Quantized detection in uplink MIMO with oversampling

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First Claim
1. A method of a quantized detection in an uplink mimo with oversampling which takes samples faster than a symbol rate for the uplink MIMO with a 1bit ADC, the method comprising the steps of:
 obtaining a relation between transmitted data symbols x and a quantized temporally oversampled observation vector r in a simple form y=Hx+n, by deriving an oversampled channel matrix H, a detector providing an estimate for the transmitted data symbols x based on the quantized temporally oversampled observation vector r, the oversampled channel matrix H and a derived simple relation between the oversampled channel matrix H and the quantized temporally oversampled observation vector r=Q(Hx+n);
wherein Q(Hx+n) is a quantizer function mapping an input of a quantizer to discrete levels, and n is a noise vector; and
wherein the detector utilizes a temporal oversampling in the uplink quantized MIMO method.
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Abstract
The invention relates to a quantized detection in uplink mimo with oversampling that is a temporal oversampling in quantized uplink MIMO systems.
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11 Claims
 1. A method of a quantized detection in an uplink mimo with oversampling which takes samples faster than a symbol rate for the uplink MIMO with a 1bit ADC, the method comprising the steps of:
obtaining a relation between transmitted data symbols x and a quantized temporally oversampled observation vector r in a simple form y=Hx+n, by deriving an oversampled channel matrix H, a detector providing an estimate for the transmitted data symbols x based on the quantized temporally oversampled observation vector r, the oversampled channel matrix H and a derived simple relation between the oversampled channel matrix H and the quantized temporally oversampled observation vector r=Q(Hx+n);
wherein Q(Hx+n) is a quantizer function mapping an input of a quantizer to discrete levels, and n is a noise vector; and
wherein the detector utilizes a temporal oversampling in the uplink quantized MIMO method. View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11)
1 Specification
The invention relates to a quantized detection in uplink mimo with oversampling that is a temporal oversampling in quantized uplink MIMO systems.
Owing to their low power consumption and cost, employing 1bit analogtodigital converters (ADC) in massive multipleinput multipleoutput (MIMO) systems has attracted significant attention, which resulted in such systems to be examined widely in the recent literature. Multiuser multiinput multioutput (MIMO) systems have the advantage of providing support for multiple users by employing the same timefrequency resources, which promotes their use in the current and future communication systems. However, as the number of user terminals increase while the number of receive antennas are fixed, the amount of multiuser interference (MUI) increases, which may deteriorate the quality of service received by the users. Therefore, suppression of MUI becomes a critical issue for the scenarios where a significant number of user terminals are present, which is a possible scenario for next generation systems. MUI suppression is possible by increasing the number of base station antennas. This brings the employment of multiuser massive MIMO structures, in which a large number of base station antennas are present, to a critical position in future communication systems. In addition to their capability of suppressing MUI substantially, massive MIMO systems provide great advantages in terms of spectral and radiated energy efficiency and throughput.
However, the mentioned advantages come with some restrictions due to large number of antennas possessed by such systems. An important limitation is the high power consumption and implementation costs. In order for the power consumption and implementation costs to be maintained at feasible levels, employing a pair of low resolution analogtodigital converters (ADC) for each antenna in the massive MIMO array is among the possible solutions. An additional motivation to employ low resolution ADCs is to maintain the data rates at feasible levels to be supported by common public interface (CPRI), which will especially be important for cloud radio access network (CRAN) applications. Among the ADCs with small number of bits, onebit ADCs have the lowest power consumption and implementation cost as they are composed of a single comparator and do not need automatic gain control units. This makes them favorable to be employed in massive MIMO systems.
