Some Systems Aspects Regarding Compressive Relaying with Wireless - - PowerPoint PPT Presentation

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook

Some Systems Aspects Regarding Compressive Relaying with Wireless Infrastructure Links

Erhan YILMAZ Raymond KNOPP David GESBERT

{yilmaz, knopp, gesbert}@eurecom.fr Mobile Communications Department EURÉCOM Sophia-Antipolis

May 15, 2008

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook

Outline

1

Introduction Some Information Theory Tools

2

Parallel Relay Networks (PaReNet) Outer Bounds Achievable Rates for PaReNet

Amplify-and-Forward (AF) Relaying Decode-and-Forward (DF) Relaying Block-Quantization and Random Binning (BQRB)

Numerical Results

3

Cellular Networks with Relay Nodes: An Implementation Single Cell System Model

Numerical Results: Single-Cell Relaying

Multi-Cell Relaying

Numerical Results: Multi-Cell Relaying

4

Summary and Outlook

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Some Information Theory Tools

Outline

1

Introduction Some Information Theory Tools

2

Parallel Relay Networks (PaReNet) Outer Bounds Achievable Rates for PaReNet

Amplify-and-Forward (AF) Relaying Decode-and-Forward (DF) Relaying Block-Quantization and Random Binning (BQRB)

Numerical Results

3

Cellular Networks with Relay Nodes: An Implementation Single Cell System Model

Numerical Results: Single-Cell Relaying

Multi-Cell Relaying

Numerical Results: Multi-Cell Relaying

4

Summary and Outlook

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Some Information Theory Tools

Slepian-Wolf Encoding (1/7)

Correlated Sources (X, Y)

E n c

• d

e r

• 1
• E

n c

• d

e r 2

• D

e c

• d

e r X Y R

1

R

2

X Y , ( )

• H(X|Y)

H(X) H(X,Y) H(X,Y) H(Y) H(Y|X) R

1

R

2

R

Correlated Sources (X, Y)

E n c

• d

e r

• 1
• E

n c

• d

e r 2

• X

Y R

1

R

2

X Y , ( )

D e c

• d

e r

• 1
• D

e c

• d

e r 2

• H(X|Y)

H(X) H(X,Y) H(X,Y) H(Y) H(Y|X) R

1

R

2

R

(a) (b)

Figure: (a) SW Decoding (Correlation exploited), (b) Regular Decoding

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Some Information Theory Tools

Slepian-Wolf Encoding (2/7)

Correlated Sources with (X, Y) ∼ p(x, y) Distributed (or separated) encoding/compression Main tool ⇒ Random Binning

Choose large random index for source sequences If the index range is large enough, then with high probability, different source sequences have different indexes. Thus, we can recover the source sequence from the index.

What are the sufficient Rates to encode sources X and Y ? Note that R ≥ H(X, Y) is sufficient if we encode the sources together (regard (X, Y) pairs as a single source!!)

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Some Information Theory Tools

Slepian-Wolf Encoding: Definitions (3/7)

A (2nR1, 2nR2, n) distributed source code for joint source (X, Y) consists of encoder maps f1 : X n → {1, 2, . . . , 2nR1} f2 : Yn → {1, 2, . . . , 2nR2} and a decoder map g : {1, 2, . . . , 2nR1} × {1, 2, . . . , 2nR2} → X n × Yn Probability of error P(n)

e

= Pr{g(f1(Xn), f2(Yn)) = (Xn, Yn)}

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Some Information Theory Tools

Slepian-Wolf Theorem (4/7)

Theorem [Slepian-Wolf]: For the distributed source coding problem for the source (X, Y) drawn i.i.d ∼ p(x, y), the achievable rate region is given by R1 ≥ H(X|Y) R2 ≥ H(Y|X) R1 + R2 ≥ H(X, Y). Main idea: Show that if the rate pair in the SW region, we can use a Random Binning encoding scheme with Typical Set decoding to

• btain a probability of error that tends to zero.

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Some Information Theory Tools

Slepian-Wolf Theorem: Coding Scheme (5/7)

Source X assigns every sourceword x ∈ X n randomly among 2nR1 bins, and source Y independently assigns every sourceword y ∈ Yn randomly among 2nR2 bins Each sends the bin index corresponding to the message The receiver decodes correctly if there is exactly one jointly typical sourceword pair corresponding to the received bin indexes, otherwise it declares error.

