Opportunistic Multiuser Scheduling for Wireless Channels - NTNU

Opportunistic Multiuser Scheduling for 

Wireless Channels 

Lecture in “Communication Theory for Wireless Channels” 

Vegard Hassel — October 25, 2004 

Opportunistic Multiuser Scheduling for Wireless Channels 1

Outline - I 

• System model 

• What is opportunistic scheduling? 

• Multiuser diversity 

• Scheduling concepts 

• HDR example 

• Calculating MASSE 


Outline - II 

• Scheduling schemes: 

– Algorithms that consider the channel conditions and feedback 

reduction 

– Algorithms that consider fairness 

– Algorithms that consider delay and power 

– Algorithms that consider QoS 

– An algorithm for a MIMO system 

– An algorithm for an OFDM system 

– Relay-aided algorithm 

• Scheduling and cross-layer design 


System Model - I 


System Model - II 

• Time Division Multiplexed (TDM) system 

• Uplink (user transmits) and down-link (user receives) at different 

frequencies 

• N users 

• Most algorithms assume that the users’ carrier-to-noise-ratios (CNR) 

are i.i.d. 


What is Opportunistic Scheduling? 

• The traditional TDM scheduling algorithm has been Round robin 

(GSM) 

– The time-slots are assigned to the users in a sequential manner, 

independently of the channel conditions 

– Resource fair, but not necessary performance fair 

• Opportunistic scheduling exploits the varying quality of the fading 

channel to increase the Maximum Average System Spectral Efficiency 

(MASSE) 

• The future challenge will be to design algorithms that are both 

opportunistic and operates according to the QoS-demands from the 

applications 

• Efficient adaptive modulation and coding is necessary to implement the 

scheduling algorithms 

[1] 


Multiuser Diversity (MUD) 

• Diversity in wireless systems arises because of independently fading 

channels 

• Traditional forms of diversity: space, time and frequency 

• Viswanath and Tse: Multiuser diversity, MUD 

• Background: With many users in a cell, there is high probability of 

finding a user with a good channel at any time 

• MUD concept: To obtain the highest rate, the user with the best 

channel has to be chosen at all times 

• Observe: While traditional forms of diversity gives better link spectral 

efficiency, multiuser diversity increases the system (sum) spectral 

efficiency 

[1] 


Scheduling Concepts 

• Scheduling policy - a rule that specifies which user is allowed to 

transmit and which user is allowed to receive at each time-slot (Q(t)) 

• Feasible - a policy that satisfies the QoS-constraints from all users 

• Throughput optimal - an algorithm that manages to keep all queues 

stable and still fulfill the QoS-requirements 

[2, 3] 


HDR Example - I 

Algorithm implemented in the High Data Rate (HDR) products from 

Qualcomm 

• The channel conditions for each user is independent 

• The channel is GOOD 50% of the time and BAD 50% of the time 

• Two users with bitrates (Markov channel): 

– User 1: 200Mbit/s or 400Mbit/s 

– User 2: 400Mbit/s or 800Mbit/s 

– The users cannot be active at the same time 

• Round robin algorithm without opportunistic scheduling: 

– R1=0.5*(0.5*200Mbit/s+0.5*400Mbit/s)=150Mbit/s 


[3] 


HDR Example - II 

• With opportunistic scheduling, the user that has the GOOD channel 

condition is chosen: 

– 25% of the time both users have BAD channel 

– 50% of the time one user has GOOD channel 

– 25% of the time both users have GOOD channel 

• The user with the relatively best channel is chosen 

• Round robin with opportunistic scheduling: 



• Opportunistic scheduling gives a 17% capacity gain 

• But what if both users need 200Mbit/s? 

[3] 


Calculating the MASSE 

Calculating the Maximum Average System Spectral Efficiency 

(MASSE) 

Optimum rate adaptation (no power adaptation): 

C ora 

W 

∫ ∞ 

= log 2 (1 + γ)p γ ∗(γ) dγ 

0 

Optimum power and rate adaptation: 

C opra 

W 

= ∫ ∞ 

γ 0 

log 2 

( γ 

γ 0 

) 

p γ ∗(γ) dγ, 

where γ 0 is found from the power constraint: 

∫ ∞ 

γ 0 

( 1 

− 1 ) 

p γ ∗(γ) dγ = 1 

γ 0 γ 

[4] 


Algorithms that Consider the Channel Conditions and 

Feedback Reduction 

• Max CNR Scheduling, MCS 

• Analyzing Feedback 

• Selective Multiuser Diversity, SMUD 

• Optimal Rate, Reduced Feedback, ORRF 

• Nested ORRF, NORRF 

• Switched Scheduling Algorithms 

• Inducing Channel Fluctuations 


Rate-Optimal TDM Scheduling - I 

Ride the peaks! 