Due to their aforementioned advantages of 1bit ADCs, many studies investigated 1bit quantized MIMO and massive MIMO systems in terms of achievable rate, capacity and error rate performance. The investigated case in those studies and the conventional receivers in uplink MIMO systems only considers the SR samples to detect the transmitted data symbols. This is not optimal under quantization noise. However, benefits of temporal oversampling, in which additional samples taken due to sampling faster than symbol rate are used to refine the data symbol estimates, are shown to exist for singleinput singleoutput (SISO) scenarios under 1bit quantization. The conventional receiver working with SR samples needs higher SNR or a larger number of receive antennas or can support limited number of users compared to the receiver that employs temporal oversampling in this invention.
This invention relates to a quantized detection in uplink mimo with oversampling. This invention proposes a receiver that employs temporal oversampling. With this invention:
 Same symbol error rate (SER) can be obtained with lower SNR levels (up to 9 dB lower) or with smaller number of receive antennas (up to 70% decrease in the necessary number of antennas is possible) compared to the conventional zeroforcing (ZF) receiver that works with SR samples to obtain the data symbol estimates.
 More users at further distance from tha base station can be supported with the same number of receive antennas by taking into account the fasterthansymbolrate (FTSR) samples.
 The invention can be directly used in the existing MIMO and massive MIMO base stations with high resolution ADCs
 Power consumption and the overall cost of the MIMO array can be reduced significantly.
 Oversampling is performed in time domain
This invention shows that the necessary number of receive antennas to serve a fixed number of users maintaining a certain errorrate performance can be reduced significantly. This provides the advantage of reduced form factors, power consumption, deployment and maintenance costs for the MIMO base stations. Furthermore, the reduction in the necessary number of antennas to serve a fixed number of users implies that the number of users that can be served with a certain number of antennas will also be increased with temporal oversampling. By oversampling, the form factor, power consumption and the overall cost of the MIMO array can be reduced significantly. Moreover, the pronounced advantages regarding the necessary number of antennas also prevail with the proposed low complexity block sequential receiver as its performance can be observed to be close to the ZF receiver for both perfect and imperfect channel state information (CSI) cases.
Another aspect of the invention, wherein the detector is zeroforcing (ZF) detector.
Another aspect of the invention, wherein the detector is block sequential linear minimum mean squared estimate (BSLMMSE) detector.
Another aspect of the invention, wherein the detector is characterized by G(r,H), based on the simple linear relation r=Q(Hx+n) and the derived oversampled channel matrix H, which is widely investigated in literature, for which various receiver types to estimate the transmit vector x are proposed (like linear minimum mean squared estimate, LMMSE, bestlinear unbiased estimator BLUE, factorgraph based receivers, etc)
Another aspect of the invention, wherein the detectors utilizing temporal oversampling in uplink quantized MIMO systems G(r,H) reduce the necessary number of receive antennas to maintain a certain error rate performance significantly.
Another aspect of the invention, wherein the receiver schemes that take into account r and the derived oversampled channel matrix are able to provide up to 4 dB signaltonoise ratio (SNR) advantage compared to SR sampling in terms of error rate performance of 1bit quantized uplink massive MIMO for narrowband fading channel scenario.
Another aspect of the invention, wherein the receiver schemes that take into account r and the derived oversampled channel matrix are able to provide up to 9 dB signaltonoise ratio (SNR) advantage compared to SR sampling in terms of error rate performance of 1bit quantized uplink massive MIMO for wideband fading channel scenario.
Another aspect of the invention, wherein the special cases of the receiver schemes that take into account r and the derived oversampled channel matrix H, namely ZF and BSLMMSE (L^{n}=6, P=M/8) receivers, can reduce the necessary number of antennas to satisfy a SER of 10^{−3 }by 70% for perfect CSI (when SNR=−12 dB) and 60% for imperfect CSI case (when SNR=−7 dB) by temporal oversampling.
Another aspect of the invention, wherein it provides up to 9 dB SNR advantage.
Another aspect of the invention, wherein the receiver is utilizing temporal oversampling in uplink quantized MIMO systems.