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Some Information Theory Tools

SW Theorem: Error Analysis (6/7)

Error events: The transmitted sourcewords are not jointly typical: E0 = {(X, Y) / ∈ A(n)

ǫ }

There exists another pair of jointly typical sourcewords in the same pair of bins, i.e. one or more of the following events E1 = {∃x′ = X : f1(x′) = f1(X), (x′, Y) ∈ A(n)

ǫ }

E2 = {∃y′ = Y : f2(y′) = f2(Y), (X, y′) ∈ A(n)

ǫ }

E12 =

• ∃(x′, y′) : x′ = X, y′ = Y, f1(x′) = f1(X), f2(y′) = f2(Y),

(x′, y′) ∈ A(n)

ǫ

• Using union of events bound:

P(n)

e

= Pr(E0 ∪ E1 ∪ E2 ∪ E12) ≤ Pr(E0) + Pr(E1) + Pr(E2) + Pr(E12).

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Some Information Theory Tools

SW Theorem: Error Analysis (7/7)

Pr(E0) → 0 by the AEP, Pr(E1) =

• (x,y)

p(x, y)P{∃x′ = x : f1(x′) = f1(x), (x′, y) ∈ A(n)

ǫ }

≤

• (x,y)

p(x, y)

• x′=x

(x′,y)∈A(n)

ǫ

P(f1(x′) = f1(x)) =

• (x,y)

p(x, y)2−nR1|Aǫ(X|y)| ≤ 2−nR12n(H(X|Y)+2ǫ) = 2−n(R1−H(X|Y)−2ǫ) → if R1 > H(X|Y) Similarly, Pr(E2) ≤ 2−nR22n(H(Y|X)+2ǫ) → 0 if R2 > H(Y|X) Pr(E12) ≤ 2−n(R1+R2)2n(H(X,Y)+ǫ) → 0 if R1 + R2 > H(X, Y)

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Some Information Theory Tools

Rate-Distortion Theory (1/7)

Goal: Rate-distortion theory calculates minimum transmission bit-rate R for a given distortion D and source. Determine the minimum rate at which information about the source must be conveyed to the sink in order to achieve a prescribed fidelity. Question 1: Given a random binary variable X, how well can one encode strings of length n with less than nH(X) bits.

Compression that tries to go below Shannon’s limit → Lossy Data Compression

Question 2: Consider a continuous random variable; how well can we encode this information using bits?

Digitizing of Analog signals → Quantization

For both cases, the optimal trade-off between the information rate and the inevitable distortion: Rate Distortion Theory

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Some Information Theory Tools

Rate-Distortion Theory: Geometric View (2/7)

Figure: A Geometric Representation of Rate-Distortion Theory.

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Some Information Theory Tools

Rate-Distortion Theory: Distortion (3/7)

The distortion between sequences xn and ˆ xn is defined by d(xn;ˆ xn) = 1 n

n

• i=1

d(xi;ˆ xi) In other words, it is the distortion per symbol. The analysis here is based on this average distortion measure between sequences. A distortion function or distortion measure is a mapping d : X × ˆ X → R+ ∪ {0} from the set of source-reproduction pairs into the set of non-negative real numbers. Squared Error distortion function: d(x,ˆ x) = (x − ˆ x)2

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Some Information Theory Tools

Rate-Distortion Code (4/7)

A (2nR, n) rate distortion code consists of an encoding function fn : X → {1, 2, . . . , 2nR}, and a decoding function gn : {1, 2, . . . , 2nR} → ˆ X, The distortion associated with this code is D = E[d(Xn, gn(fn(Xn)))] =

• xn

p(xn)d(xn, gn(fn(xn))).

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Some Information Theory Tools

Codebook and Vector Quantization (5/7)

f −1

n (1), f −1 n (1), . . . , f −1 n (2nR) are called the assignment regions;

i.e., f −1

n (k) is the region associated with index k.

ˆ Xn(1), . . . , ˆ Xn(2nR) constitute the codebook. Any X in region k is represented by the code point ˆ Xn(k). D is the averaged distortion between Xn and ˆ Xn. A rate-distortion pair (R, D) is achievable if there exists a sequence of (2nR, n) rate-distortion codes such that lim

n→∞ E[d(Xn, gn(fn(Xn)))]

≤ D.

