................................................................................................ 13

Chapter 3 ................................................................................................................................................... 14 Implementation of the Channel Sounding Measurement Analysis Tool ................................................... 14

Introduction to the Analysis Tool .......................................................................................................... 14 Insight into the Tool .............................................................................................................................. 15 3.1 System Function Plots [Amplitude and Phase Response] ............................................................... 15 3.2 System Correlation Functions ......................................................................................................... 18

3.2.1 Delay Cross Spectral Density (DyCSD) ..................................................................................... 18 3.2.2 Time Frequency Correlation Function (TFCF) .......................................................................... 19 3.2.3 Scattering Function (SF) ........................................................................................................... 19 3.2.4 Doppler Cross Spectral Density (DpCSD) ................................................................................. 19

3.3 Special Correlation Functions and Condensed Parameters ............................................................ 19 3.3.1 Power Delay Profile [mean delay and delay spread] ............................................................... 20 3.3.2 Frequency Correlation Function [coherence bandwidth] ....................................................... 20 3.3.3 Time Correlation Function [coherence time] .......................................................................... 21 3.3.4 Doppler Spectral Density [mean Doppler and Doppler spread] .............................................. 21

3.4 Channel Selection ............................................................................................................................ 21 3.5 Filtering and Windowing of the System Functions ......................................................................... 22

3.5.1 Filtering .................................................................................................................................... 22 3.5.2 Windowing ............................................................................................................................... 22

Chapter 4 ................................................................................................................................................... 25 Future Work .............................................................................................................................................. 25 References ................................................................................................................................................. 26 List of Figures............................................................................................................................................. 27

7 Chapter 1

Chapter 1 System-Theoretic Description of the Mobile Radio Channel

1.1 Characterization of Deterministic Linear Time-Variant Systems A mobile radio channel, also called a wireless channel, can be described by the theory given by Bello [1], which is further explored by Molisch [2] and Kattenbach [3].

As stated in [2], if the transmitter, receiver and the interfering objects are all static, i.e., not moving, the channel is said to be time-invariant. For such cases, the theory of linear time invariant (LTI) systems is applied and the channel is described by the time-invariant impulse response h(τ) where τ is the delay.

In general, however, the physical characteristics of the wireless medium are constantly changing due to which the channel is time-variant. Hence, the theory of linear time variant (LTV) systems is used. The channel is described by the complex response |ℎ(𝑡𝑡, 𝜏𝜏)| of the channel at observation time t to a delta-shaped excitation τ seconds in the past. Following the naming convention in [1], the time-variant impulse response h(t,τ) is called the Input Delay Spread Function (IDSF).

Applying a Fourier transform to the IDSF with respect to the variable τ, we get the Time Variant Transfer Function (TVTF) T(f,t):

𝑻𝑻(𝒇𝒇, 𝒕𝒕) = � 𝒉𝒉(𝒕𝒕, 𝝉𝝉) 𝒆𝒆−𝒋𝒋𝒋𝒋𝒋𝒋𝒇𝒇𝝉𝝉𝒅𝒅𝝉𝝉∞

−∞

where f is the frequency.

A Fourier transformation of the IDSF with respect to the variable t leads to the Delay Doppler Spread Function (DDSF) U(τ,v):

𝑼𝑼(𝝉𝝉,𝒗𝒗) = � 𝒉𝒉(𝒕𝒕, 𝝉𝝉) 𝒆𝒆−𝒋𝒋𝒋𝒋𝒋𝒋𝒇𝒇𝒕𝒕𝒅𝒅𝒕𝒕∞

−∞

where v is the Doppler shift.

Yet another Fourier transformation pair exists. Transforming the TVTF with respect to the variable t leads to the Output Doppler Spread Function (ODSF) H(f,v):

𝑯𝑯(𝒇𝒇,𝒗𝒗) = � 𝑻𝑻(𝒇𝒇, 𝒕𝒕) 𝒆𝒆−𝒋𝒋𝒋𝒋𝒋𝒋𝒗𝒗𝒕𝒕𝒅𝒅𝒕𝒕∞

−∞

According to [1], the IDSF, TVTF, DDSF and the ODSF are called system functions and are a means of describing a deterministic time-variant channel.

A summary of the interrelation between system functions is shown in Fig.1:


Figure 1: Interrelation between system functions

1.2 Stochastic System Functions Since there are a large number of propagation environments, the channel is randomly time-variant, and so the system functions become stochastic processes. In order to describe such stochastic processes completely, a multidimensional probability density function of the impulse response is required as in [1], [2] and [3] which is much too complicated in practice. Instead, we resort to a second order description – namely, the Auto Correlation Function (ACF) as in [3]:

𝑹𝑹𝒉𝒉(𝒕𝒕, 𝒕𝒕′ ; 𝝉𝝉, 𝝉𝝉′) = 𝑬𝑬{𝒉𝒉∗(𝒕𝒕, 𝝉𝝉)𝒉𝒉(𝒕𝒕′ , 𝝉𝝉′)}

where t’ and τ’ are variables associated with the autocorrelation of time and delay.