[5, 6] 


Rate-Optimal TDM Scheduling - II 

The Max CNR scheduling (MCS) policy can be stated as: 

i ∗ (t) = argmax 

1≤i≤N 

γ i (t) 

Equivalently: 


1≤i≤N 

R i (t) 

• Also called the greedy algorithm 

• Only fair if the users’ CNRs are i.i.d. (dependent on coherence time) 

• Only rate-optimal if the capacity degradation due to feedback is ignored 

[5] 


Rate-Optimal TDM Scheduling - III 

The cumulative distribution of the best user is found by using order 

statistics: 

P γ ∗(γ) = P N γ (γ), 

The probability density function (PDF) of the best user is found by 

differentiating the cumulative distribution function (CDF) with respect to 

γ: 

p γ ∗(γ) = N · Pγ 

N−1 (γ) · p γ (γ), 

For a Rayleigh channel we get the following PDF: 

p γ ∗(γ) = N · (1 − e −γ/γ ) N−1 · e−γ/γ 

γ 

To make integration easier, it is often preferable to use binomial 

expansion: 

[5] 

p γ ∗(γ) = N γ 

N−1 

∑ 

n=0 

( N − 1 

n 

) 

(−1) n e −(1+n)γ/γ 


Rate-Optimal TDM Scheduling - IV 

[5] 


Analyzing Feedback 

• The MCS algorithm assumes that each user feeds back its CNR for 

every time-slot 

• We will look at how to reduce the feedback load of the MCS algorithm 

• Normalized Feedback load (NFL) is defined as the average ratio of users 

that give feedback for every time-slot 

• To analyze the feedback in depth it is also interesting to investigate the 

feedback rate, i.e. the number of bits that are fed back for every 

time-slot 


SMUD: Selective Multiuser Diversity - I 

• Algorithm that reduces the feedback load by using a CNR threshold 

• The scheduler asks for the instantaneous CNR level only from the users 

that have CNR above a threshold, γ th 

• If none of the users feed back their CNR, a random user is chosen 

• The algorithm is not rate-optimal, but gives a significant reduction in 

the feedback load 

i ∗ (t) = 

⎧ 

⎨ 

⎩ 

rand(i), 

argmax 

1≤i≤N 

γ i (t), 

if all γ i (t) ≤ γ th 

if it exists a γ i (t) > γ th 

[7] 


SMUD: Selective Multiuser Diversity - II 

CDF: 

P γ ∗(γ) = 

{ 

P 

N−1 

γ (γ th ) · P γ (γ), γ ≤ γ th 

Pγ N (γ), 

γ > γ th 

PDF can be found by differentiating the CDF with respect to γ: 

p γ ∗(γ) = 

{ 

P 

N−1 

γ (γ th ) · p γ (γ), γ ≤ γ th 

N · Pγ N−1 (γ) · p γ (γ), γ > γ th 

The NFL for the SMUD algorithm can be shown to be given by: 

¯F = 1 − P γ (γ th ) 

[7] 


SMUD: Selective Multiuser Diversity - III 

[7] 


ORRF: Optimal-Rate, Reduced Feedback - I 

• Based on the SMUD algorithm 

• If all users fail to meet the CNR threshold value, the base station 

requests full feedback 

• Obtains optimal rate, but has a significant reduction in feedback 

• Disadvantage: Needs more time to collect feedback information (guard 

interval) 

[7, 8] 


ORRF: Optimal-Rate, Reduced Feedback - II 

[8] 


ORRF: Optimal-Rate, Reduced Feedback - III 

For the ORRF algorithm, it can be shown that the normalized average 

feedback load can be expressed as: 

¯F = 1 − P γ (γ th ) + P N γ (γ th ), N = 2, 3, 4, · · · 

Differentiating this expression with regard to γ th and setting the expression 

equal to zero gives the optimal threshold value: 