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Some Information Theory Tools

Information Rate-Distortion Function (6/7)

Given a source X ∼ p(x) and a distortion measure d(x,ˆ x), and any D ≥ 0 R(I)(D) = min

p(ˆ x|x):Ed(X,ˆ X)≤D

I(X; ˆ X) i.e. minimize I(X; ˆ X) over all reproduction sets ˆ X which satisfy

• x
• ˆ

x

d(x,ˆ x)p(ˆ x|x)p(x) ≤ D

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Some Information Theory Tools

Example: Gaussian Source (7/7)

Gaussian source with X ∼ N(0, σ2) Mean Square Error (MSE) distortion measure: D = E[(x − ˆ x)2] R(D) = 1 2 log2 σ2 D

• ,

D ≥ 0 D(R) = σ22−2R, R ≥ 0 Each additional bit reduces average distortion by a factor of 4 The R(D) for non-Gaussian sources with the same variance σ2 is always below Gaussian R(D) curve. For R = 1 (1 bit quantization), D(R = 1) = 0.25σ2. Consider 1-D (scalar) quantization (n = 1) ⇒ Ed(X, ˆ X) = 0.3633σ2 Why a gap ? ⇒ Achievability proof requires n → ∞

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Outer Bounds Achievable Rates for PaReNet Numerical Results

Parallel Relay Networks with Phase Fading

Figure: Parallel Relay Network setup with phase fading

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Outer Bounds Achievable Rates for PaReNet Numerical Results

Parallel Relay Networks: Signal Model

The received signals at the relays and the destination, respectively, Yi,k = AiejΦ1i,kXk + Zi,k, i = 1, 2 Yk =

2

• i=1

BiejΦ2i,kXi,k + Z3,k, fork = 1, 2, . . . , n Full-duplex Relay Nodes Channel is memoryless and undergoes Ergodic Phase Fading (Φn

ti) and Path-Loss (Ai, Bi)

Ps and Pr are the source and relay power constraints Φn

ti are RVs uniformly distributed over [−π; π], perfectly known

to the relevant receiver and unknown to the transmitter

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Outer Bounds Achievable Rates for PaReNet Numerical Results

Outline

1

Introduction Some Information Theory Tools

2

Parallel Relay Networks (PaReNet) Outer Bounds Achievable Rates for PaReNet

Amplify-and-Forward (AF) Relaying Decode-and-Forward (DF) Relaying Block-Quantization and Random Binning (BQRB)

Numerical Results

3

Cellular Networks with Relay Nodes: An Implementation Single Cell System Model

Numerical Results: Single-Cell Relaying

Multi-Cell Relaying

Numerical Results: Multi-Cell Relaying

4

Summary and Outlook

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Outer Bounds Achievable Rates for PaReNet Numerical Results

Outer Bounds (Converse Analyasis) (1/2)

˜ Yn = (Yn, Φn

11, Φn 12, Φn 21, Φn 22), ˜

Yn

1 = (Yn 1, Φn 11) and ˜

Yn

2 = (Yn 2, Φn 12)

The source messages are chosen uniformly over W ∈ {1, 2, . . . , 2nR} nR = H(W) = I(W; ˜ Yn) + H(W|˜ Yn) (1)

(a)

≤ I(W; ˜ Yn) + nǫn

(b)

≤ I(Xn; ˜ Yn) + nǫn (2)

(c)

≤

n

• i=1

I(Xi; ˜ Yi) + nǫn (3)

(d)

≤ nCnet + nǫn. (4) X(W) → (˜ Y1, ˜ Y2) → (X1, X2) → ˜ Y forms a Markov chain γr,i =

A2

i Ps

N

and γd,i =

B2

i Pri

N

for i = 1, 2. For a symmetric network: Ai = A, Bi = B, Pri = Pr, hence γr,i = γr and γd,i = γd.

