Channel Model

Under the 60 GHz RF band, there are some special properties when waves are transmitted in the air that is much different from those below 10GHz RF band channel.

Due to strong directivity, wave reflexes, diffracts, and scatters slightly. Also, the energy of the wave centralizes in a certain angles. Since the oxygen absorbs the wave in this RF band, the transmission distance is very short, less than 10 meters, which leads to negligible multipath effect. Based on these properties, IEEE 802.15.3c standard is pronounced for the indoor, over Gbps data rate wireless transmission using 60 GHz RF band. In general, for such a high data rate, the channel would be influenced a lot by line-of-sight (LOS)/non-light-of-sight (NLOS) channel, root-mean-square (RMS) delay spread, Doppler Effect, and negligible multipath effect when the wireless communication system operates under the 60 GHz RF band. These

properties are listed below:



High Path Loss

While the EM wave passes through the medium, the medium absorbs the energy and limits the distance that the EM wave can travel. The more energy it lost, the shorter it can travel. The ratio of energy loss is mainly depends on the characteristic of the medium and the EM wavelength. The wavelength of 60 GHz wave is close to the length of the oxygen chemical bond, so the wireless communication in 60 GHz RF band suffers tremendously high path loss. As the result, the transmission distance is limited to about 10 m in maximum. Moreover, the effect of the multi-path fading is reduced since the non-line-of-sight (NLOS) wave travels more distance and loses more energy than the line-of-sight (LOS) wave.



Strong Directivity

The strong directivity means that the EM wave energy almost centralizes in a small angle path. Based on physical principle of diffraction, the beam width is inversely proportional to the operating frequency [8]. This phenomenon shows that the antenna can only receive the signal from the transmitter antenna within a small angle range. In conclusion, the NLOS path has lower path gain relative to the LOS path, and the multi-path fading effect is small.

The channel model is based on the golden set released by IEEE 802.15.3c group [9] [10]. The golden channel with RMS delay spread 3.2ns is chosen as the simulation channel model. Fig. 2-8 and Fig. 2-10 are SC channel impulse response and channel frequency response with sampling rate 1.76GHz, respectively. Fig. 2-9 and Fig. 2-11 are HSI channel impulse response and channel frequency response with sampling rate

2.64GHz, respectively.

Fig. 2-8 SC channel impulse response

Fig. 2-9 HSI channel impulse response

Fig. 2-10 SC channel frequency response

Fig. 2-11 HSI channel frequency response

Chapter 3 SC/OFDM Dual-Mode Frequency and Time Domain Equalizer

This chapter will review frequency and time domain equalization with channel estimation in Section 3.1 and 3.2 respectively. Section 3.3 is the proposed frequency and time domain equalizer.

3.1 Review of Frequency Domain Equalization (FDE) [11]

A simple illustration of fully parallel FDE is shown in Fig. 3-1. The input passes through Serial-to-Parallel block and transforms to frequency domain by FFT. Then, the frequency domain data is multiplied with coefficients W and then transformed back to time domain by IFFT. Unlike TDE, the number of coefficients in FDE is fixed without regard to the length of the channel impulse response. The potential problem is when the length of the CIR is longer than the length of the CP. In that case, the circular convolution is ruined and FDE fails to equalize the channel effect. However, the channel model shows that the maximum length of CIR is far less than the length of CP, so this system does not have each problem.

FFT IFFT

Fig. 3-1 Structure of fully parallel FDE

The formula of circular convolution can be transformed into a simple multiplication in the frequency domain, and the capital letter means frequency domain signal:



= Η

R D

(3.1)

,where H is a diagonal matrix, R is a received signal vector, and D is transmitted data vector. To recover the transmitted data, we multiply the inverse of H on both sides of equation:

1 1



 



  

H R H H D D

(3.2)

, where the inverse of H is also a diagonal matrix. After CP removal, we can fully recover the transmitted signal D.

The above equations describe the ideal case: no AWGN and time-variant channel.

