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Advanced Wireless Networks - 4G Technologies

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448 ADAPTIVE RESOURCE MANAGEMENT

(k)

1° x-2(k) x-1(k) x0(k) x1(k) x2(k)

2° x-2(k) x-1(k) x0(k) x1(k) x2(k)

3° x-2(k) x-1(k) x0(k) x1(k) x2(k)

4° x-2(k) x-1(k) x0(k) x1(k) x2(k)

5° x-2(k) x-1(k) x0(k) x1(k) x2(k)

x0(k)

x0(k+1)

x 0(k+2)

 

 

x0(k+19

 

F1

F2

F3

 

 

 

F20

x-2 x-1 x0 x1 x2

x-2 x-1 x0 x1 x2

x-2 x-1 x0 x1 x2

 

 

x-2 x-1 x0

x1 x2

S

 

S

 

 

 

 

 

 

 

S

S

S

S

 

Σ

Σ

Σ

Σ

Σ

Σ

SX-2

SX-1

SX0(F)

SX0(B)

SX1

SX2

 

 

)

)

 

 

W-2 (i)

W-1 (i)

 

 

W1 (i)

W2 (i)

 

Y1

 

 

Y2

 

FPF

 

-

-

 

BPF

 

 

 

 

 

 

 

 

 

 

 

EX1

EX2

 

 

Figure 12.25 Signal processing.

samples per frame (M = 2). Central samples, within each frame, carry the same information about the useful signal and the interference symbols, and, since each sample belongs to a different frame, all those samples originate from different instances of time. Similarly, samples from different frames equally distant from the central sample carry the correlated interference signal. Therefore, an equivalent signal may be formed in the following way: Mth equivalent signal sample is the sum of Mth samples from each frame. Adaptation of filter weights using LMS algorithm and interference prediction is performed using the equivalent signal samples.

As already mentioned, the changes of the symbol in the interfering signal will disrupt the estimation process so that a forward and backward prediction are used simultaneously. When the symbol change occurs, the filter with less disruption (smaller error at its output) is used to deliver the estimates. This process is described in the following in more detail. For additional insight into the problem the reader is also referred to Cox and Reudink [31]. Possible moments of the transition to happen are shown in Figure 12.25 and are denoted with 1◦, 2◦, 3◦ and 4◦. Therefore, at frame rate BPF(F) (backward prediction filter) and FPF(F) (forward prediction filter) filters are operating with weights being forwarded from the LMS algorithm adapted by the equivalent signal. BPF(F) and FPF(F) filters have the

DYNAMIC SPECTRA SHARING IN WIRELESS NETWORKS

449

same weights during the useful signal bit interval, i.e. within all the frames belonging to the same bit interval. So the interference is predicted using the same weights computed using the equivalent signal. If, in cases 1◦, and 2◦, we discard samples belonging to the BPF(F) filter we will also discard the interference transition influence on the prediction. For cases 3◦ and 4◦, samples that belong to the FPF(F) filter should be discarded. This sample discarding is performed in the selector S at the outputs of BPF(F) and FPF(F) filters, based on the error signal.

Therefore, if there is no interference signal transition during the sampling within one frame, the equivalent signal will be formed using all the samples from that frame. Also, the same equivalent central sample (SX0(B) = SX0(F)) is passed to both BPF(B) and FPF(B) LMS algorithms. On the other hand, if there is interference signal transition during the sampling within one frame, the equivalent signal will be formed using samples from FPF(F) (cases 1◦ and 2◦) or BPF(F) (cases 3◦ and 4◦), and there will be two different equivalent central samples.