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Outer Bounds Achievable Rates for PaReNet Numerical Results

Outer Bounds (Converse Analyasis) (2/2)

The network capacity is given by Cnet = sup

f(Xn)

1 nI(Xn; Yn). BC and MAC upper bounds, respectively, 1 nI(Xn; Yn) ≤ 1 nI(Xn; ˜ Yn) ≤ 1 nI(Xn; ˜ Yn

1, ˜

Yn

2),

(5) 1 nI(Xn; Yn) ≤ 1 nI(Xn; ˜ Yn) ≤ 1 nI(Xn

1, Xn 2; ˜

Yn). (6) Then we have following cut-set bound Cnet ≤ 1 n min

• I(Xn; ˜

Yn

1, ˜

Yn

2), I(Xn 1, Xn 2; ˜

Yn)

• (7)

= min {log2 (1 + 2γr) , log2 (1 + 2γd)} . (8)

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Outer Bounds Achievable Rates for PaReNet Numerical Results

Outline

1

Introduction Some Information Theory Tools

2

Parallel Relay Networks (PaReNet) Outer Bounds Achievable Rates for PaReNet

Amplify-and-Forward (AF) Relaying Decode-and-Forward (DF) Relaying Block-Quantization and Random Binning (BQRB)

Numerical Results

3

Cellular Networks with Relay Nodes: An Implementation Single Cell System Model

Numerical Results: Single-Cell Relaying

Multi-Cell Relaying

Numerical Results: Multi-Cell Relaying

4

Summary and Outlook

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Outer Bounds Achievable Rates for PaReNet Numerical Results

Amplify-and-Forward (AF)

Assuming symmetric network The scaling factors at the relay nodes α =

• Pr

A2Ps+N .

The received SNR is given by γAF = 2γrγd(1 + cos(Φ11 + Φ21 − (Φ12 + Φ22))) γr + 2γd + 1 The corresponding AF achievable rate: RAF = EΦ {log2 (1 + γAF)} (9) ≤ log2

• 1 +

2γrγd γr + 2γd + 1

• .

(10)

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Outer Bounds Achievable Rates for PaReNet Numerical Results

Decode-and-Forward (DF)

Assuming symmetric network In BC part, transmitted message from the source node can be decoded by both relay nodes if RBC

DF

≤ 1 n min{I(Xn(W); Yn

1), I(Xn(W); Yn 2)}

(11) ≤ log2 (1 + γr) . (12) At the relays we send independent signals which can be implemented using a (distributed) space-time code, yielding the following relay-to-destination rate RMAC

DF

≤ 1 nI (Xn

1(W), Xn 2(W); Yn) ≤ log2 (1 + 2γd) .

(13) The end-to-end system achievable rate for DF: RDF = min {log2 (1 + γr) , log2 (1 + 2γd)} . (14) If γr ≥ 2γd then DF achievable rate is the capacity of the network

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Outer Bounds Achievable Rates for PaReNet Numerical Results

Block-Quantization and Random Binning (BQRB)

Figure: Block diagrams for Block-Quantization and Slepian-Wolf Encoding

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Outer Bounds Achievable Rates for PaReNet Numerical Results

BQRB: Introduction

Without phase fading using AF relaying mode achieves the network capacity if the MAC part is strong enough due to the coherent combining effect [Schein02] We shown that for phase fading Gaussian networks using AF relaying cannot achieve the network capacity even for high SNR values at the MAC part Goal: To find an achievable scheme that mimics multiple-antenna reception performance in the sense that the destination jointly processes the representations of the relay received signals At the destination there are two decoding steps:

The first is channel decoder for the relay Bin Indexes corresponding to the representations of the relay observations The second one is the source message decoding

Note that if there is an error in the first decoding step, we declare an error for the source message

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Outer Bounds Achievable Rates for PaReNet Numerical Results

BQRB: Theorem

Theorem: For the parallel relay network with Gaussian phase fading memoryless

broadcast channel f(y1, y2|x) and broadcast channel f(y|x1, x2). Choose any probability density function f(x) and any pair of conditional densities f(v1|y1) and f(v2|y2). We can reliably achieve rate Rach Rach ≤ I(X; V1, V2), (15) provided I(Y1; V1) − I(V1; V2) ≤ R1 ≤ I(X1; Y|X2), (16) I(Y2; V2) − I(V1; V2) ≤ R2 ≤ I(X2; Y|X1), (17) I(Y1; V1) + I(Y2; V2) − I(V1; V2) ≤ R1 + R2 ≤ I(X1, X2; Y). (18) These values are computed with respect to the density f(x, y1, y2, v1, v2, x1, x2, y) = f(x) f(y1, y2|x) f(v1|y1) f(v2|y2) f(x1|v1) f(x2|v2) f(y|x1, x2).