γ ∗ th = P −1 

γ ∗ 

( ( 1 

N 

) 1 

) 

N−1 

, N = 2, 3, 4, · · ·, 

For a Rayleigh channel this expression is given as: 

γ ∗ th = −γ ln(1 − (1/N) 1 

N−1), N = 2, 3, 4, · · ·, 

[8] 


ORRF: Optimal-Rate, Reduced Feedback - IV 

[8] 


ORRF: Optimal-Rate, Reduced Feedback - V 

Delays can be analyzed using two different scenarios: 

• Scenario 1: Scheduling delay: 

– Arises because the scheduler received channel estimates, takes a 

scheduling decision and notifies the selected user 

– The selected user transmits using a constellation size based on a 

channel estimate without delay 

– When the user is transmitting, it doesn’t necessarily have to be the 

best anymore. Therefore, we will experience a degradation in MASSE 

compared to the optimal rate 

[8] 


ORRF: Optimal-Rate, Reduced Feedback - VI 

• Scenario 2: Outdated channel estimates: 

– Leads to both a scheduling delay and suboptimal modulation 

constellations with increased BER 

– Both the scheduling decision and the decision of the modulation 

constellation is based on an outdated channel estimate 

– The selected user experiences a CNR degradation, but does not adjust 

its modulation constellation accordingly (as for the previous scenario) 

– The rate is not lowered, but the BER will increase with the degree of 

outdatedness 

[8] 


ORRF: Optimal-Rate, Reduced Feedback - VII 

[8] 


ORRF: Optimal-Rate, Reduced Feedback - VIII 

[8] 


NORRF: Nested ORRF - I 

• Employs multiple (nested) feedback thresholds 

• Denoting the thresholds by γ th,L >γ th,L−1 > · · ·>γ th,0 (γ th,L = ∞ and 

γ th,0 = 0) 

• The base station initially requests feedback from those users whose 

CNR is above γ th,L−1 . If there are none, the threshold is successively 

lowered to γ th,L−2 , γ th,L−3 , · · ·, γ th,0 

• The best user is always selected, but the average feedback load is 

significantly reduced compared to the MCS algorithm 

[9] 


NORRF: Nested ORRF - II 

For the NORRF algorithm the feedback load can be expressed as: 

¯F NORRF = 1 N 

L−1 

∑ 

N∑ 

l=0 n=1 

( ) N 

n (P γ (γ th,l+1 ) − P γ (γ th,l )) n · Pγ N−n (γ th,l ) 

n 

Using the binomial expansion formula, it can be shown that this expression 

can be written as: 

¯F NORRF = 

L−1 

∑ 

l=0 

(P γ (γ th,l+1 ) − P γ (γ th,l )) · P N−1 

γ (γ th,l+1 ) 

[9] 


NORRF: Nested ORRF - III 

Taking the gradient of this expression with regard to the thresholds γ th,l 

and setting the result equal to zero yields: 

γ ∗ th,l = P −1 

γ 

(S l · P γ (γ th,l+1 )) , l = 1, 2, 3, · · ·, L−1 

Pγ 

−1 (·) is the inverse CDF of the CNR for a single user 

The expression for S l is: 

S l = 

where N ≥ 2. 

{ 

N 

1 

1−N , l = 1 

[N − (N − 1)S l−1 ] 

1 

1−N , 

l = 2, 3, · · ·, L−1 

[9] 


NORRF: Nested ORRF - IV 

[9] 


Switched Scheduling Algorithms - I 

• Key observation: algorithms originally devised to select between 

antennas in a spatial diversity combiner may also be applied as 

multiuser access schemes 

• The switched algorithms work as follows: 

– The base station probes users in a sequential fashion 

– If a probed user is under a CNR threshold, the next user is probed 

– The probing process continues until a good enough user is found or 

all N users have been checked 

– The sequential probing process is done during a guard interval 

[10] 


Switched Scheduling Algorithms - II 

The expression for the feedback load is the same for all the switched 

algorithms: 

¯F SWITCH = 1 N 

1 − P N γ (γ th ) 

1 − P γ (γ th ) 

[10] 