In reality, the white noise always exists due to the thermal noise, and the channel varies with time due to many effects, such as related movement, air flow, or moving object. Thus, the equation should be:

k

 J

k

( ) t  H

k



k



k

R D N

(3.3)

, where Jk

(t) means the time-variant effect matrix, N

k is a AWGN vector, and k is the index of the subchannels. If we simply multiply the inverse of Hk all the time, the time-variant effect will corrupt the data. Furthermore, to get the accurate inverse of Hk

is a difficult job under AWGN. To break through the predicament, the first thing is to overcome AWGN and get the inverse of Hk as accurate as possible. Then, an adaptive algorithm is performed to track the changes in the time-variant channel. In this way, the time-variant component J_k

(t) is no more an issue in the equalization.

3.1.1 Channel Estimation

,where U512 is the frequency domain constant value of u512, and k is the sub-carrier index.

This solution is known as zero-forcing (ZF) method. The benefit is the simple implementation, but this method suffers from a problem: noise enhancement. With AWGN, Eqn. (3.4) is revised as Eqn. (3.5).

The noise enhancement occurs when the channel gain Hk is so small that the noise

N

k is the dominant part in received signal. In that case, especially with large Nk, the

estimation result is far away from perfect estimation.

Since there are 2 U512 in CES, using Least-Square (LS) method is a better way than using ZF. The main point of LS is to minimize the sum of the squares of the error.

First of all, the equalization can be described as:

U

512,_k

Then, we need to minimize the sum of the squares, so let the partial derivative on

W

k be zero.

Finally, the solution of ˆ

W indicates the system will have minimum of S.

_k

2

2

Substituting R_k with U₅₁₂, the channel estimation result is:

512, 512, time-variant channel. However, we do not have any known message in the frequency domain when the system is SCBT. Thus, our FDE requires an adaptive algorithm against the time-variant channel.

There are many adaptive algorithms developed in the literals. These algorithms mainly focus on their computational complexity and convergence speed. The widely used algorithms are Minimum-Mean-Square-Error (MMSE), Recursive-Least-Square (RLS), and Least-Mean-Square (LMS) [12],[13]. Due to 2640MHz sampling rate, high computational complexity algorithms are not suitable for such high sampling rate system because of high hardware complexity and power consumption. Furthermore, using the information of SNR is not practical in the hardware design. Based on above the considerations, we will show that LMS is a good choice for the FDE.

Let’s consider the block diagram of the adaptive FDE shown in Fig. 3-2. R is the output from FFT, and the adaptive FDE do the equalization and update filter

coefficients W. The FDE output is transformed back to time domain and decision of data is made by the demapper. The error E is the difference between FDE output and the training sequence (or sliced output when the data is transmitted).

Update

Fig. 3-2 Illustration of adaptive FDE

The idea of LMS algorithm is to use the method of the steepest descent to find a set of W which minimizes the cost function. In our design, the FDE takes a subblock into the equalization, so the cost function should involve a block of errors, which is so called Block LMS (BLMS) [14]. However, since the equalization is independent of each subchannel, we can consider each cost function C_k in each subchannel independently instead of whole subblock.

{ 2}

k k

C  Ex E

(3.12)

The notation of Ex{.} is used to denote the expect value because we don’t want to be confused with the error E. Then, applying the steepest descent is to take the partial derivative with respect to the filter coefficients W.

* *

{ } 2 { }

C Ex Ex

   EE   EE

(3.13)

Since the equalization is independent of each subchannel, Eqn. (3.13) is equal to

zeros when the error E and coefficient W are in different subchannel. Then, substituting E with received signal R, we can rewrite Eqn. (3.13) as

*

, where k is the subchannel index. Now, these derivatives show the steepest ascent of the cost function. To find out the minimum of the cost function, we take a step size of

2



in the opposite direction of the derivatives.

, *

, where n indicates the subblock index or symbol index at SC or OFDM mode.

The expected value can be simplified, and the whole LMS algorithm can be expressed as:

LMS:

W

_{k n, 1}

 W

_{k n,}

  R E

_{k k}^* (3.16)

The derivations of MMSE and RLS can be found in [16], [17]:

MMSE:

, where n indicates the subblock index or symbol index at SC or OFDM mode,



_n² and



_s²are variance of noise and signal respectively, Y is equalized signal, U is the intermediate vector, and g_n is the gain vector.