The other three correlation functions are [3]:

𝑹𝑹𝑻𝑻(𝒇𝒇,𝒇𝒇′ ; 𝒕𝒕, 𝒕𝒕′) = 𝑬𝑬{𝑻𝑻∗(𝒇𝒇, 𝒕𝒕)𝑻𝑻(𝒇𝒇′, 𝒕𝒕′)}

𝑹𝑹𝑼𝑼(𝝉𝝉, 𝝉𝝉′ ;𝒗𝒗,𝒗𝒗′) = 𝑬𝑬{𝑼𝑼∗(𝝉𝝉,𝒗𝒗)𝑼𝑼(𝝉𝝉′ ,𝒗𝒗′)}

𝑹𝑹𝑯𝑯(𝒇𝒇,𝒇𝒇′ ,𝒗𝒗,𝒗𝒗′) = 𝑬𝑬{𝑯𝑯∗(𝒇𝒇,𝒗𝒗)𝑯𝑯(𝒇𝒇′,𝒗𝒗′)}

As in the case of the deterministic system functions, the correlation functions are also related to each other by 2-D Fourier transforms as in [3]. This is because the ACF depends on four variables since the stochastic process is two-dimensional.

1.3 The WSSUS Model In context with mobile radio channels, assumptions about the physical properties of the channel are usually made to simplify its description. The most common is the Wide Sense Stationary Uncorrelated Scattering (WSSUS) [2]. Simply stated, the WSS part of the assumption defines that contributions with different values of the Doppler shift v are uncorrelated while the US part states that contributions with different values of the delay τ are uncorrelated [2].

With this assumption, US means that RT depends only on the frequency difference, while WSS means that RT depends only on the time difference. Hence, RT takes the form as in [2] and [3]:

𝑹𝑹𝑻𝑻(𝒇𝒇,𝒇𝒇′ ; 𝒕𝒕, 𝒕𝒕′) = 𝑹𝑹𝑻𝑻(𝒇𝒇,𝒇𝒇 + ∆𝒇𝒇; 𝒕𝒕, 𝒕𝒕 + ∆𝒕𝒕) = 𝑹𝑹𝑻𝑻(∆𝒇𝒇,∆𝒕𝒕) = 𝑬𝑬{𝑻𝑻∗(𝒇𝒇, 𝒕𝒕)𝑻𝑻(𝒇𝒇 + ∆𝒇𝒇, 𝒕𝒕 + ∆𝒕𝒕)}

9 System-Theoretic Description of the Mobile Radio Channel

Similarly, with the WSSUS assumption, the other correlation functions assume the form as in [2] and [3]:

𝑹𝑹𝒉𝒉(𝒕𝒕, 𝒕𝒕′ ; 𝝉𝝉, 𝝉𝝉′) = 𝑹𝑹𝒉𝒉(𝒕𝒕, 𝒕𝒕 + ∆𝒕𝒕; 𝝉𝝉, 𝝉𝝉′) = 𝑷𝑷𝒉𝒉(∆𝒕𝒕, 𝝉𝝉)𝜹𝜹(𝝉𝝉 − 𝝉𝝉′)

𝑹𝑹𝑼𝑼(𝝉𝝉, 𝝉𝝉′ ;𝒗𝒗,𝒗𝒗′) = 𝑷𝑷𝑼𝑼(𝝉𝝉,𝒗𝒗)𝜹𝜹(𝒗𝒗 − 𝒗𝒗′)𝜹𝜹(𝝉𝝉 − 𝝉𝝉′)

𝑹𝑹𝑯𝑯(𝒇𝒇,𝒇𝒇 + ∆𝒇𝒇;𝒗𝒗,𝒗𝒗′) = 𝑷𝑷𝑯𝑯(∆𝒇𝒇,𝒗𝒗)𝜹𝜹(𝒗𝒗 − 𝒗𝒗′)

where the delta functions 𝛿𝛿�𝑣𝑣 − 𝑣𝑣 ′� and 𝛿𝛿�𝜏𝜏 − 𝜏𝜏 ′� show that different values of the Doppler and delay respectively are uncorrelated.

As can be seen, the P-functions [2] arising from the WSSUS assumption are sufficient to determine the correlation functions [3]. Although they are power spectral densities in the strict sense, they are still referred to as being correlation functions of the WSSUS channel. The following naming convention corresponding to [3] is followed for the p-functions:

𝑷𝑷𝒉𝒉(∆𝒕𝒕, 𝝉𝝉) as delay cross power spectral density (DyCSD) 𝑹𝑹𝑻𝑻(∆𝒇𝒇,∆𝒕𝒕) as time frequency correlation function (TFCF) 𝑷𝑷𝑼𝑼(𝝉𝝉,𝒗𝒗) as scattering function (SF) 𝑷𝑷𝑯𝑯(∆𝒇𝒇,𝒗𝒗) as Doppler cross power spectral density (DpCSD)

The correlation functions are related to each other by Fourier transforms in a manner as shown in Fig.2:

Figure 2: Relationship between the correlation functions by the Fourier transform

Another important observation is that the correlation functions based on the WSSUS are simplified, since they are now functions of two variables instead of four.