For the described Interference rejection circuit we have: the first part of the interference rejection circuit processes data at frame level, and at each frame the following input signal processing is performed. At filter A, the signal is sampled very close in time to the useful signal. For −M ≤ m ≤ M we have:

Alm (n) = AIml (n) + j AQlm (n)

 

(n+1)

 

Tf

 

−

 

τl

 

Tf

 

 

 

 

 

AIlm (n) =

Tc

Tc

 

 

τl

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

r I (k)g k − n

−

− h(n) − m

 

 

T

 

 

 

 

 

τ

Tc

 

Tc

 

 

k=n

 

 

f

 

−

 

 

l

 

 

 

 

 

 

 

 

 

 

 

 

Tc

Tc

 

 

 

 

 

 

 

 

 

 

(n+1)

Tf

−

τl

 

 

Tf

 

 

 

 

 

AQlm (n) =

Tc

Tc

 

 

 

 

τl

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

r Q(k)g k − n

−

− h(n) − m

 

 

T

 

 

 

 

 

τ

Tc

Tc

 

k=n

f

 

−

l

 

 

 

 

 

 

 

 

 

 

 

Tc

 

Tc

 

 

 

 

 

 

 

 

 

For filter B we have:

Bml (n) = B Iml (n) + j B Qlm (n)

 

(n+1)

Tf

 

−

 

τl

 

Tf

 

 

 

 

 

 

 

 

BIlm (n) =

Tc

Tc

 

 

τl

 

 

 

 

 

 

 

 

 

 

 

 

 

 

r I (k)g k − n

 

 

 

−

 

 

 

− h(n) − m −

 

 

 

 

 

T

 

 

 

 

 

τ

Tc

Tc

Tc

 

k=n

 

 

f

 

−

 

l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Tc

Tc

 

 

 

 

 

 

 

 

 

 

 

 

 

(n+1)

Tf

−

τl

 

 

Tf

 

 

 

 

 

 

 

 

BQlm (n) =

Tc

Tc

 

 

 

 

τl

 

 

 

 

 

 

 

 

 

 

r Q(k)g k − n

 

−

 

− h(n) − m −

 

 

 

T

 

 

 

 

 

τ

Tc

Tc

Tc

 

k=n

f

 

−

l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Tc

 

Tc

 

 

 

 

 

 

 

 

 

 

 

 

(12.137)

(12.138)

(12.139)

(12.140)

(12.141)

(12.142)

450 ADAPTIVE RESOURCE MANAGEMENT

After that, variables C1 and C2, which the operation of one side of filter X (A and B) is based on, are determined:

CX1l (n)

0,

−1

Xml (n)Wm (i)]

=

m=−M

 

−

1

Xml (n)Wm (i)]

 

1,

 

 

 

m=−M

 

 

M

 

2

 

0,

 

Xml (n)Wm (i))

CX2l (n)

m=1

=

2

 

M

 

 

1,

m=1

Xml (n)Wm (i))

 

 

 

2

M

2

≥ A1

m=1

Xml (n)Wm (i)]

2

2

< A1

M

Xml (n)Wm (i)]

m=1

 

 

 

−1

2

≥ A2

Xml (n)Wm (i))

 

m=−M

2

< A2

−1

Xml (n)Wm (i))

 

m=−M

 

(12.143)

(12.144)

where Ai (i = 1, 2) are constants (for Ai → ∞, the selector selects all the samples and the structure operates as a traditional LMS algorithm). These gains are introduced because of the decrease of noise influence on the irregular selections.

The second part of the interference rejection circuit operates at

bit interval level

Tb = N Tf, and for each ith bit we have the following signals:

 

SXlm (i) =

(i+1)N

(n)C X1l (n) − M ≤ m ≤ −1

 

Xml

(12.145)

 

n=i N

 

 

SXlm (i) =

(i+1)N

(n)C X2l (n)1 ≤ m ≤ M

 

Xml

(12.146)

 

n=i N

 

 

 

(i+1)N

 

SX1l (i) =

X0l (n)C X1l (n)

(12.147)

 

 

n=i N

 

 

(i+1)N

 

SX2l (i) =

X0l (n)C X2l (n)

(12.148)

 

 

n=i N

 

The error signal used for w coefficients adaptation is:

EX1l (i) = S X1l (i) −

−1

 

S Xml (i)Wm (i)

(12.149)

m=−M

 

EX2l (i) = S X2l (i) −

M

 

S Xml (i)Wm (i)

(12.150)

 

m=1

 

The filter output signal, being led to the RAKE combiner, is:

 

DXl (i) = E X1l (i) + E X2l (i)

(12.151)

DYNAMIC SPECTRA SHARING IN WIRELESS NETWORKS

451

The adaptation algorithm is defined as:

μE X1l (i) S Xml (i) *

 

 

Wm (i + 1) = Wm (i) +

 

 

 

 

,

−M ≤ m ≤ −1

(12.152)

 

−

1

2

 

 

 

S Xl (i)

 

 

 

 

j=−M

j

 

 

 

 

 

 

 

 

Wm (i + 1) = Wm (i) +

μE X2l (i) S Xml (i) *

, 1 ≤ m ≤ M

(12.153)

 

M

2

 

 

 

 

 

S Xl (i)

 

 

 

 

 

 

j

 

 

j=1

Finally, the interference rejection circuit is made symmetrical in the following way:

Wm (i + 1) =

 

 

Wm (i + 1) + W−m (i + 1)*

1 ≤ m ≤ M

(12.154)

 

 

 

 

2

 

 

 

 

 

 

 

,

 

Wm (i + 1) = W−m (i + 1)*,

−1 ≤ m ≤ −M

(12.155)

12.6.12 Performance analysis

 

 

 

 

 

 

 

 

 

 

The error probability per bit is:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

Ni

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Pe =

 

 

Pe (i)

 

(12.156)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

where

 

 

 

 

 

 

Ni i=1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Na

 

 

 

 

 

 

SNR(i)

 

 

 

 

 

 

 

 

 

erfc

,

 

 

 

 

 

ai

d j (i) ≥ 0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2

2

 

 

 

 

 

 

 

 

Pe (i) =

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

j=1

(12.157)

1

 

 

 

 

SNR(i)

 

 

 

 

 

 

Na

1 −

 

erfc

 

 

 

 

 

 

,

 

ai

d j (i) < 0

 

2

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

j=1

 

Ni is the bit ensemble size (measured in number of information bits) used for averaging the result and Na is the number of ensemble members.

Estimated signal-to-noise ratio per bit is:

 

 

 

 

1

 

Na

 

 

 

2

 

 

 

 

 

 

 

d j (i)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SNR (i) =

 

 

 

 

Na

j=1

 

 

(12.158)

 

 

 

 

 

 

 

 

 

1

Na

 

 

 

2

 

1

 

Na

2

 

 

d j (i)

−

 

 

d j (i)

 

 

 

 

 

 

 

 

 

 

 

 

 

Na

j=1

 

 

Na

j=1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

where d j (i) is the jth ensemble member.

12.6.13 Performance examples

Figure 12.26 presents the results for BER as a function of signal to noise ratio SNR, in the presence of different PSK/QAM type interfering signals. Additional parameters of the signals are: filter length M = 4, = 5 ns, vbJ = 100 Msymbol/s, vbTH = 5 Mbt/s,

452 ADAPTIVE RESOURCE MANAGEMENT

0.01

 

e

 

 

 

 

d1

 

a

d

Pe

 

 

f, f1

 

b, b1

 

 

 

 

c

1×10-3

 

g

6

8

10

SNR (dB)

Figure 12.26 Error probability as a function of signal-to-noise ratio. Error probability based on Monte-Carlo simulation: a, no interference, without interference rejection filter; b, no interference, with interference rejection filter; c, PSK interference, J: S = 40 dB, with interference rejection filter; d, QPSK interference, J: S = 40 dB, with interference rejection filter; e, 16QAM interference, J: S = 40 dB, with interference rejection filter; f, 64QAM interference, J: S = 40 dB, with interference rejection filter; g, 256QAM interference, J: S = 40 dB, with interference rejection filter; Error probability based on estimated detection variable signal to noise ratio: b1, the same parameters as b; d1, the same parameters as d; f1, the same parameters as f; fc = 800 MHz, M = 4, = 5 ns, vbJ = 100 Msymbol/s, vbTH = 5 Mbt/s, Tframe = 10 ns.

fc = 800 MHz and Tframe = 10 ns. One can see: (1) fair agreement of simulation and numerical results; (2) the performance results are close to no interference case, although interference with the level of 40 dB above the UWB signal is present; (3) there is also a slight degradation of the performance when the interfering signal constellation size is increased.

