Traditionally, diversity techniques such as frequency, space and time diversity are used to mitigate the fading introduced in wireless links. Multi-user diversity techniques; on the other hand, provide diversity by exploiting the channel fading rather than compensating it. At any given time, a user with the highest transmission quality in terms of the signal to noise ratio, is granted access to the channel. This diversity can be deployed in point to multi-point links unlike previous diversity schemes, which are specific to point to point links.
In this survey, I have discussed three important multi-user diversity techniques namely; opportunistic beam-forming using dumb antennas, selective multi-user diversity and multi-user diversity based on switched multi-user access schemes and studied their system models and working in detail. In order to compare these techniques, I have selected four crucial parameters; average spectral efficiency (ASE), average feedback load (AFL), fairness of scheduling among the users and diversity gain improvement .I have tabulated my analysis in the last section of this report. The analysis shows that none of the three techniques can be considered the best, as there is an inherent tradeoff between the parameters defined above.
1. Introduction
Wireless channels are time-varying due to the multipath fading phenomenon. Traditionally, channel fading is viewed as a destructive factor that reduces the communication reliability. An effective way to combat fading is to obtain multiple independent replicas of the transmitted signal at the receiver by means of diversity. Time, frequency and spatial diversity compensate fading for point to point links.
In a wireless network, independent paths between a base station and individual users form a new type of diversity. Recent studies on this multiuser diversity were motivated by Knopp and Humblet who showed in [1] that the total uplink (mobile to base) capacity can be maximized by picking the user with the best channel to transmit. Essentially, independent variations of channels for many users make it very likely that the communication always occurs over a strong channel. As such, the system throughput can benefit from the randomness due to the fading effect. The study of [1] was extended in [2] which showed that the same access scheme is valid also for the downlink case. Such type of diversity can be used for point to multi-point links.
The multi-user diversity techniques can be categorized as: selective multi-user diversity techniques, opportunistic beam-forming using dumb antennas and multi-user diversity based on switched multi-user access schemes. The techniques differ in the user selection criterion and the amount of feedback provided to the base station and can be used in the uplink or downlink channel of a cellular system.
The aim of this survey is to analyze and compare the different multi-user diversity techniques to find out how these different techniques perform under different parameters. Therefore, I have selected some crucial parameters to base my survey on. These parameters include the average feedback load, average spectral efficiency, fairness of scheduling among users and the diversity gain.
The rest of the report is organized as follows. Section 2 discusses each of the multi-user diversity techniques in detail. Section 3 gives a detailed analytical comparison of the three techniques based on the selected parameters using the simulations and results of the studied papers and tabulates the analysis. Section 4 concludes the report.
2. Multi-User Diversity Techniques
In this section, I have discussed the three multi-user diversity techniques by describing their system model and working.
2.1 Opportunistic beam-forming using dumb antennas
This diversity technique induces random fading in the channel when the environment has little scattering and/or the fading is slow. After the channel fluctuations are induced, they are exploited for multi-user diversity.
2.1.1 System model
The scheme utilizes the downlink of the cellular system. Multiple dumb antennas are used at the base station while the receiver uses single antenna. The antennas are dumb as the receivers are completely ignorant of the fact that there are multiple transmit antennas; moreover, no additional processing is required at the antennas.
2.1.2 Working
The same information signal is transmitted on each antenna modulated by a complex gain whose phase and magnitude is changed in time in a controlled but pseudorandom fashion as shown in Figure1.
Figure 1: The same signal is transmitted on each of the two antennas
Where hk(t) is the complex channel gain given by
The αn(t)'s denote the fractions of power allocated to each of the transmit antennas, and the θn(t)'s the phase shifts applied at each antenna to the signal. Hence each transmit antenna has a different gain. The constructive and destructive addition of signal paths from the transmitter to the receiver (user) introduces channel variation. Each user tracks the channel quality as the signal-to-noise ratio and feedback's this information to the base station to form a basis for scheduling. A single pilot signal which is repeated at each of the antennas, just like the data is to track the channel. Opportunistic beam-forming is achieved as the phases and power allocated at the transmit antennas are varied in a pseudorandom manner, and at any time transmission is scheduled to the user which is currently closest to being in its beam-forming configuration.
