- Research
- Open Access
R bits user selection switch feedback for zero forcing MU-MIMO based on low rate codebook
- Shiyuan Li^{1}Email author,
- Qimei Cui^{1},
- Xiaofeng Tao^{1} and
- Xin Chen^{1}
https://doi.org/10.1186/1687-1499-2012-7
© Li et al; licensee Springer. 2012
- Received: 20 July 2011
- Accepted: 10 January 2012
- Published: 10 January 2012
Abstract
Channel feedback for multi-user (MU)-multiple-input multiple-output (MIMO) has been widely studied and some results have been got with random vector quantization scheme. However, while the low rate fixed codebook feedbacks are adopted, the performance of zero forcing (ZF) MU-MIMO will decrease as the unpredictable inter-user interference is introduced because of quantized channel state information (CSI). To decrease inter-user interference in low rate fixed codebook feedback, an enhanced user selection switch (USS) feedback scheme for ZF MU-MIMO is proposed in this article. In USS feedback, the extra USS information is added after quantized CSI and received signal-to-noise ratio feedback. The USS information indicates inter-user interference and it can be used in user selection procedure to avoid large inter-user interference. Simulation results show that the proposed USS feedback scheme is efficient to solve the problems of unpredictable inter-user interference in conventional feedback scheme with low rate codebook in ZF MU-MIMO.
Keywords
- MU-MIMO
- feedback
- user slection
- user pairing
1. Introduction
It is well known that multiple-input multiple-output (MIMO) can make full use of spatial diversity and enhance data rate by spatial multiplexing. In rich scattering environment, the data rates increase linear with the minimal antenna number of the base station (BS) and user equipment (UE) compared to the single-input single-output (SISO) scheme [1]. Usually, BS equips more antennas than UE, so the spatial diversity of MIMO system is not fully utilized. To overcome this drawback, the multi-user MIMO (MU-MIMO) technique is introduced. In downlink MU-MIMO transmission, the data streams of multiple UEs are simultaneously transmitted from BS to UEs at same time and frequency resource. Each UE demodulates its data only by his own channel state information (CSI) and the data of other UEs are treated as interference.
While BS and UEs know the perfect CSI, "Dirty Paper Coding" (DPC) [2–6] is known to achieve the capacity of the MIMO downlink channel, but DPC has very high complexity to be realized in actual system. To reduce the complexity of coding, zero forcing (ZF) [7–10] is proposed as the sub-optimal solution and the performance of ZF is close to DPC in many scenarios [11].
ZF technique needs CSI between BS and UEs while performing user selection and computing precoding matrix. The exact CSI can be got by channel reciprocity in TDD system. However, BS only can get quantized CSI by UE feedback in FDD system because the feedback channel has limited rate. So, the signals of paired UEs cannot be perfectly separated by ZF precoding and UE will receive the unwished signals of other paired UEs which is called inter-user interference. Hence, the MU-MIMO performance will be decreased with the quantized CSI in FDD system [12, 13]. Some important conclusions with limited feedback for MU-MIMO have been got [14–19], and these studies show that the quantization bit scales linear with number of transmit antennas and logarithmic with received SNR of UE while a constant performance gap are hold compare to perfect-CSI.
- (1)
It needs a great deal feedback bits in the case of high SNR and large number of transmit antennas [16–18]. For example, while SNR is 10 dB with 4 transmit antennas, it needs about 14 bits (16,384 codebooks) and while SNR is 20 dB with 8 transmit antennas, it needs about 35 bits (34,359,738,368 codebooks).
- (2)
The codebook needed in RVQ scheme should randomly be generated by UE before CSI feedback, and then the codebook is sharing with BS through feedback channel. So, the large codebook number will also increase feedback overhead of codebook sharing, the computational complexity of codebook generation, and cache costs of codebook storage.
- (3)
RVQ needs different quantized bits for different SNR cases, so it will bring some design problems. For examples, if the feedback bits are fixed, it will cause waste for low SNR case and not enough for high SNR case. If feedback bits are flexible, new codebook will be retransmitted while SNR changed and it will decrease the effects of user selection between UEs with different SNR.