Switched Scheduling Algorithms - III 

Scan-and-Wait Transmission, SWT 

• The base station probes users in a sequential fashion 

• If the scheduler fails to find a good enough user, there is a deliberate 

outage for one coherence time 

• The PDF can be given by: 

p γSWT (γ) = 

{ 

pγ (γ) 

1−P γ (γ th ) 

γ ≥ γ th 

0 γ < γ th 

p γSWT (γ) = 

{ ∑N−1 

n=0 [P γ(γ th )] n p γ (γ) γ ≥ γ th 

[P γ (γ th )] N−1 p γ (γ) γ < γ th 

[10] 


Switched Scheduling Algorithms - IV 

Switch-and-Examine Transmission, SET 


• If the scheduler fails to find a good enough user, the last probed user is 

chosen to transmit 

p γSET (γ) = 

{ ∑N−1 


[P γ (γ th )] N−1 p γ (γ) γ < γ th 

[10] 


Switched Scheduling Algorithms - V 

SET with Post-Selection, SETps 


• If the scheduler fails to find a good enough user, the best user is chosen 

• Alternative: To increase the short-term fairness, the user which have 

waited the longest time for transmission can be chosen 

p γSETps (γ) = 

{ ∑ N−1 


N[P γ (γ)] N−1 p γ (γ) γ < γ th 

[10] 


Switched Scheduling Algorithms - VI 

[10] 


Switched Scheduling Algorithms - VII 

[10] 


Switched Scheduling Algorithms - VIII 

[10] 


Inducing Channel Fluctuations - I 

• If the channel fluctuations are too small, no MUD gain will be 

experienced 

• This is mainly a problem for static users 

• By using multiple TX-antennas which are fed by a randomly varying 

amplitude and phase, fluctuations can be induced 

• The increase in channel variations for the users, will lead to a higher 

MUD gain 

• Especially efficient when users have different γ 

[1, 11] 


Inducing Channel Fluctuations - II 

[1, 11] 


Inducing Channel Fluctuations - III 

[1, 11] 


Inducing Channel Fluctuations - IV 

[1, 11] 


Inducing Channel Fluctuations - V 

[1, 11] 


Algorithms that Consider Fairness - I 

• General Algorithm 

• Opportunistic Round Robin Algorithm 

• Proportional Fair Algorithm 


Algorithms that Consider Fairness - II 

• Fairness can be seen as: 

– Time-slots are fairly shared between the users 

– Spectral efficiency fairly shared between the users 

• Fairness is always considered with regard to time: 

– Short-term 

– Long-term 


Algorithms that Consider Fairness - III 

General Algorithm with a Short-Term Fairness Constraint 

Optimization problem for window size of M time-slots: 

max 

M−1 

∑ 

t=0 

N∑ 

E[R i (t)I Q(t)=i ] 

i=1 

Subject to the constraint: 

M−1 

∑ 

t=0 

I Q(t)=i ≥ Mφ i 

R i (t): Instantaneous rate in time-slot t 

Q(t): Scheduling policy 

I Q(t)=i : Indicator function which is one when the ith user is chosen and 

zero otherwise 

φ i : The minimum share of time-slots allocated to user i 

[12] 


Algorithms that Consider Fairness - IV 

Opportunistic Round Robin Algorithm 

The optimization problem is a special case of the general algorithm with 

M = N and φ i = 1/N: 

max 

N−1 

∑ 

t=0 

N∑ 

E[R i (t)I Q(t)=i ] 

i=1 

Subject to the constraint: 

N−1 

∑ 

t=0 

I Q(t)=i = 1 

Each user has to be selected once within a time window of N time-slots 

[12, 6] 


Algorithms that Consider Fairness - V 

Proportional Fair Algorithm 

Implemented in Qualcomm’s HDR (CDMA2000/1xEV) standard 

Step 1: Choose the user with the highest relative bit-rate 

Step 2: Update the average rate 

C i (t + 1) = 


1≤i≤N 

( ) 

Ri (t) 

C i (t) 

( 

1 − 1 

t C 

) 

C i (t) + 1 

t C 

R i (t)I Q(t)=i 

C i (t): Average rate over a time window t C 

[13] 


Algorithms that Consider Fairness - VI 

PF-algorithm: tries to serve each user near its peak. 