2.1.3 Proportional Fair Scheduling
In order to cater fairness and delay, proportional fair scheduling (PFS) algorithm is used. The algorithm works as follows: It keeps track of the average throughput Tk(t) of each user in a past window of length tc. In time slot t, the scheduling algorithm simply transmits to the user with the largest Rk(t) /Tk(t) among all active users in the system. The average throughputs Tk(t) can be updated using an exponentially weighted low-pass filter as
2.2 Multi-user Diversity using switched multiuser access Schemes
2.2.1 System model
A TDM system is considered where one user transmits at a time. The timeslot consists of guard time equal to the time needed to probe the users and a transmission time. i.i.d. Rayleigh fading channels across the different users are assumed, and the individual users and the base station are all equipped with just a single antenna.
A rate-adaptive coding scheme using N = 8 multidimensional trellis codes originally designed for AWGN channels is utilized [3].The codes are based on QAM signal constellations of growing size {Mn}N n=1 = {4, 8, 16, 32, 64, 128, 256, 512}. Rate adaption is performed by splitting the SNR range into N + 1 fading regions (bins). The lower limit of each fading region is equal to the smallest SNR which guarantees that a predefined target BER (BER0 = 10−4) is achieved.
Switched multi user access schemes
In order to probe the user sequentially, three multi-user access schemes have been proposed in [4].
Scan and wait transmission (SWT)
In this scheme, during the guard time interval, a sequential search is initiated by the BS, requesting the SNR of each user and comparing it to a switching threshold ƔT. The SNR probing process continues until either one user is above ƔT (this user is selected for the subsequent transmission time) or all K users have been examined and all have failed to exceed ƔT. In the latter case, the BS simply waits a period longer than the channel coherence time (deliberate outage) before carrying out another search. This procedure can be repeated indefinitely until a user with an acceptable SNR is found.
Switch-and-examine transmission (SET)
This scheme is similar to the previous scheme except that the last probed user is allowed to transmit information if all K users have failed to exceed ƔT and the reported SNR is above Ɣl (the lowest SNR needed to meet the target BER0). Thus, in practice, the switching threshold for the SET scheme is relaxed to ƔT = Ɣl for the last probed user in order to reduce the outage probability. This leads to an improvement in the ASE of the SET scheme compared to the SWT scheme.
SET with post-selection (SETps)
This scheme is similar to SET, except that if no acceptable link has been found, the best one of all the probed users exceeding Ɣl is selected at the end instead of just picking the last one for simplicity.
2.3 Selective Multiuser Diversity
This technique was proposed in order to minimize the number of users that will feedback the channel quality to the base station hence reducing the feedback load. Only the users with SNR greater than a threshold value request access to the channel.
2.3.1 System Model
A single interference free cell is considered with k simultaneously active users served by one access point. The scheduling is organized on a slot by slot basis. Moreover the system is single input and single output.
2.3.2 Working
At each timeslot t, a user k will feedback its channel quality to the access point if and only if
Æ”k(s) ≥ Æ”th. The thresholding is applied to the average SNR. In case all the users have the same average SNR, then the instantaneous SNR can be used for thresholding. Proportional fair scheduling algorithm (PFS) is used in each timeslot to schedule the user k*(s) with the maximum normalized capacity at a particular time.
k*(s) = argmaxk=1,…k C(k,s)
R(k,s)
In the case when no user feedbacks its channel information, there is a scheduling outage. In such scenario, the scheduler either reverts to conventional 'blind' fair selection mode or assumes that the previous best user remains optimal, given some finite coherence time for the channel.
3. Comparative Analysis
In this section, I have analyzed the three techniques based on four crucial parameters that I have identified before.
3.1 Opportunistic beam-forming using dumb antennas
3.1.1 Average Feedback Load
The feedback load in this technique is high as all the users have to provide the channel quality to the base station even if its channel quality is low, which results in a waste of the user's bandwidth. Hence, as the number of users increases, the feedback load also increases.