Compared with MMSE [15]-[17] and RLS [18], [19], the LMS algorithm has less computational complexity than RLS since there is only one multiplication for updating at each sub-channel. In hardware design, more operations on updating will cause a longer feedback latency. The latency will impact the performance since the coefficient of equalizer can not be updated immediately. In high sampling rate system, high computational operations will required more pipelined stages, thus the latency is much longer. Furthermore, the low computational complexity leads to low power consumption. The low power issue is more important in the modern SOC design. In that case, LMS also has the advantage of low power consumption property. On the other hand, MMSE also has less computational complexity than RLS, but it requires the information of SNR, which is hard to be evaluated since there are Doppler and channel Effect on the received signal. Although there are some algorithms [15]-[17]

trying to do SNR evaluation, the result is still not reliable in the practical system.

Based on these considerations, LMS is suitable for FDE in high sampling rate design and can also achieve the required bit error rate (BER) with LS channel estimation that will be mentioned in Section 3.3.2.

3.2 Review of Time Domain Equalizer (TDE)

The basic structure of the TDE is the FIR filter, which performs the convolution between data stream and the filter coefficients. A simple illustration of the FIR filter is shown in Fig. 3-3, which is known as Zero Forcing (ZF). A robust adaptive decision

3.1.2. The Least Mean-Square (LMS) equalizer coefficients updating method is chosen to minimize the mean-square error, instead of ZF [20].

………

D D ……… D

＊ ＊ ＊

∑

………

input

＊

W0 W1 W2

w

n

output

Fig. 3-3 FIR filter structure

However, the computational complexity of the convolution in both ZF and LMS is proportional to the length of the filter taps, which is determined by the length of the CIR. From the channel model in Fig. 2-8 and Fig. 2-9, the filter coefficients must satisfy the mathematical property in Eqn. (3.19).

 

* 1 0 0 0

h w 

(3.19)

Although the parallel architecture can increase the throughput of TDE, the complexity grows linearly with the number of coefficients.

3.2.1 Multi-path Interference Cancellation

Multi-path Interference Cancellation (MPIC) [21] method is an efficient way for suppressing Inter-path Interference (IPI). MPIC is composed of two parts. The first part is multi-path interference replica, and the second part is multi-path interference cancellation [22].

The following lower-case variables are all in time domain. In Fig. 3-4, during data transmission, dominant data path could be interfered by other multi-path data and  is the multi-path delay. path gains. The rest channel path gains almost equal to zeros. Therefore, the received signal is expressed like

, where h means channel impulse response matrix, x is the transmitted data vector, and y is the received signal vector. Define main data path gain vector

1,1 2,2 ,

and second data path gain vector

1,1+ 2,2+ - ,

where N is the number of total sub-channels.

A modified MPIC [21] has two stages. In initial stage, we can obtain the channel impulse response after channel estimation. Assume multi-path gain is small, so we don’t consider the multi-path gain m[t]. Then, we have

ˆ[ ] [ ], 1, 2,..., [ ]

t t t N

 y t 

x h

(3.23) , where

x ˆ[ ] t

is initial data vector without considering multi-path effect. Because the second path delay is

, it means the dominant received signal will be affected by the

second received signal after time

. In update stage, the received signal cancels the

second path interference and the result is divided by the main path gain to get the updated transmitted data x[t].

[ ] [ ] ˆ[ ]

The equation from (3.22) can be simplified as

[ ] [ ]

3.2.2 Golay-Sequence Aided Channel Estimation [15]

A set of complementary series is defined as a pair of equally long, finite sequences of two kinds of elements which have the property that the number of pairs of like elements with any one given separation in one series is equal to the number of pairs of unlike elements with the same given separation in the other series. For example, the two series a = 00010010 and b = 00011101 are complementary [23].



Golay Sequence Property

Golay sequences with N of length are generated by delay and weight vectors with M of each length and a recursive algorithm [24], [25]. Binary Golay sequences are generated when the delay vector

D  [ D

₀

... D

_M1

]

is chosen as any permutation of

0 1

[2 ...2

^M

]

and the weight vector

W  [ W W

₀

...