Moreover, most of the current communication system adopt small codebook size and fixed codebook structure, which both known by UE and BS, to reduce the system complexity feedback overhead. In this feedback scheme, the former performance analysis for RVQ will be not suitable. In low rate fixed codebook feedback scheme, the interference between paired users is the key problem and conventional feedback and user selection scheme have on mechanism to avoid large inter-user interference. To overcome this drawback in low rate fixed codebook feedback scheme, the reasons of large inter-user interference are analyzed detailed and an enhanced scheme named user selection switch (USS) feedback is proposed here. The USS feedback adds some extra information besides CSI and SNR to show the inter-user interference while performing ZF MU-MIMO transmission. With USS information, BS can avoid large inter-user interference in MU-MIMO transmission in user selection procedure and enhance MU-MIMO performance.
The rest of the article is organized as follows. Section 2 introduces conventional MU-MIMO transmission model and analyzes the problem of low rate fixed codebook feedback scheme. Section 3 proposes USS feedback to enhance MU-MIMO performance and gives related user selection procedure. Section 4 gives the numerical simulation to verify the performance enhancement. Section 5 provides some conclusions.
2. System model
where g_{ i } is pathloss between BS and UE _{ i }, H_{ i } ∈ C^{1 × M}is the normalized channel matrix between BS and UE _{ i }, x_{ i } is the transmitted signals with an average power constraint E{||x_{ i } ||^{2}} = P_{ i } , ||·|| stands for norm operator, P_{ i } is the power constraint of each user's data stream, n_{ i } is the additive white Gaussian noise with σ^{2} variance, and y_{ i } is the signal received by UE_{ i }.
The procedure of conventional ZF MU-MIMO is as follows [10, 18].
2.1. Quantized CSI feedback
Then the index k is fed back to BS, and BS treats w_{ i } = c_{ k } as the channel matrix H_{ i } of UE_{ i }.
2.2. SNR Feedback
UE can measure it by reference signals (RS), as the RS sequence and its power are known to UE. In the practical system, this information is quantized with small number of bits. In order to concentrate on the effect of CSI quantization and user selection, it assumes that the SNR is directly fed back without quantization.
2.3. User selection
where |·| stands for absolute value, (·) ^{ H } stands for Hermite transpose, V is paired user set in which the users are scheduled together to form MU-MIMO.
2.4. ZF precoding
where p_{ i } is precoding vector of UE _{ i }, w_{ i } is the quantized CSI of UE_{ i }, (·)^{+} stands for pseudo-inverse operation.
where $\sqrt{{g}_{i}}{H}_{i}\frac{{\beta}_{i}}{{\alpha}_{i}}{p}_{i}{s}_{i}$ is wanted signal and $\sqrt{{g}_{i}}{H}_{i}\sum _{j=1,j\ne i}^{M}\frac{{\beta}_{j}}{{\alpha}_{j}}{p}_{j}{s}_{j}$ is inter-user interference.
2.5. MU-MIMO performance with conventional feedback
2.6. The problems of conventional feedback
In the conventional feedback scheme, BS and UE cannot know the MU_SNR clearly. For UE_{ i }, it knows its channel matrix H_{ i } , but does not know the channel of paired users. For BS, it knows paired users, but does not know exact channel matrix of UEs. So, the ||H_{ i }p_{ j } ||^{2} cannot be known for BS and UE. Hence, the transmitting rate R is evaluated in conventional user selection.
Usually R is evaluated with the assumption of no inter-user interference, which means ||H_{ i }p_{ j } ||^{2}≈0. But for the paired user, the inter-user interference may be very large and lead the performance decrease heavily, while ||H_{ i }p_{ j } ||^{2}≫0. In user pairing, BS does not know the exact inter-user interference, so it has no mechanism to avoid large inter-user interference in user selection criteria.