Figure 12.27 presents the results for BER as a function of interference to signal ratio J:S, in the presence of different PSK/QAM-type interfering signals. Additional parameters of the signals are: filter length M = 4, SNR=7 dB, = 5 ns, vbJ = 100 Msymbol/s, vbTH = 5 Mbt/s, fc = 800 MHz and Tframe = 10 ns. One can see that, when J:S becomes larger than zero (5 dB), the BER increases rapidly if there is now interference suppression (curves A). The performance is very similar if a standard LMS algorithm is used (curves C). On the other hand the U-type filter is performing significantly better (curves B). There is again a slight

DYNAMIC SPECTRA SHARING IN WIRELESS NETWORKS

453

 

 

 

A (a, b, c, d, e)

 

 

 

 

C (a, b, c, d, e)

 

0.1

 

 

 

 

 

 

Pe

 

 

 

 

 

 

 

 

B

 

 

 

 

 

 

 

e

 

 

 

 

 

d

c

b

a

 

0.01

 

 

 

 

 

 

-20

0

20

40

 

60

80

J:S (dB)

Figure 12.27 Error probability as a function of interference-to-signal ratio. A, without interference rejection; B, with interference rejection circuit; C, with classical LMS interference rejection filter; a, PSK interference; b, QPSK interference; c, 16QAM interference; d, 64QAM interference; e, 256QAM interference;fc = 800 MHz, M = 4, SNR = 7 dB, = 5 ns; vbJ = 100 Msymbol/s, vbTH = 5 Mbt/s, Tframe = 10 ns.

degradation of the performance when the interfering signal constellation size is increased. Figure 12.28 presents the results for BER as a function of interference symbol duration Tj / Tc in the presence of different PSK/QAM-type interfering signals. Additional parameters of the signals are J: S = 30 dB, SNR = 7 dB, M = 4, = 5 ns, vbTH = 5 Mbt/s, fc = 800 MHz and Tframe = 10 ns. One can see that BER decreases when Tj / Tc increases. There is again a slight degradation of the performance when the interfering signal constellation size is increased. Figure 12.29 presents the results for BER as a function of interference symbol duration Tj / Tc and the number of subcarriers N in the presence of OFDM-type interfering signals. Additional parameters of the signals are J: S = 30 dB, SNR = 7 dB, M = 4, = 5 ns, vbTH = 5 Mbt/s and Tframe = 10 ns, fc = 800 MHz and 16QAM per subcarrier. One can see that BER decreases when Tj / Tc increases up to Tj / Tc ≈ 200. Beyond that point there is no significant reduction in BER if Tj / Tc is further increased. There is a significant degradation of the performance when the number of subcarriers in the OFDM signal is increased.

0.1

 

 

 

 

 

 

 

 

 

 

 

 

e

 

 

 

 

 

 

 

 

d

 

Pe

 

 

 

 

 

 

 

 

a

 

 

 

 

 

 

 

 

b

 

 

 

 

 

 

 

 

 

c

 

 

 

0.01

 

 

 

 

 

 

 

5

10

15

20

25

30

35

40

 

 

 

Tj /Tc

 

 

 

 

Figure 12.28 Error probability as a function of interference bit duration. a, PSK interference; b, QPSK interference; c, 16QAM interference; d, 64QAM interference; e, 256QAM interference; fc = 800 MHz; J: S = 30 dB; SNR = 7 dB; M = 4; = 5 ns; vbTH = 5 Mbt/s; Tframe = 10 ns.

0.1

Pe

0.01

200

400

T

/

T

j

 

 

 

c

600

4

 

800

2

 

1000

8

64

32

16

N

Figure 12.29 Error probability as a function of OFDM interference bit duration and the number of subcarriers. OFDM/16QAM interference; fc = 800 MHz; J : S = 30 dB; SNR = 7 dB; M = 4; = 5 ns; vbTH = 5 Mbt/s; Tframe = 10 ns.