1.4 Special Correlation Functions and Condensed Parameters

1.4.1 Special Correlation Functions The deterministic system functions and the WSSUS-assumed stochastic correlation functions are functions of two variables, and thus, offer a complicated description of the channel. A function of a single variable, or better still, a single parameter would be the most suitable way of describing the channel.


Fortunately such representations are possible. One of them is the Power Delay Profile (PDP), which is the power spectral density in the delay domain. It is obtained as in [2]:

𝑷𝑷𝒉𝒉(𝝉𝝉) = � |𝒉𝒉(𝒕𝒕, 𝝉𝝉)|𝒋𝒋𝒅𝒅𝒕𝒕∞

−∞

Another is the Doppler Spectral Density (DSD) obtained as in [2]:

𝑷𝑷𝑯𝑯(𝒗𝒗) = � |𝑯𝑯(𝒗𝒗,𝒇𝒇)|𝒋𝒋𝒅𝒅𝒇𝒇∞

−∞

Two more functions are: the Frequency Correlation Function (FCF) that can be obtained from the TFCF by

setting Δt = 0 i.e., RT (Δf) = RT (Δf,0) as in [3]:

𝑹𝑹𝑻𝑻(∆𝒇𝒇) = 𝑬𝑬{𝑻𝑻∗(𝒇𝒇, 𝒕𝒕)𝑻𝑻(𝒇𝒇 + ∆𝒇𝒇, 𝒕𝒕)}

and the Temporal Correlation Function (TCF) RT (Δt) = RT (0,Δt) also as in [3]:

𝑹𝑹𝑻𝑻(∆𝒕𝒕) = 𝑬𝑬{𝑻𝑻∗(𝒇𝒇, 𝒕𝒕)𝑻𝑻(𝒇𝒇, 𝒕𝒕 + ∆𝒕𝒕)}

1.4.2 Moments of the PDP Based on the PDP, normalized moments are calculated to give a description of the channel using a single parameter. The zeroth-order moment [2] is first calculated.

𝑷𝑷𝒎𝒎 = � 𝑷𝑷𝒉𝒉(𝝉𝝉)𝒅𝒅𝝉𝝉∞

−∞

The normalized first-order moment is computed as follows to give the mean delay [2]:

𝑻𝑻𝒎𝒎 = ∫ 𝑷𝑷𝒉𝒉(𝝉𝝉)𝝉𝝉𝒅𝒅𝝉𝝉∞−∞

𝑷𝑷𝒎𝒎

The rms delay spread is basically the normalized second-order central moment and is defined by [3] as:

𝑺𝑺𝝉𝝉 = �∫ (𝝉𝝉 − 𝑻𝑻𝒎𝒎)𝒋𝒋𝑷𝑷𝒉𝒉(𝝉𝝉)𝒅𝒅𝝉𝝉∞−∞

𝑷𝑷𝒎𝒎

1.4.3 Moments of the DSD The moments of the DSD are calculated just like those for the PDP. The integrated power is:

𝑷𝑷𝑯𝑯𝒎𝒎 = � 𝑷𝑷𝑯𝑯(𝒗𝒗)𝒅𝒅𝒗𝒗∞

−∞

The normalized first-order moment, the mean Doppler shift, is:

11 System-Theoretic Description of the Mobile Radio Channel

𝒗𝒗𝒎𝒎 = ∫ 𝑷𝑷𝑯𝑯(𝒗𝒗)𝒗𝒗𝒅𝒅𝒗𝒗∞−∞

𝑷𝑷𝑯𝑯𝒎𝒎

The normalized second-order central moment is known as the rms Doppler spread and defined as [3]:

𝑺𝑺𝒗𝒗 = �∫ (𝒗𝒗 − 𝒗𝒗𝒎𝒎)𝒋𝒋𝑷𝑷𝑯𝑯(𝒗𝒗)𝒅𝒅𝒗𝒗∞−∞

𝑷𝑷𝑯𝑯𝒎𝒎

1.4.4 Coherence Bandwidth and Coherence Time The coherence bandwidth defines the window of frequencies over which the signal frequency components of the communication signal fade coherently or in a correlated manner. From [2], it is usually taken to be the 3-dB bandwidth of the frequency correlation function. The PDP and the FCF are related by the Fourier transform. Moreover, the rms delay spread Sτ is derived from the PDP while the coherence bandwidth Bcoh is derived from the FCF. Hence there exists a relationship between Sτ and Bcoh. Based on this insight, Bcoh is defined by [4] as:

𝑩𝑩𝒄𝒄𝒄𝒄𝒉𝒉 = 𝟏𝟏

𝒋𝒋𝒋𝒋𝑺𝑺𝝉𝝉

On the other hand, the coherence time is the measure of the duration over which the channel’s response is essentially invariant. Analogous to the coherence bandwidth, there exists a relationship between the rms Doppler spread Sv and the coherence time tcoh given by [4] as:

𝒕𝒕𝒄𝒄𝒄𝒄𝒉𝒉 = 𝟏𝟏

𝒋𝒋𝒋𝒋𝑺𝑺𝒗𝒗


Chapter 2 A Brief Guide to the Keithley Channel Sounder

2.1 Introduction The wireless test bed utilized by ComLab is provided by Keithley Instruments. It consists of a transmitter (TX) station and a receiver (RX) station where each station consists of [5]:

1-4 Keithley 2920 VSG(s) and 1-4 Keithley 2820 VSA(s) respectively 1 Keithley 2895 MIMO synchronization unit (provides a common 100 MHz sample

clock to all the VSGs and VSAs) 1 PRS10 Rubidium Frequency Reference (provides a stable frequency reference to

each station) 1 Ethernet Switch

The test bed can be configured in two ways [5]:

SISO configuration: with a maximum of 4 stations. Each station consists of a vector signal generator (VSG), vector signal analyzer (VSA), a synchronization unit and a frequency reference. The SISO configuration is shown in Fig.3 [5]:

Figure 3: The Wireless Test Bed in the SISO Configuration

MIMO configuration: a transmitter (TX) station consisting of a maximum of 4 VSGs and a receiver (RX) station consisting of up to 4 VSAs including the synchronization unit and frequency reference. This is shown in Fig.4 [5]:

Figure 4: The Wireless Test Bed in the MIMO Configuration

13 A Brief Guide to the Keithley Channel Sounder

2.2 Channel Sounding Algorithm The wireless test bed works on an Orthogonal Frequency Division Multiplexing – Time Division Multiple Access (OFDM-TDMA) scheme as explained in [5]. This means that each transmitter is allowed to transmit its OFDM signal only in the time slot that is allocated to it.

The following is an analysis of an exemplary sounding symbol that consists of 750 samples as given in the Keithley guide [5]:

An FFT size of 128 points with a sample rate of 50 Msample/s is used The DC component, the lower 13 and the upper 12 carriers are unused. This is done so as to

avoid problems at the band edges. Hence only 102 carriers (51 below and 51 above DC) are used resulting in an occupied bandwidth of 39.84 MHz

A 28 sample (560 ns) cyclic prefix, a 29 sample (580 ns) gutter a 1 sample post fix and a 1 sample prefix are used

The aforementioned breakdown totals 1 + 28 + 128 + 1 + 29 = 187 sample bursts for each transmitter, hence 748 samples for the 4 transmitters (the other two samples are also unused to make up 750 samples)

2.3 Configuration File The wireless test bed can be configured for making a measurement by editing the SounderGlobals.asv file (which can be remotely accessed via Ethernet).

Various parameters can be changed in the file, most important of which are: NumberDataPoints (the number of measurements) measInterval_s (the measurement interval in seconds) numberTXStations (the number of 2920 VSG TX stations to use) numberRXStations (the number of 2820 VSA RX stations to use) fftSize (the number of subcarriers in the OFDM sounding waveform)

2.4 Header Format The headers of the *.arb file (containing the sounding waveform) and *.bin file (containing the received waveform) are similar and their format is the following as in [5]:

The first 32-bits in the header are in the unsigned integer format and contain the number of samples. The sample rate is contained in the next 32-bits. The next 4 bytes are in the float format and contain the cal factor in dB. The final 4 bytes in the header are reserved and contain 0.0.


Chapter 3 Implementation of the Channel Sounding Measurement Analysis

Tool

Introduction to the Analysis Tool As mentioned earlier, the goal of the project is to implement a channel sounding measurement analysis tool for the wireless test bed utilized by ComLab at the University of Kassel. A glance of this tool can be seen in Fig.5:

Figure 5: A Glance of the Tool

As can be seen on the bottom half of the tool, the user is given the option to plot either of the system functions, system correlation functions or special correlation functions & condensed parameters corresponding to the mobile radio channel theory in [1], [2] and [3].

Since the wireless test bed is configured in a 4X4 MIMO mode, the user is also allowed to select which of the 16 MIMO channels he intends to characterize in the “Channel Selection” menu. Noisy channel components can be reduced by applying averaging filter methods with variable filter length. Furthermore, to avoid errors affecting the FFT due to non-periodic signals, an option to window the data is also given to the user. The filtering and windowing options are provided in the “Filtering/Windowing” menu.