- (1)
The performance gain of MU-MIMO will decrease, especially in high SNR case. Figure 3 shows the MU-MIMO (two paired users) performance of 4 bits feedback with DFT codebook, compared to SISO case and perfect CSI feedback. It can be seen that MU-MIMO with perfect CSI feedback has very high rate about double of that in SISO case. But for low rate quantized feedback (4 bits), the performance gain falls largely compare to perfect CSI feedback, as the CSI is the quantized version with low codebook size. The performance gain is little at high SNR region because the inter-user interference of paired users is randomly in quantized feedback with conventional user selection methods, and MU-MIMO performance is sensitive to inter-user interference in high SNR case.
- (2)
While the quantized bits increase, the performance enhancement may not be obvious for some codebook types. Figure 4 shows the sum data rate of MU-MIMO quantized with DFT codebook of different bits. It can be seen that while the number of quantized bits increase from 2 to 3 bits the performance enhancement is obvious, and performance enhancement is little while number of quantized bits increase from 3 to 6 bits. Concluded from the growth trend, when the number quantized bit is more than 6 bits, the performance is near to case of 6 bits. So, increasing codebook size is no use to enhance MU-MIMO performance. The reason is that the increasing number of quantized bits cannot decrease the inter-user interference of paired users for fixed codebook structure unlike RVQ feedback scheme.
3. Algorithm
To decrease the bad effect of random inter-user interference in low rate fixed codebook feedback scheme, a novel USS feedback scheme is proposed. In the USS feedback, extra USS information is added after CSI feedback to show the inter-user interference. And this information is used in user selection algorithm to avoid large inter-user interference. The detailed process of the proposed scheme is elaborated as follows.
3.1. Grouping quantized codebook
where C_{ k } is subset of codebook C satisfied $C=\underset{k=1,...,m}{\cup}{C}_{k}$ and C_{k 1}∩C_{k 2}=∅(k 1≠k 2), c_{ ki } is element of codebook C, m is number of groups, l is element number of subset, N is codebook size with the relevance N = l*m, R is correlation threshold between code vector in subset, which means the correlation between any two paired users are no more than R.
Only the users which their feedback belong to same group can be paired together, so the correlation between any two paired users are no more than R. At most M users can be transmit at same time in MU-MIMO, so lets l ≥ M, and all the M users can be selected in the same set. In the simulation of this article, the DFT codebook is adopted with setting l = M and r = 0, as DFT codebooks are naturally separated into orthogonal groups, which has M orthogonal vectors.
3.2. USS information feedback
In USS feedback scheme, (l-1)*r additional bits named USS information are fed back to BS besides CSI and SNR, and this information is used to indicate the MU-MIMO performance. In sub-codebook groups, user can be paired with other (l-1) vector, so USS information uses r bit(s) for each vector to show the MU-MIMO performance while user is paired with this vector. The feedback contents are (USS_{1},..., USS_{i-1}) and USS _{ i } corresponding to the i th vector in sub-codebook except the vector which user is fed back. For example, if r = 1, the user can be paired with i th vector while USS _{ i } = 1, and the user cannot be paired with i th vector while USS _{ i } = 0.
The value of USS information is relative to transmission and feedback configuration, such as number of paired user m and USS information bits r. The details of the value calculation will be shown in Section 3.4 for different configurations.
3.3. User selection procedure
- (1)
BS defines three sets: serving user set U = {UE_{1},...,UE_{ K }}, corresponding to all the users served by BS; (2) user CSI set W = {w _{1},...,w_{ K } }, corresponding to users' CSI; (3) paired user set MU = ∅, corresponding to the users scheduled together to adopt MU-MIMO. BS sets the number of paired users (more than 1 and no more than the number of transmit antennas).
- (2)
BS selects first two users (i,j) from set U. The UE _{ i } and UE _{ j } should satisfy the conditions: (a) their CSI feedback should be in the same codebook group C_{ k } , that means w_{ i }, w_{ j } ∈ C_{ k } ; (b) the USS information for paired vector should not be equal to zero, that means (USS_{il 1}> 0, USS_{jl 2}> 0, c _{kl 1}= w_{ j }, c _{kl 2}= w_{ j } ); (c) the summation of USS information for paired vector should be maximum in all users which satisfy conditions (a) and (b), that means $\left(i,j\right)=\underset{\mathsf{\text{U}}{\mathsf{\text{E}}}_{i},\mathsf{\text{U}}{\mathsf{\text{E}}}_{j}\phantom{\rule{2.77695pt}{0ex}}\mathsf{\text{satisfy(a)and(b)}}}{max}\left(\mathsf{\text{US}}{\mathsf{\text{S}}}_{il1}+\mathsf{\text{US}}{\mathsf{\text{S}}}_{jl2}\right)$.