[11] 


Algorithms that Consider Fairness - VII 

Mobile environment: The channel varies faster 

[11] 


Algorithms that Consider Fairness - VIII 

Mobile environment: 3km/h, Rayleigh fading 

Fixed environment: 2Hz Rician fading with E fixed /E scattered 

[11] 


Algorithms that Consider Delay and Power 

• Analysis of MCS Packet Delay 

• Lazy Scheduler with a Deadline 


MCS Packet Delay 

Packet delay for MCS algorithm assuming constant packet length: 

[14] 


Algorithms that Consider the Tradeoff Energy-Delay - I 

• Trade-off between power and delay 

[15, 16, 17, 18] 


Algorithms that Consider the Tradeoff Energy-Delay - II 

Lazy Scheduler with a Deadline - I 

• The goal is to minimize the transmission energy subject to a delay 

constraint 

• Key observation: in many coding schemes, the energy required to 

transmit a packet can be significantly reduced by lowering transmission 

power and transmitting the packet over a longer period of time 

• Because information often is time-critical, transmission times cannot be 

made arbitrarily long 

• From an optimal offline algorithm (all arrival times known at time 0), a 

lazy online algorithm is devised 

[17, 18] 


Algorithms that Consider the Tradeoff Energy-Delay - III 

Lazy Scheduler with a Deadline - II 

• The lazy algorithm varies transmission times (τ) for packets transmitted 

at time t < T , according to a backlog (b): 

τ(b, t) = 

max 

k∈{1,...,M} 

{ 

1 

k + b 

} 

k∑ 

D i , 

i=1 

where M is the random number of packets that arrive in the time 

interval [0, T ) and D i are the inter-arrival times of the packets. 

[17, 18] 


Algorithms that Consider the Tradeoff Energy-Delay - IV 

Lazy Scheduler with a Deadline - III 

[17, 18] 


Algorithms that Consider QoS - I 

• M-LWDF with a guarantee that the delay is not longer than a threshold 

• M-LWDF with a guarantee that the throughput is not below a threshold 


Algorithms that Consider QoS - II 

M-LWDF: Modified Largest Weighted Delay First 

• Assumes queuing at the base station for each user 

• The following scheduling policy is used: 


1≤i≤N 

(ρ i W i (t)R i (t)) , 

where W i (t) is the head-of-the-line packet delays and ρ i is a constant 

for controlling delay distributions (priority) 

• The algorithms picks the users that have large delays and large 

instantaneous bit-rates 

• It is surprising that such a simple algorithm is throughput optimal 

[3] 


Algorithms that Consider QoS - III 

M-LWDF does not give a dramatical throughput degradation compared to 

the MCS algorithm: 

[19] 


Algorithms that Consider QoS - IV 

M-LWDF: Modified Largest Weighted Delay First 

• The M-LWDF algorithm can be modified to provide minimum 

throughput guarantees 

• The following scheduling policy is used to guarantee minimum 

throughput R i (Leaky bucket?): 


1≤i≤N 

(ρ i W i (t)R i ) , 

where R i is the constant bucket arrival rate for bucket (user) i, W i is 

the delay of the longest delay token in bucket and ρ i is a constant for 

controlling the time-scale on which throughput guarantees are provided 

[3] 


Algorithms for MIMO Systems - I 

We consider a specific algorithm: 

• Each user transmits over a MIMO link 

• The base station induces rapid variation by using a transmission 

randomizing matrix 

• A common pilot is used and each user estimates the mutual information 

between the sender and the transmitter 

• The Proportional fair algorithm is used to schedule the users 

[20, 21] 


Algorithms for MIMO Systems - II 

• Maximum mutual information between sent and received signal 

I(X; Y) = log det(I M + HQH † ) 

• A non–negative definite Q such that I(X; Y) is maximum and 

tr(Q) ≤ P remains to be found 

• H known at the transmitter (“waterfilling solution”): Choose Q 

diagonal, such that 

Q ii = (α − λ −1 

i ) + , i = 1, . . . , N 

with (·) + max(·, 0), (λ 1 , . . . , λ N ) the eigenvalues of H † H and α such 

that ∑ i Q ii = P . The capacity is given by: 

[20, 21] 

N∑ ( 

C WF = log(αλi ) ) + 

[bits/s/Hz] 

i=1 


Algorithms for MIMO Systems - III 

[20, 21] 