_M1

]

has

 1

of elements. The recursive algorithm for generating Golay sequences is described as follows:

,(0)( ) ( ) Golay sequences are complementary sequences, which have an attractive property that the sum of their autocorrelations has single maximum peak and no side-lobe.

A pair of Golay sequences for

i  0,..., N  1

, with

N 

2^M:

( )

a i

and

b i ( )

. (3.32)

Autocorrelation property: The symbol “*” denotes complex conjugate.



Estimation Procedure

The received channel estimation sequence (CES) is expressed by

1

Fig. 3-5 Golay Sequences of CES

Both parts have a common configuration, that is, NRCE repetitions of base

sequences with length N_CE and cyclic prefix and postfix with length N_CPCE. The base sequences for “Parts a and b” are Golay sequences ( )

NCE

a i and _{( )}

NCE

b i , respectively.

Then, the total length of CES is 2(2NCPCE + NRCE

N

CE).

First, the Golay correlator calculates correlation values between the received CES and Golay sequences



( )

t

and



( )

t

:

Then, CPs are removed from the correlation values:

ˆ( ) t ( t N

_CPCE

), t 0,..., N

_RCE

N

_CE

1

The derived noiseless channel impulse response can be used in MPIC equalization.

3.3 Proposed Architecture for IEEE 802.15.3c

3.3.1 Proposed Adaptive LS-LMS FDE [11]

The proposed adaptive LS-LMS FDE operates based on equations in Section of 3.1.1, and 3.1.2, and the block diagram is shown in Fig. 3-6.

Frequency

Fig. 3-6 Block diagram of the proposed adaptive LS-LMS FDE

The pseudo code of the system flow is explained as followed:

1. If (received signals == training sequences) the LS channel estimation evaluates the channel coefficients, else the received signals will be equalized by FDE.

2. If (mode == SC) the equalized data will be transformed to time domain by IFFT and sent to decision circuit, else will be sent to decision circuit straightly.

3. If (mode == SC) the errors between equalized and sliced signal will be transformed to frequency domain by FFT and sent to LMS adaptive algorithm, else will be sent to LMS adaptive algorithm straightly.

4. While (received signals == valid data) LMS adaptive algorithm will update the channel coefficients in FDE.

The proposed adaptive LS-LMS FDE needs additional two FFT (FFT and IFFT) for SC/OFDM dual mode system. In SC mode, the equalized signal must be transformed to time domain to do slicing, and the error between equalized data and decision data will be transformed back to frequency domain for adaptive algorithm. Although the hardware complexity is large, the adaptive LS-LMS FDE can track the change of time-variant channel.

LMS has to do training to achieve convergence before any data is ready to be equalized. To accelerate the convergence speed, a fast LMS algorithm is applied by simply increasing the step size [26]. However, compared with other algorithms, LMS still suffers the slow convergence speed problem [27]. Therefore, the training time of LMS is longer than others, and it requires longer training sequence to do training.

According to the standard, the training sequence is available in CES field of PHY preamble. However, there are only two a₂₅₆

b

₂₅₆ for training before payload, so the training result of LMS is not good enough as compared with LS channel estimation.

The learning curves are shown in Fig. 3-7. The simulation is under the channel model which RMS delay is 3.2ns and SNR is 18 dB. LMS algorithm takes about extra12 data subblocks to achieve the same performance of LS-LMS combined algorithm. The result supports that the convergence speed of the combined algorithm is indeed faster than single LMS algorithm.

Fig. 3-7 Learning curves

3.3.2 Proposed LOS Golay-MPIC TDE

The proposed LOS Golay-MPIC TDE operates based on equations in Section of 3.2.1 and 3.2.2, and the block diagram is shown in Fig. 3-8.

Fig. 3-8 Block diagram of the proposed LOS Golay-MPIC TDE

The pseudo code of the system flow is shown below:

1. If (received signals == training sequences) the Golay sequences aided channel estimation evaluates the channel impulse response, else the received signals will be equalized by MPIC TDE.

2. If (mode == HSI) the equalized data will be transformed to frequency domain by FFT, else will go through next block straightly.