If the two users can be found, BS will put them into paired user set MU = {UE_{ i }, UE_{ j }}, and remove them from serving user set U = U-{UE_{ i }, UE_{ j }}. Otherwise, user pairing will be stopped and single user mode will be adopted.
- (3)
If the number of paired user is enough, start ZF procedure to compute precoding matrix. Otherwise, select the next user o from set U. The UE _{ o } should satisfy the conditions: (a) its CSI feedback should be in codebook group C_{ k } , same to users in set MU, that means w_{ o } ∈ C_{ k } ; (b) the USS information for paired vector of UE _{ o } and users in set MU should be more than zero, that means (USS _{ oli } > 0, USS _{ ilo } > 0, c_{ kli } = w_{ i }, c_{ ilo } = w_{ o } , UE _{ i } ∈ MU); (c) the summation of USS information for paired vector should be maximum in all users which satisfy conditions (a) and (b), that means $\left(o\right)=\underset{\mathsf{\text{U}}{\mathsf{\text{E}}}_{o}\phantom{\rule{2.77695pt}{0ex}}\mathsf{\text{satisfy}}\phantom{\rule{2.77695pt}{0ex}}\left(\mathsf{\text{a}}\right)\phantom{\rule{2.77695pt}{0ex}}\mathsf{\text{and}}\phantom{\rule{2.77695pt}{0ex}}\left(\mathsf{\text{b}}\right)}{max}\phantom{\rule{2.77695pt}{0ex}}\sum _{\mathsf{\text{U}}{\mathsf{\text{E}}}_{i}\in \mathsf{\text{MU}}}\left(\mathsf{\text{US}}{\mathsf{\text{S}}}_{\mathsf{\text{oli}}}+\mathsf{\text{US}}{\mathsf{\text{S}}}_{\mathsf{\text{ilo}}}\right)$.
- (4)
If the number of paired user is enough, start ZF procedure to transmit users' data. Otherwise, go to step 3 to select another user.
3.4. USS value calculation
- (a)
r = 1 and m = 2
where α_{ i } is coefficient scaling factor, β_{ i } is power allocation factor. The total power should no more than max transmit power P_{total}, and the constraint is $\frac{{\beta}_{1}}{{\alpha}_{1}}\mid \mid {p}_{1}{\mid \mid}^{2}+\frac{{\beta}_{2}}{{\alpha}_{2}}\mid \mid {p}_{2}{\mid \mid}^{2}={P}_{\mathsf{\text{total}}}$.
Each user knows its channel matrix and the vector of paired user is selected in subset C_{ k } . So, user can calculate the exact SNR of MU-MIMO for each vector in set C_{ k } .
This result can be used in USS information calculation. In USS feedback scheme, a correlation threshold R is used in codebook subset. It means in above equations that the correlation σ must be no more than R as the paired vector is selected from same subset. With different value of R, it can be divided into two categories:
where SNR _{ i } is the measured SNR defined in Equation(4).
Because user does not know the vector which BS will be schedule in user pairing, the actual transmit rate cannot be known. In USS feedback scheme, all the paired vectors are in one subcodebook C_{ k } = {c_{k 1},...,c_{ kl } }, and for one UE, the number of candidate pairing vector is l-1. So, for each candidate pairing vector in subcodebook, user will evaluate its throughput when this vector is selected as paired vector, and the USS information is calculated based on this evaluated throughput.
User assumes that the paired user has the same correlation of quantized CSI a and the same inter-user interference level b, so the evaluated sum throughput is R_{ kj } = 2R_{ i } (j≠i). If the sum throughput for the vector c_{ kj } is more than MISO throughput R_{su} = log(1+SNR), set USS _{ kj } = 1, which means the performance is better while UE _{ i } paired with vector c_{ kj } , otherwise set USS _{ kj } = 0, which means the inter-user interference is large while UE _{ i } paired with vector c_{ kj } and UE _{ i } should avoid to pair with this vector.
