# Decentralized power control with two-way training for multiple access

TL;DR: It is shown that with relatively simple power control, regardless of the number of transmitters, a MIMO multiple access wireless system can achieve double the maximum diversity order of a system with no instantaneous channel state information at the transmitters.

Abstract: In this work, we analyze the diversity-multiplexing performance of a MIMO multiple access wireless system with non-cooperating transmitters. Each of the transmitters and receiver use noisy and mismatched versions of the channel estimate to implement decentralized power control. While accounting for the resources consumed in training, we show that with relatively simple power control, regardless of the number of transmitters, we can achieve double the maximum diversity order of a system with no instantaneous channel state information at the transmitters. Intuitively, the gain can be attributed to using temporal degrees of freedom enabled by power control without coding over multiple coherence intervals.

## Summary (2 min read)

### Introduction

- In scenarios where many users attempt to communicate to a single receiver, multiple antenna systems have been employed to increase reliability or the supported data rates.
- None of them account for errors and resource consumption on the feedback channel.
- For the case of SIMO channel (single input multiple output), the authors showed that the maximum diversity order can be doubled compared to a system which employs no feedback.
- The key contribution in [6] was the two-way channel formulation and an analysis which accounts for the mismatch in channel state information at the transmitter and receiver.
- While analyzing the multi-user DMT for MIMO, the authors also furnish one possible method to extend [6] to the point-to-point MIMO scenario for low multiplexing gain.

### B. Training and Power Control

- The training symbols, which adhere to the same power constraints as data symbols, are transmitted at a constant power equal to the average power constraint of the transmitter denoted by P .
- One of the training protocol begins with the transmission of nτRT training symbols (τRT from each of the receive antennas) from the receiver to the K transmitters.
- For reasons explained in detail in [6], the receiver tries to estimate the power controlled channels Gi = √ p(Ĥi) Hi.
- The power controlled channel is again split into two parts Ĝi, the estimate of the power controlled channel, and G̃i, the estimation error, such that Gi = Ĝi + G̃i. (4) The entries of G̃i and H̃i are ZMCSCG with variance σ2{G̃i,H̃i} = 1 τ{TR,RT}P (5) meeting the Cramèr-Rao bound.

### C. Outage Definition and DMT

- Sit is the unit power complex signal prior to power control.
- The receiver can without loss of optimality, cancel its contribution from the received signals.
- The authors consider the symmetric case where all users have the same rate requirement.
- The authors consider Gaussian codes to determine an achievable bound for the exponent of outage probability.
- For the current work, the authors assume a joint ML detector.

### III. CHARACTERIZATION FOR MISO MAC

- The authors bound (16) by the sum of two terms that intuitively separate the effects of uncertainty in the channel state at the transmitters and the receiver.
- (18) In (a) the authors have substituted the distribution for the χ2-square variable with 2Km degrees of freedom and in (b), they have substituted (5).
- Unlike the case of no CSIT [2], where the DMT is divided into lightly loaded and heavily loaded regions with single user and K user performances respectively, the authors get single user performance for almost the full range of permissible multiplexing gain, also known as Remark 3.2.

### IV. MIMO MAC FOR LOW MULTIPLEXING GAINS

- Let the receiver implement selection and decode the messages at the n antennas separately.
- Clearly, the outage event OW for such a scheme occurs when all the n MISO links are in outage.
- In deriving the achievable DMT for multi-user MIMO channel, the authors have also shown a method of extending the results of [6] for a SIMO channel to the single user point-to-point MIMO channel.
- For higher multiplexing gains, centralized power control seems to become necessary as the bound quickly falls off.

### V. CONCLUSION

- The authors analyzed multiple access systems using the two-way formulation for feedback channel introduced in [6].
- The authors results clearly indicate that decentralized power control by non-cooperating transmitters is extremely beneficial at low multiplexing gains even when training the transmitters consumes extra resources and has errors.
- The maximum diversity in their model with noisy and mismatched channel estimates at the transmitters and the receiver is double that achieved with no side information at the transmitter [2].

Did you find this useful? Give us your feedback

...read more

##### Citations

18 citations

### Cites background from "Decentralized power control with tw..."

...While the model and subsequent analysis clearly shows that reduced channel information at the transmitter can lead to significant performance gains due to channel knowledge, a key requirement is that the receiver knows what the transmitter knows (even if there is an error in feedback link)....