3. While (received signals == valid data) the equalized data will be sent to decision circuit and demapper.

The proposed LOS Golay-MPIC TDE has low hardware complexity, which doesn’t need additional IFFT/FFT for SC/OFDM dual mode system. In each PCES period, the LOS Golay-MPIC TDE will update the channel impulse response again by Golay sequence aided channel estimation.

The LOS channel model provided by IEEE 802.15.3c standard has only two higher channel path gains. Also, the second path gain of LOS channel model is at most 0.3 and the other paths are less than the main path [9] [10]. Therefore the MPIC TDE can be efficiently implemented. For evaluating the influence of the multi-path gain and delay, different test patterns with AWGN and test channels are created. The test channels have one main path and one delayed path, and the second path gain and delay differs from 0.1 to 0.5 and differs from 8 to 56 samples which is normalized to main path, respectively. The modulations of SC and HSI mode are pi/2 QPSK and QPSK respectively. In Fig. 3-9 and Fig. 3-10, it shows BER is very sensitive to second path gain, but rarely affected by second path delay.

Fig. 3-9 BER of TDE SC mode for 2 channel paths

Fig. 3-10 BER of TDE HSI mode for 2 channel paths

If the number of LOS channel paths has more than two paths, the proposed Golay-MPIC TDE can still work. But the BER will be worse as long as the third path gain becomes larger. Take SC mode with three channel paths as example, Fig. 3-9 shows the BER is 4.89*10^-4 and 6.64*10^-4 when the second path gain is 0.35 and delay is 8 and 40, respectively. If the third channel path is involving for these two cases, the BERs are shown in Fig. 3-11 and Fig. 3-12. In Fig. 3-11 and Fig. 3-12, when the third path gain becomes small, the BER is near 4.89*10^-4 and 6.64*10^-4, respectively. The performance of different delay of the third path is almost the same.

Fig. 3-11 TDE SC mode BER for 3 channel paths & 2^nd Path gain=0.35 and delay=8

The proposed LOS Golay-MPIC TDE can achieve the BER requirement of IEEE 802.15.3c standard. If the number of LOS channel paths is more, the computation is more complex. Also, the number of register becomes more with the longer delay path.

Therefore, we consider the general case of two higher gain channels. It can reduce hardware complexity and achieve the required BER. Section 4.2.1 will describe an efficient architecture design of Golay-sequence aided channel estimation.

Chapter 4

Architecture Design and Performance Analysis

This chapter describes architecture design of the proposed adaptive LS-LMS FDE and LOS MPIC TDE in Section 4.1. The detail sub-blocks design is shown in Section 4.2. Section 4.3 is the synthesis result and performance of the proposed adaptive LS-LMS FDE and LOS MPIC TDE. The comparison of the proposed adaptive LS-LMS FDE and LOS MPIC TDE is presented in Section 4.4

4.1 Design Specifications and Architecture

IEEE 802.15.3c and IEEE 802.11ad standards focus on over Gbps data rate wireless communication. To achieve the target, there are two key features in the standard. The first one is the usage of the 60 GHz RF band. The unlicensed RF bandwidth is wide enough to support the usage of large bandwidth. The transmission rate is proportional to the bandwidth, so using the unlicensed 60 GHz RF band is essential. The second one is the ultra-high sampling rate. Although there are many methods to achieve the target of high data rate, like using higher modulation or multi-input and multi-output (MIMO) system [28], raising the sampling rate is the most direct way since the data rate is proportional to the sampling rate. With the moderate modulation scheme, the data rate could be twice or three times of the

IEEE 802.15.3c and IEEE 802.11ad standards focus on over Gbps data rate wireless communication. To achieve the target, there are two key features in the standard. The first one is the usage of the 60 GHz RF band. The unlicensed RF bandwidth is wide enough to support the usage of large bandwidth. The transmission rate is proportional to the bandwidth, so using the unlicensed 60 GHz RF band is essential. The second one is the ultra-high sampling rate. Although there are many methods to achieve the target of high data rate, like using higher modulation or multi-input and multi-output (MIMO) system [28], raising the sampling rate is the most direct way since the data rate is proportional to the sampling rate. With the moderate modulation scheme, the data rate could be twice or three times of the

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