A systematic description of how the correlation functions, special correlation functions and condensed parameters are obtained from the system functions is shown in Fig. 6:

15 Implementation of the Channel Sounding Measurement Analysis Tool

Figure 6: Systematic description of the calculation of all system functions, correlation functions special

correlation functions and condensed parameters

Insight into the Tool

3.1 System Function Plots [Amplitude and Phase Response] As explained in Chapter 1, to describe a deterministic linear time-variant channel, system functions are used corresponding to the mobile radio channel theory in [1], [2] and [3]. Accordingly, the tool has a section dedicated to these system functions. As can be seen in Fig. 7, the user can plot the amplitude and/or phase response corresponding to the four different system functions namely, Input Delay Spread Function (IDSF), Time Variant Transfer Function (TVTF), Delay Doppler Spread Function (DDSF) and Output Doppler Spread Function (ODSF).

Figure 7: System Functions Menu

The core system function which is used for the calculation of the rest of the system functions is the TVTF which is calculated using the transfunc.m function file as follows: the *.arb and *.bin files are read out using the te_read_arb_file and te_read_bin_file

functions the channel sounding algorithm (explained in Chapter 2) is applied to extract the input

and output data sequences


Fourier transform in the form of FFT is applied to each of these sequences the TVTF is then calculated

At the end of the calculation, the following parameters are saved in the parameters.mat file for later calculations: number of measurements, number of samples, sample rate, measurement interval and FFT point size.

The following code is an excerpt from the transfunc.m file, giving an overview of the calculation of the TVTF.

%************************************************************************** % Reading of the *.arb files containing the input channel sounding waveform %************************************************************************** [X1,samplerate, powerfactor] = te_read_arb_file('sounder1.arb'); %.... [X4,samplerate, powerfactor] = te_read_arb_file('sounder4.arb'); %************************************************************************** % Application of the Channel Sounding Algorithm specified by Keithley %************************************************************************** switch tx case 1 in = X1((((tx-1)*(prefix + FFT_points + postfix)) + presym + prefix + 1):(((tx-1)*(prefix + FFT_points + postfix)) + FFT_points + postfix)); %.... case 4 in = X4((((tx-1)*(prefix + FFT_points + postfix)) + presym + prefix + 1):(((tx-1)*(prefix + FFT_points + postfix)) + FFT_points + postfix)); otherwise disp ('Invalid'); end %************************************************************************** % Reading of the *.bin files containing the output signal waveform %************************************************************************** [Y1,gainconst1,sampleratekHz,nummeas] = te_read_bin_file('ias_091028_IQ1.bin'); %.... [Y4,gainconst4,sampleratekHz,nummeas] = te_read_bin_file('ias_091028_IQ4.bin'); %************************************************************************** % Application of the Channel Sounding Algorithm specified by Keithley %************************************************************************** switch rx case 1


out = Y1(((((rx-1)*(prefix + FFT_points + postfix)) + presym + prefix + 1):(((rx-1)*(prefix + FFT_points + postfix)) + FFT_points + postfix)),:); %.... case 4 out = Y4(((((rx-1)*(prefix + FFT_points + postfix)) + presym + prefix + 1):(((rx-1)*(prefix + FFT_points + postfix)) + FFT_points + postfix)),:); otherwise disp ('Invalid'); end %************************************************************************** % Calculation of the Transfer Function for system function calculation %************************************************************************** % Calculating the Fourier transform of the input sequence f_in = fft(in); % extracting only the used samples (based on the Keithley Guide) f_in = [f_in(2:((FFT_points/2) - lower + DC)) f_in(((FFT_points/2)+ upper + DC + 1):FFT_points)]; numsamp = length(f_in); % Calculating the Fourier transform of the output sequence f_out = fft(out); f_out = f_out.'; % extracting only the used samples (based on the Keithley Guide) f_out = [f_out(:,(2:((FFT_points/2) - lower + DC))) f_out(:,(((FFT_points/2)+ upper + DC + 1):FFT_points))]; Tft = zeros(nummeas,numsamp); % Division of the output Fourier transform with input Fourier transform to % get transfer function Tft = f_out*diag(1./f_in); Tft = Tft.'; %************************************************************************** % Calculation of the Transfer Function for corresponding correlation funcs is similar to that done above %.... nTft = nTft.'; %************************************************************************** % Save parameters for use in later calculations save parameters nummeas numsamp samplerate measinterval FFT_points % Save fftshifted transfer function for use in calculation of corresponding % correlation functions save nTft nTft

The rest of the three system functions that were explained in Section 1.1 are calculated using the sysfunc.m function file. Here, the Fourier transform is applied to the TVTF to get the other system functions. This is summarized in Fig.8:


Figure 8: Calculation of other system functions from the TVTF

3.2 System Correlation Functions Since there are a large number of propagation environments, the channel is randomly time-variant, and so the system functions become stochastic processes. As was seen in Chapter 1, a stochastic process, with the WSSUS assumption, can be described by P-functions [2] that are sufficient to determine the correlation functions [3]. The analysis tool gives the user the facility to describe such channels in the “System Correlation Functions” section, Fig.9, described in detail below.