Algorithms for OFDM Systems - I 

• N users share M OFDM subchannels 

• Two scheduling algorithms are proposed to reduce the feedback load: 

– Fixed reporting: Each user feeds back the CNRs of K predetermined 

subchannels 

– Best reporting: Each user feeds back the CNRs of the K best 

subchannels 

[22] 


Algorithms for OFDM Systems - II 

[22] 


Relay-Aided Algorithm - I 

[23] 


Relay-Aided Algorithm - II 

• An unfortunate user relays via a fortunate user nearby 

• Both link and system/network capacity is increased 

• Relay or not criterion: 

r ∗ (t) = argmax[min(R s,r , R r,d )] 

r 

Direct mode when r = d and relaying when r ≠ d 

[23] 


Embedded Modulation and Scheduling - I 

• Way to increase system capacity for downlink transmission 

• Because of fairness constraints, it may be necessary to serve a user with 

low CNR 

• The base station transmits to this user with a small modulation 

constellation 

• By using embedded modulation, the base station can transmit to a user 

with a higher CNR at the same time 

[24] 


Embedded Modulation and Scheduling - II 

[24] 


Embedded Modulation and Scheduling - III 

[24] 


Scheduling and Cross-Layer Design - I 

TCP/IP-layers: 

• Application 

• Transport (TCP, UDP) 

• Internet (IP) 

• Network access (MAC, LLC) 

• Physical 

[25, 26] 


Scheduling and Cross-Layer Design - II 

Today: Some adaptation between neighbouring layers. 

Tomorrow: Network stack that take advantage of the interdependencies 

between the layers. 

Variations follow different time scales: 

• SNR variations ~ microseconds 

• Congestion of packets ~ seconds 

• Cumulative user traffic ~ 10-100 seconds 

Goldsmith: Because of the different timescales, adaptation between layers 

is reasonable only if problems cannot be fixed locally within a layer. 

[25, 26] 


References 

[1] P. Viswanath, D. N. C. Tse, and R. Laroia, “Opportunistic beamforming using dumb antennas,” IEEE Trans. Inform. 

Theory, vol. 48, pp. 1277–1294, June 2002. 

[2] X. Liu, E. K. P. Chong, and N. B. Shroff, “A framework for opportunistic scheduling in wireless networks,” in Computer 

Networks Journal (Elsevier), vol. 41, pp. 451–474, 2003. 

[3] M. Andrews, K. Kumaran, K. Ramanan, A. Stolyar, P. Whiting, and R. Vijayakumar, “Providing quality of service over a 

shared wireless link,” IEEE Communications Mag., pp. 150–154, Feb. 2001. 

[4] A. J. Goldsmith and P. P. Varaiya, “Capacity of fading channels with channel side information,” IEEE Trans. Inform. 

Theory, vol. IT-43, pp. 1896–1992, Nov. 1997. 

[5] R. Knopp and P. A. Humblet, “Information capacity and power control in single cell multiuser communications,” in IEEE 

Int. Conf. on Communications (ICC’95), (Seattle, WA), pp. 331–335, June 1995. 

[6] M. Johansson, “Issues in multiuser diversity.” 

http://www.signal.uu.se/Research/PCCWIP/Visbyrefs/Johansson Visby04.pdf. Presentation at 

WIP/BEATS/CUBAN workshop Wisby, Sweden, Aug. 2004. 

[7] D. Gesbert and M.-S. Alouini, “How much feedback is multi-user diversity really worth?,” in IEEE Int. Conf. on 

Communications (ICC’04), (Paris, France), pp. 234–238, June 2004. 

[8] V. Hassel, M.-S. Alouini, G. E. Øien, and D. Gesbert, “Rate-optimal multiuser scheduling with reduced feedback load and 

analysis of delay effects.” Submitted to IEEE Int. Conf. on Comm. (ICC’05), (Seoul, South Korea), May 2005. 

[9] V. Hassel, M.-S. Alouini, D. Gesbert, and G. E. Øien, “Minimizing feedback load for nested scheduling algorithms.” 

Submitted to IEEE Veh. Tech. Conf. (VTC’05-spring), (Stockholm, Sweden), May 2005. 