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Outer Bounds Achievable Rates for PaReNet Numerical Results

BQRB: Achievability (Roughly) (1/2)

Randomly generate 2nRach input codewords of block length n using the input density f(x) Randomly generate Vn

1(j), j = 1, 2, . . . , 2n(I(Y1;V1)+δ)

quantization codewords of block length n for Relay-1 using the marginal density f(v1) Having randomly generated the Relay-1 quantization codebook, randomly and uniformly assign each Relay-1 quantization codeword, vn

1, to one of B1 ∈ {1, 2, . . . , 2nR1} bins. Denote the

randomly chosen bin assignments by the function B1 = ϕ1(vn

1(j))

Independently generate Xn

1(B1), B1 ∈ {1, 2, . . . , 2nR1}

codewords of length n using the density f(x1) Similar steps hold for Relay-2

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Outer Bounds Achievable Rates for PaReNet Numerical Results

BQRB: Achievability (Roughly) (2/2)

Upon receiving Y1, Relay-1 looks for any quantization codeword that is jointly typical with Y1

If one is found, Relay-1 sends the appropriate index to the decoder The rate-distortion theorem, such a quantization codeword exists with high probability provided we generate more than 2nI(Y1;V1) quantization codewords Able to choose the Relay-1 quantization map f(v1|y1) that achieves the rate-distortion function for the observation source Y1

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Outer Bounds Achievable Rates for PaReNet Numerical Results

BQRB: Example (1/3)

Assume the relays first phase compensated the received signals Then, the relays generate the quantized codewords according to the distribution f(vi|yi) ∼ CN(yi, Di) Vi = Y′

i + Zd,i = AiX + Z′ i + Zd,i

where Z′

i = e−jΦiZi ∼ CN(0, N) and Zd,i ∼ CN(0, Di) for

i = 1, 2 With these settings we have Rach ≤ log2

• 1 +

A2

1Ps

N + D1 + A2

2Ps

N + D2

• eY

Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Outer Bounds Achievable Rates for PaReNet Numerical Results

BQRB: Example (2/3)

Provided that log2

• σ2

v1

D1 (1 − ρ2)

• ≤ R1 ≤

log2 (1 + γd,1) log2

• σ2

v2

D2 (1 − ρ2)

• ≤ R2 ≤

log2 (1 + γd,2) log2

• σ2

v1

D1 σ2

v2

D2 (1 − ρ2)

• ≤ R1 + R2 ≤

log2 (1 + γd,1 + γd,2) where ρ is the correlation factor between V1 and V2, and σ2

vi = A2 i Ps + N + Di,

for i = 1, 2.

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Outer Bounds Achievable Rates for PaReNet Numerical Results

BQRB: Example (3/3)

For the symmetric case, Di = D, and Ri = R for i = 1, 2, after some algebra we can lower bound D as D ≥ N

• 1 + γr +
• (1 + γr)2 + 4γrγd + 2γd
• 2γd

. The corresponding achievable rate Rach ≤ log2

• 1 + 2A2Ps

N + D

• =

log2  1 + 2γr 1 + 1+γr+√

(1+γr)2+4γrγd+2γd 2γd

 

γd→∞

− → log2 (1 + 2γr) (the capacity!).

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Outer Bounds Achievable Rates for PaReNet Numerical Results

Outline

1

Introduction Some Information Theory Tools

2

Parallel Relay Networks (PaReNet) Outer Bounds Achievable Rates for PaReNet

Amplify-and-Forward (AF) Relaying Decode-and-Forward (DF) Relaying Block-Quantization and Random Binning (BQRB)

Numerical Results

3

Cellular Networks with Relay Nodes: An Implementation Single Cell System Model

Numerical Results: Single-Cell Relaying

Multi-Cell Relaying

Numerical Results: Multi-Cell Relaying

4

Summary and Outlook

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Outer Bounds Achievable Rates for PaReNet Numerical Results

Numerical Results

5 10 15 20 25 30 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 γd [dB] Average Rate [bits/sec/Hz] Symmetric phase fading parallel relay network with γr = 10 [dB] Upper Bound AF DF BQ + Binning

Figure: Symmetric parallel Gaussian phase fading relay network average rates with γr = 10[dB].