3.1.2 Diversity Gain
The simulation in [3] shows that the total throughput increases with the number of users in both the fixed and mobile environments, but the increase is more dramatic in the mobile case. While in channel fading, in the cases, the dynamic range and the rate of the variations is larger in the mobile environment than in the fixed one. The peaks of the channel fluctuations are likely to be higher in the mobile environment over the latency timescale, and the peaks determine the performance of the scheduling algorithm. Thus, the inherent multiuser diversity is limited in the fixed environment.
Figure 2: Multiuser diversity gain in fixed and mobile environments
3.1.3 Fairness among users
The scheduling algorithm used in this technique introduces proportional fairness among the users as it not only serves all users when they have same fading statistics but also when they have different fading statistics. The users in this technique compete for resources not directly based on their requested data rates, rather after being normalized by their respective average throughputs [2]. The user with a statistically stronger channel will have a higher average throughput. Thus, the algorithm schedules a user when its instantaneous channel quality is high relative to its own average channel condition over the time scale tc.
3.1.4 Average spectral efficiency
The plot in [3] of the total capacity in (b/s/Hz) of the downlink channel versus the number of users, when users undergo independent Rayleigh fading with average received SNR 0 dB shows that the capacity increases with the number of users in the system. While, in a nonfaded downlink channel, with fixed additive white Gaussian noise (AWGN) channel and SNR 0 dB for each user, the sum capacity is constant irrespective of the number of users. With a moderate number of users, the fading channel has greater sum capacity than that of a nonfaded channel. By giving access to users with strong channels at all times, the overall spectral efficiency of the system turns out to be significantly higher than that of a nonfading channel with the same average SNR.
Figure 3: Sum capacity of two channels, Rayleigh fading channel and AWGN with average SNR = 0 dB
3.2 Selective Multi-User Diversity
3.2.1 Average Feedback Load
In classical multi-user diversity techniques, the feedback load is fixed equal to the number of users, k, whereas in this scheme it can range from 0 to k within each timeslot. The normalized average feedback load is defined here as the ratio of average load per timeslot by the total number of users. In a scenario where the threshold is fixed, the feedback load tends to stabilize around the mean, as the number of users increases. The following graph shows feedback load as a function of threshold. At Ɣth =9 dB, the load is less than 10% of what it is with the original PFS algorithm.
Figure 4: Average Feedback Load vs threshold
3.2.2 Diversity Gain
Until a threshold of 9dB, very little performance loss is observed. At Ɣth =9 dB and uptil k= 28 users, diversity gain is high but after an increase in feedback of 10%, the increase in users does not increase the gain as the following graphs in [5] show
Figure 5: Average system capacity vs required feedback load for different number of users
Figure 6: System capacity vs Number of users at different thresholds
3.2.3 Fairness among users
Proportional fair scheduling algorithm is used hence each user gets a chance to access the channel. Therefore, fairness among the users exists in this scheme.
3.2.4 Average Spectral Efficiency
The ASE in this scheme is medium as there will be a timeslot when no user transmits if none of them feedbacks the channel information if Æ”k(s) ≥ Æ”th is not satisfied. But if the feedback load stabilizes around the mean number of users, then the ASE will be high.
3.3 Multi-User Diversity using multi-user switched access schemes
3.3.1 Average feedback load
The multiuser access schemes described above reduce the feedback compared to the traditional approach. The feedback load Ne will no longer be deterministic, but can be modeled as a discrete random variable [4].
ƔT (for fixed K and Ɣ) is the switching threshold that maximizes the ASE subject to a possible average feedback load (AFL) constraint.
AFL = 1 - pK where p = 1− e− Æ”T / Æ”.