Figure 9: Correlation Functions Menu

3.2.1 Delay Cross Spectral Density (DyCSD) The Delay Cross Spectral Density (DyCSD) corresponds to the IDSD calculated by [3]:

𝑷𝑷𝒉𝒉(∆𝒕𝒕, 𝝉𝝉) = 𝑹𝑹𝒉𝒉(𝒕𝒕, 𝒕𝒕 + ∆𝒕𝒕; 𝝉𝝉, 𝝉𝝉′) = 𝑬𝑬{𝒉𝒉∗(𝒕𝒕, 𝝉𝝉)𝒉𝒉(𝒕𝒕 + ∆𝒕𝒕, 𝝉𝝉′)}

The computation is done using the PhDyCSD.m function file. The parameters saved during the calculation of the transfer function are loaded along with the system function IDSF. The correlation function is then calculated using the acorr.m file defined by [6] and based on the following algorithm:

Take the conjugate of the data set in reverse order (last element first, first element last)

Take the FFT of both the data set and its conjugate Multiply the FFT of the data set with the FFT of the conjugate Inverse transform the product.


The following code is an excerpt from the PhDyCSD.m function file:

load parameters % load the Input Delay Spread Function IDSF load systemfunctions htE htE = ifftshift(htE,2); % Calculation of the Delay Cross Spectral Density Phtau = htE; Phtau = [Phtau;zeros(nummeas-1,numsamp)]; for i = 1:nummeas Phtau(i,:) = (acorr(Phtau(i,numsamp))).'; end

3.2.2 Time Frequency Correlation Function (TFCF) This correlation function [3]:

𝑹𝑹𝑻𝑻(𝒇𝒇,𝒇𝒇′ ; 𝒕𝒕, 𝒕𝒕′) = 𝑹𝑹𝑻𝑻(𝒇𝒇,𝒇𝒇 + ∆𝒇𝒇; 𝒕𝒕, 𝒕𝒕 + ∆𝒕𝒕) = 𝑹𝑹𝑻𝑻(∆𝒇𝒇,∆𝒕𝒕) = 𝑬𝑬{𝑻𝑻∗(𝒇𝒇, 𝒕𝒕)𝑻𝑻(𝒇𝒇 + ∆𝒇𝒇, 𝒕𝒕 + ∆𝒕𝒕)}

is calculated using the RTTFCF.m function file by taking the 2-D autocorrelation function of the TVTF by using the acorr2 file also defined by [6].

3.2.3 Scattering Function (SF) The Scattering Function is calculated from the DDSF [3] in the PUSF.m function file as:

𝑷𝑷𝑼𝑼(𝝉𝝉,𝒗𝒗) = |𝑼𝑼(𝝉𝝉,𝒗𝒗)|𝒋𝒋

3.2.4 Doppler Cross Spectral Density (DpCSD) The DpCSD is calculated using the PHDpCSD.m function file by taking the Fourier Transform of the TFCF as in [3]:

𝑷𝑷𝑯𝑯 (∆𝒇𝒇,𝒗𝒗) = � 𝑹𝑹𝑻𝑻(∆𝒇𝒇,∆𝒕𝒕)𝒆𝒆−𝒋𝒋𝒋𝒋𝒋𝒋𝒗𝒗∆𝒕𝒕𝒅𝒅∆𝒕𝒕∞

−∞

3.3 Special Correlation Functions and Condensed Parameters As was seen in Section 1.4, a function of a single variable, or better still, a single parameter are the most suitable representation for the description of the channel. Accordingly, the tool integrates a section for these simple descriptions as shown in Fig. 10:

Figure 10: Special Correlation Functions & Condensed Parameters section


3.3.1 Power Delay Profile [mean delay and delay spread] The Power Delay Profile (PDP) is calculated from the IDSF in the PDP.m function file by [2]:

𝑷𝑷𝒉𝒉(𝝉𝝉) = � |𝒉𝒉(𝒕𝒕, 𝝉𝝉)|𝒋𝒋𝒅𝒅𝒕𝒕∞

−∞

The corresponding condensed parameters, first of which is the mean delay is calculated by [2]:

𝑻𝑻𝒎𝒎 = ∫ 𝑷𝑷𝒉𝒉(𝝉𝝉)𝝉𝝉𝒅𝒅𝝉𝝉∞−∞

𝑷𝑷𝒎𝒎

where

𝑷𝑷𝒎𝒎 = � 𝑷𝑷𝒉𝒉(𝝉𝝉)𝒅𝒅𝝉𝝉∞

−∞

And the rms delay spread is defined by [3]:

𝑺𝑺𝝉𝝉 = �∫ (𝝉𝝉 − 𝑻𝑻𝒎𝒎)𝒋𝒋𝑷𝑷𝒉𝒉(𝝉𝝉)𝒅𝒅𝝉𝝉∞−∞

𝑷𝑷𝒎𝒎

The following code gives an overview of how it is done:

load parameters % load the Input Delay Spread Function load systemfunctions htE htE = ifftshift(abs(htE),2); % Calculation of the Power Delay Profile nPDP = trapz((1:nummeas)',htE.^2); % trapz is used to numerically integrate the function %******************************************* % Calculation of Condensed Parameters %******************************************* Pm = trapz(1:numsamp,nPDP); % Mean Delay Tm = (trapz(1:numsamp,(1:numsamp).*nPDP))/Pm; Stauz = trapz(1:numsamp,(((1:numsamp)-Tm).^2).*nPDP); % rms Delay Spread Stau = sqrt (Stauz/Pm);