The figures used to better explain quantized detection in uplink massive mimo with temporal oversampling developed with this invention and their descriptions are as follows:

FIG. 1 : Simulation based SER vs. SNR curves for M=400, K=20, oversampling rate β=1,2,4 with ZF and BSLMMSE (L^{n}=4, P=M/4) receivers for perfect and imperfect CSI (σ_{h}^{2}=0.2). 
FIG. 2 : Simulation based SER vs number of receive antennas (M) for oversampling rate β=1,2,4 with ZF and BSLMMSE receivers (L^{n}=4, P=M/8) when SNR=−12 dB for perfect and imperfect CSI (σ_{h}^{2}=0.2). 
FIG. 3 : Simulation based SER vs SNR curves for oversampling rate β=1,2,4 with ZF and BSLMMSE (L^{n}=6, P=M/4) receivers for frequency selective channel (L=3) for perfect and imperfect CSI (σ_{h}^{2}=0.4). 
FIG. 4 : Simulation based SER vs number of receive antennas (M) for oversampling rate β=1,2,4 with ZF and BSLMMSE receivers (L^{n}=6, P=M/8) for frequency selective channel (L=3) when SNR=−7 dB for perfect and imperfect CSI (σ_{h}^{2}=0.4). 
FIG. 5 : System diagram
To better explain a quantized detection in uplink mimo with temporal oversampling developed with this invention, the details are as presented below.
This invention propose temporal oversampling in quantized uplink MIMO systems. In this invention receiver schemes are proposed for uplink (the data transmission is from users to base station). With this invention, the relation between the transmit data vector and the unquantized observation vector are obtained in linear form y=Hx+n, where y, x and n are the observation, data and noise vectors, respectively, by deriving the matrix H for oversampled case. This linear form is widely investigated in literature, for which various receiver types to estimate the transmit vector x are proposed (like linear minimum mean squared estimate, LMMSE, bestlinear unbiased estimator BLUE, factorgraph based receivers, etc). The detectors providing an estimate for the transmitted data symbols x based on the quantized observation vector r, the derived oversampled channel matrix H and the simple relation between them r=Q(Hx+n), which are referred to as G(r,H), can provide significant advantages regarding error rate performances of such systems. This fact is shown by examining two examples of such detectors, namely zeroforcing (ZF) detector and block sequential LMMSE (BSLMMSE) detector. The terms “receiver” and “detector” will be used interchangeably in this document. The block sequential receiver is of lower complexity compared to the ZF receiver. With the subexample receivers we present, we show that the receiver schemes that take into account r and the derived oversampled channel matrix H are able to provide up to 4 dB signaltonoise ratio (SNR) advantage compared to SR sampling in terms of error rate performance of 1bit quantized uplink massive MIMO for narrowband fading channel scenario. For wideband fading channel case, this SNR advantage is up to 9 dB. This means that the cell coverage of the base stations incorporating massive MIMO arrays with lowresolution ADCs can be much larger if temporal oversampling is utilized. Moreover, with the receiver schemes G(r,H), we also show that the necessary number of receive antennas to serve a fixed number of users maintaining a certain errorrate performance can be reduced significantly. This provides the advantage of reduced form factors, power consumption, deployment and maintenance costs for the MIMO base stations. Furthermore, the reduction in the necessary number of antennas to serve a fixed number of users implies that the number of users that can be served with a certain number of antennas will also be increased with temporal oversampling.
Notation: b is a scalar, b is a column vector, b_{m }is the m^{th }element of vector b, B is a matrix, B^{H }and B^{T }represents the Hermitian and the transpose of C, respectively. Re(.)and Im(.) takes the real and imaginary parts of their operands and represents the L_{2 }norm. I is an identity matrix and 0 is a zero vector of appropriate dimension.