[10] B. Holter, M.-S. Alouini, G. E. Øien, and H.-C. Yang, “Multiuser switched diversity transmission.” Accepted for IEEE Veh. 

Tech. Conf. (VTC’04-spring), (Los Angeles, CA), Sept. 2004. 

[11] D. Tse, “Opportunistic communication: Smart scheduling and dumb antennas.” 

http://www.eecs.berkeley.edu/~dtse/intel128.pdf. Presentation at Intel Jan. 2004. 

[12] S. S. Kulkarni and C. Rosenberg, “Opportunistic scheduling policies for wireless systems with short term fairness 

constraints,” in IEEE Global Communications Conf. (GLOBECOM), (San Francisco, CA), pp. 533–537, Dec. 2003. 

[13] J. M. Holtzman, “Asymptotic analysis of proporional fair algorithm,” in Proc. IEEE Symp. on Personal, Indoor and Mobile 

Radio Communications (PIMRC), vol. 2, (San Diego, CA), pp. F–33–F–37, Sept. 2001. 


[14] P. Liu, R. Berry, and M. L. Honig, “Delay-sensitive packet scheduling in wireless networks,” in IEEE Wireless 

Communications and Networking Conf., vol. 3, (New Orleans, LA), pp. 1627–1632, Mar. 2003. 

[15] R. A. Berry and R. G. Gallager, “Communication over fading channels with delay constraints,” IEEE Trans. Inform. Theory, 

vol. 48, pp. 1135–1149, May 2002. 

[16] M. Agarwal and A. Puri, “Base station scheduling of requests with fixed deadlines,” in IEEE Joint Conference of the 

Computer and Communications Societies (INFOCOM), vol. 2, (New York, NY), pp. 487–496, June 2002. 

[17] B. Prabhakar, E. Uysal-Biyikoglu, and A. E. Gamal, “Energy-efficient transmission over a wireless link via lazy packet 

scheduling,” in IEEE Joint Conference of the Computer and Communications Societies (INFOCOM), (Anchorage, AK), 

pp. 386–394, Apr. 2001. 

[18] E. Uysal-Biyikoglu, B. Prabhakar, and A. E. Gamal, “Energy-efficient packet transmission over a wireless link,” IEEE/ACM 

Trans. on Networking, vol. 10, pp. 487–499, Aug. 2002. 

[19] K. Kim, I. Koo, S. Sung, and K. Kim, “Multiple qos support using m-lwdf in ofdma adaptive resource allocation,” in IEEE 

Workshop on Local and Metropolitan Area Networks (LANMAN’04), (San Francisco, CA), pp. 217–222, Apr. 2004. 

[20] T. L. Liang Dong and Y.-F. Huang, “Opportunistic transmission scheduling for multiuser MIMO systems,” in IEEE Int. 

Conf. on Acoustics, Speech, and Signal Proc. (ICASSP), vol. 5, (Hong Kong), pp. V65–V68, Apr. 2003. 

[21] S. de la Kethulle, “An overview of MIMO systems in wireless communications.” Lecture in Communication Theory for 

Wireless Channels, NTNU, Sept. 2004. 

[22] J. Moon and Y.-H. Lee, “Performance analysis of opportunistic scheduling with partial channel information.” Submitted to 

IEEE Trans. on Wireless Comm. 

[23] M. Hu and J. Zhang, “Two novel schemes for opportunistic multi-access,” in IEEE Workshop on Multimedia Signal 

Processing (MMSP), (St. Thomas, US Virgin Islands), pp. 412–415, Dec. 2002. 

[24] L. M. C. Hoo, J. Tellado, and J. M. Cioffi, “Multiuser loading algorithms for multicarrier systems with embedded 

constellations,” in IEEE Int. Conf. on Communications (ICC’00), vol. 2, (New Orelans, LA), pp. 1115–1119, June 2000. 

[25] S. Shakkottai, T. S. Rappaport, and P. C. Karlsson, “Cross-layer design for wireless networks,” IEEE Communications Mag., 

vol. 41, pp. 74–80, Oct. 2003. 


[26] A. J. Goldsmith and S. B. Wicker, “Design challenges for energy-constrained ad hoc wireless networks,” IEEE Wireless 

Communications, vol. 9, pp. 8–27, Aug. 2002.

Opportunistic Multiuser Scheduling for Wireless Channels - NTNU

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?