3.3.2 Frequency Correlation Function [coherence bandwidth] The Frequency Correlation Function (FCF) is computed by taking the autocorrelation function of the TVTF as [3]:

𝑹𝑹𝑻𝑻(∆𝒇𝒇) = 𝑬𝑬{𝑻𝑻∗(𝒇𝒇, 𝒕𝒕)𝑻𝑻(𝒇𝒇 + ∆𝒇𝒇, 𝒕𝒕)}

This calculation is done in the FCF.m function file using the acorr.m defined by [6], an excerpt of which is the following code:


load parameters % load the Time Variant Transfer Function load nTft % Calculation of the Frequency Correlation Function nFCF = zeros(numsamp,2*nummeas-1); for i=1:numsamp nFCF(i,:) = acorr(nTft(i,:)); end nFCF = trapz(nFCF.'); nFCF = abs(nFCF); % Frequency Correlation Function

The coherence bandwidth, Bcoh defined by [4] is computed in the cohBW.m function file as:

𝑩𝑩𝒄𝒄𝒄𝒄𝒉𝒉 = 𝟏𝟏

𝒋𝒋𝒋𝒋𝑺𝑺𝝉𝝉

3.3.3 Time Correlation Function [coherence time] The Time Correlation Function (TCF) is calculated by [3]:

𝑹𝑹𝑻𝑻(∆𝒕𝒕) = 𝑬𝑬{𝑻𝑻∗(𝒇𝒇, 𝒕𝒕)𝑻𝑻(𝒇𝒇, 𝒕𝒕 + ∆𝒕𝒕)}

The computation is similar to that of the FCF and is done in the TCF.m function file.

The coherence time tcoh as in [4] is calculated in the cohTime.m function file:

𝒕𝒕𝒄𝒄𝒄𝒄𝒉𝒉 = 𝟏𝟏

𝒋𝒋𝒋𝒋𝑺𝑺𝒗𝒗

3.3.4 Doppler Spectral Density [mean Doppler and Doppler spread] The Doppler Spectral Density (DSD) is calculated from the ODSF in the DSD.m function file by [2]:

𝑷𝑷𝑯𝑯(𝒗𝒗) = � |𝑯𝑯(𝒗𝒗,𝒇𝒇)|𝒋𝒋𝒅𝒅𝒇𝒇∞

−∞

The corresponding condensed parameters in the form of mean Doppler and Doppler spread are also calculated similar to those for the PDP. The implementation of the DSD is similar to that of the PDP explained in Section 3.3.1.

3.4 Channel Selection Since the wireless test bed can be configured in up to a 4X4 MIMO mode, there are up to 16 combinations of TX- RX channels in the MIMO setup e.g., between TX station 1 and RX station 2. Due to this fact, the tool gives the user an option to select which of the 16 MIMO channels he intends to characterize, as shown below in Fig.11.


Figure 11: Channel Selection Menu

3.5 Filtering and Windowing of the System Functions

3.5.1 Filtering In order to average out the noise, a moving average filter is used, the length of which can be typed in the field below “Filter Length” shown in Fig.12. “Enter” is pressed on the keyboard, and then the desired system functions, correlation functions or special correlation functions are plotted.

Figure 12: Filtering/Windowing Menu

The filtering is done via the mavgfilter.m function file.

function nTft = mavgfilter(val,tx,rx) %where val is the length of the moving average filter % definition of the moving average filter coefficients b = ones(1,val)/val; a = 1; % TVTF for calculating system functions Tft = transfunc (tx,rx); % TVTF for calculating correlation and special correlation functions load nTft nTft % averaging out the noise in the TVTF Tft = filter(b,a,Tft); nTft = filter(b,a,nTft); [Hfv, htE, UEv] = sysfunc (Tft); save systemfunctions Tft Hfv htE UEv


3.5.2 Windowing The FFT command assumes that the signal being transformed is periodic. If, however, the signal is not periodic i.e., it doesn’t start and end at the same value, this leads to spectral leakage (error in the FFT measurement) due to which additional frequency components that do not exist in the original waveform are observed. Windowing is a means to counter this effect.