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Single Cell System Model Multi-Cell Relaying

Outline

1

Introduction Some Information Theory Tools

2

Parallel Relay Networks (PaReNet) Outer Bounds Achievable Rates for PaReNet

Amplify-and-Forward (AF) Relaying Decode-and-Forward (DF) Relaying Block-Quantization and Random Binning (BQRB)

Numerical Results

3

Cellular Networks with Relay Nodes: An Implementation Single Cell System Model

Numerical Results: Single-Cell Relaying

Multi-Cell Relaying

Numerical Results: Multi-Cell Relaying

4

Summary and Outlook

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Single Cell System Model Multi-Cell Relaying

Relaying for Cellular Networks

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Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Single Cell System Model Multi-Cell Relaying

Single-Cell Network with Relaying

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Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Single Cell System Model Multi-Cell Relaying

Single Cell System Model

K MSs want to communicate with the BTS through the N RSs: No direct-link All terminals are assumed to be equipped with single antennas At the first hop (from the MSs to the RSs) between MS k and RS i, hik = √ Υik ˜ hik where ˜ hik is an i.i.d complex Gaussian RV with CN(0, 1) and Υik is the parameter representing channel gain from k-th MS to i-th RS. In the second hop (from the i-th relay to the BTS), gi = √ GiejΦi, i = 1, 2, . . . , N where Gi is channel gain (or path-loss component) and Φi is ergodic phase fading with uniform distribution over [−π, π]

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Single Cell System Model Multi-Cell Relaying

Single Cell Relaying: Assumptions

Communication between each of the N relays to the BTS without cross interference A set of N highly directive beams at the BTS, each one being directed to a distinct relay The BW allocated to the first hop is W1 and to the second hop is W2, F = W2/W1 ∈ N +. Frequency division duplex (FDD) relaying: Orthogonal frequencies at the first and the second hop communications. AF and CF relaying strategies are considered

For CF we mean only Block-Quantization For AF BW expansion (F > 1) is not needed; instead we increase relays TX power by a factor of F!

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Single Cell System Model Multi-Cell Relaying

Which System Models ?

We compare for UL: Conventional Cellular System

Where the BTS has K co-located antennas No Shadowing Diversity Gain

Distributed Antenna System (DAS)

Where the BTS has K distributed antennas Perfect link between the distributed antennas and the BTS Shadowing Diversity Gain

Cellular System with Relaying

AF and CF relaying strategies Relay nodes have GOOD wireless links to the BTS Mimics MIMO system when the links between the relays to the BTS is GOOD.

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Single Cell System Model Multi-Cell Relaying

Single Cell Relaying: Simulation Parameters

The cell radius is taken R = 1km, RSs are places circularly and uniformly around the BTS at a distance of 0.5km. N = 3 RSs and K = 3 MSs are present in the cellular system Channel gains includes path-loss, shadowing and antenna gain terms which is given by Υi,k(dB) = −PLi,k(dB) + GTX + GRX + ξ GTX = 16[dB] is the TX antenna gain, GRX = 4[dB] is the RX antenna gain, and the Log-normal shadowing, ξ ∼ N(0dB, 8dB). Path-loss (simplified COST-231 model): PLi,k(dB) = 138 + 39.6 log10(di,k) T = 290K and operation BW (first hop BW) is W1 = 20 MHz

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Single Cell System Model Multi-Cell Relaying

Single Cell Relaying: Simulation Results (1/2)

2 4 6 8 10 12 14 16 18 20 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5x 10

8

γs in [dB] Average Sum Rate [bps] 3 MSs, 3 RSs, γr = 20 [dB], where RSs are placed 0.5 km away from the BTS CONVENTIONAL DISTRIBUTED AF, W

2/W1 = 1

AF, W

2/W1 = 2

AF, W

2/W1 = 3

CF, W

2/W1 = 1

CF, W

2/W1 = 2

CF, W

2/W1 = 3

Figure: The sum-of-rates [bits/sec] versus average received SNR at the BTS from a MS placed on the edge of the cell, γs.

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Single Cell System Model Multi-Cell Relaying

Single Cell Relaying: Simulation Results (2/2)

5 10 15 20 25 30 35 40 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10

8

γr in [dB] Average Sum Rate [bps] 3 MSs, 3 RSs, γs = 10 [dB], where RSs are placed 0.5 km away from the BTS CONVENTIONAL Ideal DAS AF, W

2/W1 = 1

AF, W

2/W1 = 2

AF, W

2/W1 = 3

CF, W

2/W1 = 1

CF, W

2/W1 = 2

CF, W

2/W1 = 3

Figure: The sum-of-rates [bits/sec] versus the average received SNR at the BTS from a RS placed 0.5 km away, γr.