DYNAMIC SPECTRA SHARING IN WIRELESS NETWORKS

455

 

 

 

d

B

 

 

 

 

 

 

a

 

 

 

 

 

 

 

 

 

 

c

0.1

b

d

 

 

 

 

 

 

 

 

Pe

 

 

 

 

 

 

 

 

e

c

 

 

 

 

 

 

 

a

 

 

 

 

 

 

A

 

 

 

0.01

 

 

 

 

 

200

 

400

600

800

1000

 

 

 

Tj/Tc

 

 

Figure 12.30 Error probability as a function of OFDM interference bit duration. A, interference rejection circuit; B, classical LMS interference rejection filter; a, OFDM/PSK interference; b, OFDM/QPSK interference; c, OFDM/16QAM interference; d, OFDM/ 64QAM interference; e, OFDM/256QAM interference; N = 16, fc = 800 MHz, J: S = 30 dB, SNR = 7 dB, M = 4, = 5 ns; vbTH = 5 Mbt/s, Tframe = 10 ns.

Figure 12.30 presents the results for BER as a function of interference symbol duration Tj / Tc in the presence of OFDM-type interfering signals. Additional parameters of the signals are J: S = 30 dB, SNR = 7 dB, M = 4, = 5 ns, vbTH = 5 Mbt/s and Tframe = 10 ns , fc = 800 MHz and N = 16. One can see again that BER decreases when Tj / Tc increases. There is again a slight degradation of the performance when the interfering signal constellation size is increased. Once again, the U-type filter performs much better than the classical LMS algorithm. Figure 12.31 presents the results for BER as a function of interference symbol duration Tj / Tc in the presence of MC CDMA-type interfering signals for different number of subcarriers N and number of users K. Additional parameters of the signals are J: S = 30 dB, SNR = 7 dB, M = 4, = 5 ns, vbTH = 5 Mbt/s and Tframe = 10 ns and fc = 800 MHz. One can see again that BER decreases when Tj / Tc increases. The performance are improved if the number of subcarriers is decreased.

456 ADAPTIVE RESOURCE MANAGEMENT

 

 

a

 

 

 

 

 

 

 

b

 

 

 

 

 

0.1

 

c

 

 

 

 

 

 

 

 

 

 

 

 

Pe

 

d

 

 

 

 

 

 

 

 

 

 

 

 

 

 

e

 

 

 

 

 

0.01

 

 

 

 

 

 

 

1000

2000

3000

4000

5000

6000

7000

8000

 

 

 

Tj /Tc

 

 

 

 

Figure 12.31 Error probability as a function of MC CDMA interference bit duration. a, N = 64, K = 10; b, N = 32, K = 5; c, N = 32, K = 10; d, N = 32, K = 20; e, N = 16, K = 10. MC CDMA interference; J: S = 30 dB, SNR = 7 dB, M = 4, = 5 ns; vbTH = 5 Mbt/s, Tframe = 10 ns, fc = 800 MHz.

The performance is improved if the number of users is increased for the same overall power of the interfering signal. This can be explained by the fact that a sum of MC CDMA signals will create an equivalent multicarrier signal with fewer dominant subcarriers which are suppressed more effectively by the filter because the LMS algorithm better adjusts the filter weights. This is demonstrated in Figures 12.29 and 12.30 for OFDM signal.

In this section we presented a U-type estimation filter based scheme for interference suppression in UWB systems and discussed its performance. It was shown that the scheme can be used to significantly improve the performance of UWB systems in the presence of interference from mobile communication systems such as GSM and WCDMA. It is also effective in the presence of WLAN systems which are based on OFDMA technology or in military communications where the interference is generated by intentional jamming. The section also discusses the effectiveness of the scheme to suppress MC CDMA, which is a candidate technology for 4G mobile communications. The results show that significant suppression gain up to 40 dB can be achieved in the presence of OFDM, WCDMA and MC CDMA. The effectiveness decreases if the size of the number of subcarriers is increased.

REFERENCES 457

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