- (b)
r = 1 and m > 2
If more than two users are paired together to form MU-MIMO, then the SNR of MU-MIMO user will be decreased compare to two paired users, as the inter-user interference is m-1 times and the power allocation of each user is also decreased. It assumes that the power is equally allocated to each user and the paired users have the same correlation of quantized CSI a and inter-user interference level b for each paired vector.
- (c)
r > 1
- (1)
if R_{ kj } ≤ R _{lower}, set USS _{ kj } = 0;
- (2)
if R_{ kj } ≥ R _{upper}, set USS _{ kj } = 2 ^{ r } ;
- (3)
if R _{lower} <R_{ kj } <R _{upper}, set $\mathsf{\text{US}}{\mathsf{\text{S}}}_{kj}=1+\u230a\left(\frac{{R}_{kj}-{R}_{\mathsf{\text{lower}}}}{{R}_{\mathsf{\text{upper}}}-{R}_{\mathsf{\text{lower}}}}*{2}^{r}\right)\u230b$, where ⌊·⌋ is floor function.
3.5. Feedback overhead
In USS feedback scheme, the extra USS information is added after quantized CSI, and the feedback overhead is changed. So, the overhead of USS feedback, conventional feedback, and RVQ feedback is analyzed in this section. As discussed above, it assumed that (1) the codebook size is N = 2 ^{ B } ; (2) the quantization vector c_{ j } ∈ C^{1 × M}; (3) UE will feed back one quantized CSI in each feedback period.
For conventional feedback, only a quantized CSI is fed back to BS in each feedback period, so the feedback overhead is B bits in a feedback period.
For USS feedback, in each feedback period, the extra USS information is fed back to BS besides the quantized CSI. As discussed in Section 3.4, it has l elements in subset and r bits USS information for each element in subset. So, the feedback overhead is B+(l-1)*r bits in a feedback period.
For RVQ feedback, a quantized CSI is fed back to BS in each feedback period. Besides, the random codebook should be shared between BS and UE, and this codebook is randomly generated by UE then fed back to BS through feedback channel. It is assumed the random codebook can be used in q periods and the 16 bits quantization with short floating point number is adopted for each complex element of codebook. So, the initialization overhead is N*M*16*2, and this overhead cover to each period is N*M*16*2/q. The totally feedback bits in a feedback period is N*M*32/q+B.
The overhead comparison
Scheme | Initialization | Quantized CSI | Additional | Totally feedback bits/period |
---|---|---|---|---|
Conventional | 0 | B | 0 | B |
USS | 0 | B | (l-1)*r | B+(l-1)*r |
RVQ | N*M*16*2/q | B | 0 | N*M*32/q+B |
4. Simulation
In this section, a MIMO system with M = 4 transmit antennas at the BS and single antenna at the UE is considered. The DFT codebook with different size is used in simulation. DFT codebook has orthogonal vector groups, so each orthogonal vector group is treated as one subcodebook. Hence, the correlation threshold R is equal to zero.
5. Conclusion
In this article, a novel USS feedback scheme and relative user selection procedure are proposed to avoid large inter-user interference in downlink ZF MU-MIMO for low rate fixed codebook feedback. The inter-user interference will largely decrease the MU performance gain in high SNR region and leads to the MU-MIMO throughput does not increase with the codebook size increasing. With the help of additional information, the proposed USS feedback scheme can avoid large inter-user interference in ZF MU-MIMO transmission, and it can be used in various configurations such as different codebook type, different number of antennas, and different paired users. Simulation results show that the proposed USS feedback scheme is efficiency for users with very low CSI quantization bits and paired other users at high SNR region.
Declarations
Acknowledgements
This study was supported by the National Natural Science Foundation of China Project (Grant No. 61001119, 61027003), the International Scientific and Technological Cooperation Program (Grant No. 2010DFA11060, S2010GR0902), and the National S&T Major Program (No. 2009ZX03003-011-02, No. 2009ZX03003-009).
Authors’ Affiliations
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