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Single Cell System Model Multi-Cell Relaying

Outline

1

Introduction Some Information Theory Tools

2

Parallel Relay Networks (PaReNet) Outer Bounds Achievable Rates for PaReNet

Amplify-and-Forward (AF) Relaying Decode-and-Forward (DF) Relaying Block-Quantization and Random Binning (BQRB)

Numerical Results

3

Cellular Networks with Relay Nodes: An Implementation Single Cell System Model

Numerical Results: Single-Cell Relaying

Multi-Cell Relaying

Numerical Results: Multi-Cell Relaying

4

Summary and Outlook

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Single Cell System Model Multi-Cell Relaying

Multi-Cell Relaying: Setup

Figure: Multi-Cell case UL with Relaying infrastructure

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Single Cell System Model Multi-Cell Relaying

Multi-Cell Relaying: Assumptions

Square cell layout: 2-Tier (9 cells) 1 user in each sector (for fair comparison) Relay nodes on the corners points 90o degree sectoral antennas at the relay nodes and the BST Conventional, Distributed Antenna System (DAS) and Relay Assisted Systems are compared For system-wide fairness (in terms of cost): On each sector for Conventional System we use 2 antennas!

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Single Cell System Model Multi-Cell Relaying

Multi-Cell Relaying: Numerical Results (1/3)

−10 −5 5 10 15 20 1 1.5 2 2.5 3 3.5 4x 10

8

γs in [dB] Average Sum−of−Rates [bits/sec] 4 MSs, 4 RSs, γr = 20[dB], drd = 1.41 CONV. DIST. AF, W2/W1 = 1 AF, W2/W1 = 2 AF, W2/W1 = 3 CF, W2/W1 = 1 CF, W2/W1 = 2 CF, W2/W1 = 3

Figure: The average sum-of-rates [bits/sec] versus average received SNR at the BTS from a MS placed on the edge of the cell, γs.

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Single Cell System Model Multi-Cell Relaying

Multi-Cell Relaying: Numerical Results (2/3)

−10 −5 5 10 15 20 25 30 35 40 0.5 1 1.5 2 2.5 3 3.5 4 x 10

8

γr in [dB] Average Sum−of−Rates [bits/sec] 4 MSs, 4 RSs, γs = 10[dB], drd = 1.41 CONV. DIST. AF, W2/W1 = 1 AF, W2/W1 = 2 AF, W2/W1 = 3 CF, W2/W1 = 1 CF, W2/W1 = 2 CF, W2/W1 = 3

Figure: The average sum-of-rates [bits/sec] versus the average received SNR at the BTS from a RS placed on the edge of the cell, γr.

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook Single Cell System Model Multi-Cell Relaying

Multi-Cell Relaying: Numerical Results (3/3)

−10 −5 5 10 15 20 25 30 1 2 3 4 5 6x 10

7

γr in [dB] Minimum Average User Rate [bits/sec] 4 MSs, 4 RSs, γs = 10[dB], drd = 1.41 CONV. DIST. AF, W2/W1 = 2 AF, W2/W1 = 3 CF, W2/W1 = 2 CF, W2/W1 = 3

Figure: A Fairness Issue. Average Minimum User Rates versus γr

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook

Summary

A brief summary of SW Encoding and RD Theory Parallel Gaussian Relay Networks with Phase fading

Outer Bounds and Achievable schemes Opposed to Gaussian case, in phase fading case AF is not a capacity achieving scheme For strong relay-to-destination link case: BQRB scheme is proposed BQRB achievable rate is the capacity in strong relay-to-destination links BQRB mimics SIMO system performance

Implementation: Single-Cell and Multi-Cell with Relaying

Conventional System, DAS and AF and CF relaying schemes Relay BW just twice (F = 2) that of the mobile’s BW, the system capacity approaches that of an ideal DAS Ideal DAS is much more fair in terms of Minimum User Rates than Conventional system

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook

Outlook

Multi-Source Multi-Relay Parallel Relay networks: Achievable schemes Adding Random Binning in Cellular Relaying: Is it worth ? Down-Link with good links from the BTS to the relays: Decode-and-Forward What are the best Relay positions ? Adding a Direct-Link between the MSs to the BTS

eY Seminar EURÉCOM 15 May 2008

Introduction Parallel Relay Networks (PaReNet) Cellular Networks with Relay Nodes: An Implementation Summary and Outlook

Thanks...

eY Seminar EURÉCOM 15 May 2008