1 − p
With no AFL constraint, Æ”T is identified within the set X = { Æ”∈ R : Æ”l ≤ Æ” ≤ Æ”N}
With an AFL constraint, Æ”T is identified within the set Xafl = { Æ”∈ R : Æ”l ≤ Æ”≤ Æ”*},
where Æ”- ≤ Æ”N
In SWT, the feedback load varies from low to high depending on how many users have to be probed till an acceptable user is found while in SET, at maximum, all K users will have to feedback their channel information. In SETps, the feedback is again low to high as traditional approach (SCT) is used if no acceptable user found after probing all of them.
Figure 6: Average feedback load vs the number of users for the three multiuser access schemes
3.3.2 Diversity gain
In switched multi-user access schemes, gain is increased by decreasing the feedback load although the ASE decreases.
3.3.3 Fairness among users
The three multi user access schemes provide fairness among the users.
3.3.4 Average Spectral Efficiency
The ASE of the system is obtained as a sum of the spectral efficiencies {Rn} Nn=1 = {1.5, 2.5,..., 8.5} for the individual codes, weighted by the probability Pn that code n has used:
ASE = ∑N n=1 Rn Pn,
The ASE in SWT is low as no user transmits if none of them has SNR greater than threshold but this leads to high waiting time. In SET, the ASE is better than SWT, as the threshold for last user is decreased if no other user's SNR is acceptable. In SETps , the ASE is better than SWT as the best user is selected if all have been probed.
Figure 7: ASE for multiuser access schemes vs users for different thresholds in Rayleigh fading channels
3.4 Results
Multi-user Diversity
Technique
Average Feedback load (AFL)
Average Spectral Efficiency (ASE)
Diversity Gain
Fairness of scheduling
Mode of operation
Opportunistic beam-forming
Using dumb antennas
High as all users have to feedback their channel quality
High
Increases as the number of users increases.
High as PFS is used
TDM
Selective Multi-user diversity scheme
Low as only the users with Æ”k(s) ≥ Æ”th send feedback to base-station
Medium. No user transmits if none of them feedbacks the channel information if Æ”k(s) ≥ Æ”th is not satisfied
For Ɣth =9 dB and 28 users, diversity gain is high but after a feedback of 10%, increase in users doesn't increase gain
High as PFS is used
TDM
Multi-user diversity based on switched multi-user access schemes
SWT
Low to high depending on how many users have to be probed till an acceptable user is found
Low, as no user transmits if none of them has SNR greater than threshold. Leads to high waiting time
Increases as feedback load decreases
High as all users get the chance to access the channel
TDM
SET
At maximum, all K users will have to feedback their channel information
Better than SWT, as the threshold for last user is decreased if no other user's SNR is acceptable
Increases as feedback load decreases
High as all users get the chance to access the channel
TDM
SETps
Low to high as traditional approach used if no acceptable user found after probing all of them
Better than SWT as the best user is selected if all have been probed.
Increases as feedback load decreases
High as all users get the chance to access the channel
TDM
4. Conclusion
Multi-user diversity exploits fading unlike traditional diversity techniques resulting in opportunistic communication when and where the channel is strong. At any given time, the user with the best signal to noise ratio is granted access to the channel. Therefore, the system capacity increases as the number of users increases.
In this report, I have studied three multi-user diversity techniques; Opportunistic beam-forming using dumb antennas, selective multi-user diversity and multi-user diversity based on switched multi-user access schemes. The first technique improves multi-user diversity gain in slow fading environments by inducing channel fluctuations using multiple antennas at the base station but results in high feedback load, proportional fairness among the users and high average spectral efficiency. The second technique reduces the feedback load on the base station as only selective users whose SNR is greater than the threshold participate in acquiring access to the channel. It is proportionally fair and ASE maximizes if the number of users stabilize around the mean but simulations show that the diversity gain does not increase after 28 users and a threshold of 9 dB. The third technique also reduces the feedback load on the base station and it incorporates three switched multi-user access schemes. The users are probed in a sequential manner during the guard time of the timeslot in order to find an acceptable user. There is tradeoff between ASE and AFL and the spectral efficiency is lower compared to the selection combining transmission used as the benchmark for comparing the access schemes. The diversity gain increases as the feedback load decreases and this technique is also fair.