[...]

14 citations

### Cites background or methods from "Decentralized power control with tw..."

...On the other hand, for the case of TDD, we assume that the and are perfectly correlated within one coherence interval, and adopt a phase-symmetric two-way channel model with [4], [5]....

[...]

...Theorem 4 ([5]): For , the above protocol achieves a diversity multiplexing tradeoff of ....

[...]

...In this subsection, we review the result in [5], [18] for the achievable diversity multiplexing tradeoff for a MIMO channel....

[...]

10 citations

8 citations

7 citations

##### References

4,264 citations

### "Decentralized power control with tw..." refers background or methods in this paper

...In order to capture the asymptotic performance of our system, we analyze the diversity-multiplexing tradeoff (DMT) derived in [1], where diversity, d is...

[...]

...We assume a slow fading scenario where the block length of time over which the channel stays constant equal to l symbols is assumed to be long enough to make outage errors dominate the total error probability for the sytem [1][2], l−To ≥ Km+n−1 where To is the training overhead corresponding to the number of symbols used for training either the receiver or a transmitter....

[...]

...A tradeoff between the two competing objectives when there is no channel state information at the transmitter (CSIT) was proposed as the diversity-multiplexing trade-off for the point-to-point MIMO link [1] and later extended to the multiple access channel (MAC)[2]....

[...]

^{1}

2,325 citations

605 citations

### "Decentralized power control with tw..." refers background or methods in this paper

...Section III contain the derivation of DMT for MISO MAC and and Section IV extends the DMT to MIMO MAC....

[...]

...The maximum diversity in our model with noisy and mismatched channel estimates at the transmitters and the receiver is double that achieved with no side information at the transmitter [2]....

[...]

...In this paper, we extend the model of [6] to a MAC scenario....

[...]

...We assume a slow fading scenario where the block length of time over which the channel stays constant equal to l symbols is assumed to be long enough to make outage errors dominate the total error probability for the sytem [1][2], l−To ≥ Km+n−1 where To is the training overhead corresponding to the number of symbols used for training either the receiver or a transmitter....

[...]

...Similar definitions hold for ≤̇, ≥̇. where α = (l − τRT − KmτTR)/l and α′ = (l − KmτTR)/l account for the loss of rate due to training and dR̂K,m,1( r α′ ) refers to the DMT for a MAC system with no CSIT and a trained receiver....

[...]

123 citations

### "Decentralized power control with tw..." refers background in this paper

...Section III contain the derivation of DMT for MISO MAC and and Section IV extends the DMT to MIMO MAC....

[...]

...Corollary 4.2: The point-to-point MIMO link with the twoway training model will achieve the DMT d∗MIMO,m,n(r) given below. d∗MIMO,m,n(r) = { mn ( 2 − rα ) 0 ≤ r < α dR̂MIMO,m,n( r α′ ) r ≥ α (27) where dR̂MIMO,m,n( r α′ ) is the fundamental DMT for a point-topoint link for a trained receiver [7]....

[...]

...We refer to such a system as a K transmitter m×n MIMO multiple access channel....

[...]

...The emphasis in the current work is on understanding in the multi-user context how mismatch in the knowledge of channel at the transmitters and receiver affects the system performance, and if any of the diversity order gains predicted by perfect feedback [3], [4] are achievable with information mismatch....

[...]

...While analyzing the multi-user DMT for MIMO, we also furnish one possible method to extend [6] to the point-to-point MIMO scenario for low multiplexing gain....

[...]

^{1}

66 citations

### "Decentralized power control with tw..." refers background or methods in this paper

...A two-way channel formulation was used by the authors in [6] to study the impact of errors in feedback while fully accounting for all resource usage in forward and feedback channels....

[...]

...In this paper, we extend the model of [6] to a MAC scenario....

[...]

...However, as we shall see, unlike in [6], the partitioning in (17) allows us tackle the multi-user situation better by removing the effect of estimation error at the receiver completely....

[...]

...Proof: When n = 1, we adopt the power control motivated by [6]...

[...]

...We notice a slight similarity between (41) in [6] and (17)....

[...]