Accordingly, the tool incorporates a windowing menu shown in Fig. 12, where the user can use either of the Blackman, Hamming, Hanning or Kaiser windows. The user can also opt for no windowing. This can be done by typing in the window name in the field or ‘None/none’ for no windowing. The tool is not case sensitive meaning the user can type either Hamming or hamming. In case the user types in the wrong spellings or an incorrect window, an info message is displayed:

Figure 13: Windowing Error Info

The windowing is done via the windows.m function file, the code of which is shown below:

% Time Variant Transfer Function used for the system functions temp_Tft = transfunc (tx,rx); load parameters % Time Variant Transfer Function used for the correlation and special % correlation functions load nTft % application of Blackman window if (strcmp('Blackman',str)|strcmp('blackman',str)) == 1 % windowing the TVTF since it is used for calculating IDSF and ODSF for n=1:numsamp temp_Tft(n,:) = temp_Tft(n,:).*(blackman(nummeas).'); nTft(n,:) = nTft(n,:).*(blackman(nummeas).'); end [temp_Hfv, temp_htE, temp_UEv] = sysfunc (temp_Tft); % windowing of IDSF since it is used for calculating DDSF temp_htE = temp_htE.'; for k=1:numsamp temp_htE(k,:) = temp_htE(k,:).*(blackman(nummeas).'); end temp_htE = temp_htE.'; %****************************************************** % saving the windowed versions of the system functions %****************************************************** Tft = temp_Tft; Hfv = temp_Hfv;


htE = temp_htE; UEv = temp_UEv; save systemfunctions Tft Hfv htE UEv save nTft nTft %... application of Hamming, Hanning and Kaiser is similar to Blackman % when no windowing is selected, the system functions are % re-calculated from the TVTF elseif (strcmp('None',str)|strcmp('none',str)) == 1 [temp_Hfv, temp_htE, temp_UEv] = sysfunc (temp_Tft); Tft = temp_Tft; Hfv = temp_Hfv; htE = temp_htE; UEv = temp_UEv; save systemfunctions Tft Hfv htE UEv save nTft nTft % error in the input else h1 = showinfowindow('Sorry, Incorrect Option/Spellings!'); end

25 Chapter 4

Chapter 4 Future Work

The channel sounding measurement analysis tool implemented in the current project is the very first version for the wireless test bed at ComLab. Though efforts have been made to execute an implementation that can be easily modified and extended for future versions of the tool, yet some obvious limitations exist that can be worked upon in future. Some of the limitations of the tool are as follows: The implementation does not cater for large data sets (i.e., large number of

measurements from the wireless test bed), e.g., o For a system with:

32-bit Windows XP 2 GB RAM MATLAB 7.4 (2007a)

o And a measurement campaign that contains 750 samples per measurement the maximum number of measurements that could be safely handled by the tool is of the order of ten thousand (10,000). The exact number could vary though since the RAM could be allocated to other processes running on the computer.

Only one type of filter is implemented to average out the noise The user can choose only 4 windows (Blackman, Hamming, Hann, Kaiser)

The limitations posted above provide an insight into what can be modified and extended in the Analysis Tool: An implementation that caters for large data sets Give the user more filtering and windowing options Explore into the possibility of calculating the coherence time/bandwidth using

techniques different from the 3 dB method


References

[1] Bello, Phillips A., “Characterization of Randomly Time-Variant Linear Channels”, IEEE Trans.Commun. Syst, Vol. CS-11, pp 360-393, Dec. 1963

[2] Molisch, Andreas F., “Wireless Communications”, IEEE Press and John Wiley & Sons, Chapter 6, 2009

[3] Kattenbach Ralf, “Charakterisierung zeitvarianter Indoor-Funkkanaele anhand ihrer System- und Korrelationsfunktionen”, Shaker Verlag, Chapter 3, 1997

[4] Molisch, Andreas F. and Steinbauer Martin, “Condensed Parameters for Characterizing Wideband Mobile Radio Channels”, International Journal of Wireless Information Networks, Vol. 6, No.3, 1999

[5] Keithley Instruments,” Keithley TDMA Channel Sounder User’s Guide”

[6] Schneider Dirk, “Auswertungstools fuer Impulswortmessungen in Mobilfunkkanaelen”, Diplomarbeit I, University of Kassel, 1994.

27 List of Figures

List of Figures Figure 1: Interrelation between system functions ....................................................................... 8Figure 2: Relationship between the correlation functions by the Fourier transform .................. 9Figure 3: The Wireless Test Bed in the SISO Configuration ........................................................ 12Figure 4: The Wireless Test Bed in the MIMO Configuration ..................................................... 12Figure 5: A Glance of the Tool ..................................................................................................... 14Figure 6: Systematic description of the calculation of all system functions, correlation functions special correlation functions and condensed parameters ......................................... 15Figure 7: System Functions Menu ............................................................................................... 15Figure 8: Calculation of other system functions from the TVTF ................................................. 18Figure 9: Correlation Functions Menu ........................................................................................ 18Figure 10: Special Correlation Functions & Condensed Parameters section ............................. 19Figure 11: Channel Selection Menu ............................................................................................ 22Figure 12: Filtering/Windowing Menu ........................................................................................ 22Figure 13: Windowing Error Info ................................................................................................ 23

Documents

Channel Sounding Measurement Analysis Tool · The goal of the project is to implement a channel sounding measurement analysis tool for the wireless test bed utilized by the Communications