Signal Model:
The received signal at the m^{th }receive antenna for the wideband uplink multiuser MIMO system with K users and M receive antennas is written as
where N is the block length, which is the number of symbols that are processed in a block, h_{m,k}, [l] is value of the channel impulse response between the k^{th }user and the m^{th }antenna at the time instant t=t_{l}, p_{c}(t) is the transmit pulse shaping filter impulse response, x_{n,k }is the complex valued symbol transmitted by the k^{th }user at the n^{th }symbol interval with unit average power so that E[x_{k,n}^{2}]=1 ∀k,n. T is the symbol period and z_{m}(t) is an additive white Gaussian noise process at the m^{th }antenna, whose each sample is a random variable, where represents a complex Gaussian random variable with mean μ and variance σ^{2}. The channel coefficients h_{m,k}[l] are assumed to be independent random variables, which represent Rayleigh fading and a uniform power delay profile channel scenario. The pulse matched filtered signal at the m^{th }antenna, g_{m}(t)=r_{m}(t)*p_{c}(−t), * representing the convolution operation, can be expressed as
where p(t)=p_{c}(t)*p_{c}(−t) and d_{m}(t)=z_{m}(t)*p_{c}(−t). For case of demonstration purposes, we define vector a y as
where y_{n,m}=g_{m}((n−1)T=β), n=1, . . . , βN, m=1, . . . , M, β being a positive integer oversampling rate, which is defined as the ratio of the total number of samples to the samples taken at symbol rate. Furthermore, vectors x and w are also defined as
where w_{n,m}=d_{m}((n−1)T=β), n=1, . . . , βN, m=1, . . . , M. In this case, (2) can be written in matrixvector form as
y=Hx+n, (6)
where
in which
where
and C_{l }is the matrix, whose element at its m^{th }row and the k^{th }column is equal to h_{m,k}[l].
Under quantization of the received signal vector y, the signal model in (6) becomes
r=Q(y)=Q(Hx+w), (9)
where Q(.) is the quantizer function that maps the signal at its input to discrete levels. For instance, in 1bit quantizer case, Q(y)=sgn(Re(y))+j_{sgn}(Im(y)), sgn(.) being the signum function. Moreover, the quantizer output r can be scaled to ensure that the variance of each element of y is the same as that of r, as performed for SR sampling and LloydMax quantizer case in prior art. This scaling is important for the case when amplitude modulation (like QAM) is present for the data symbols, but has no significance when constant modulus type (like phaseshift keying, PSK) modulation is used for the data symbols. The estimate for the transmitted symbol vector {circumflex over (x)} can be found as
{circumflex over (x)}=G(r,H), (10)
where G(.) is a function, either linear and nonlinear, that yields the data vector estimate {circumflex over (x)} based on the quantized observation vector r and the oversampled equivalent channel matrix H. For the case of linear receivers, G(r,H)=D(Br), B being the linear receive matrix and D(.) is the function that maps the soft symbol estimates to the nearest constellation point to find the hard symbol estimate {circumflex over (x)}. For maximalratio combining or ZF combining B=H^{H}K and B=(H^{H}H)^{−1}H^{H}, respectively, where K is a diagonal matrix whose k^{th }diagonal element is equal to 1/∥h_{k}∥_{2}, h_{k }being the k^{th }column of H.
In this invention, we prefer leaving the proposal of a channel estimation algorithm to the extended version of this invention. However, we take into account the impact of imperfect channel state information (CSI) as follows. We presume that the maximum likelihood (ML) estimates for the channel matrix C_{l }are estimated with some method. Owing to the property of the ML estimates being asymptotically Gaussian and unbiased, we obtain the estimated channel matrix C_{l}, namely Ĉ_{l}, by adding independent zero mean (since the estimates are unbiased) complex Gaussian random variables with variance σ_{h}^{2}/L to each element of the matrix C_{l}. Then, Ĥ can be obtained from Ĉ_{l }using (7) and (8).
Block Sequential Linear Receiver:
This invention proposes a sequential type linear receiver as an alternative to the ZF receiver. The reason is that for ZF receiver, in which case B=(H^{H}H)^{−1}H^{H}, the number of multiplications to obtain B grows with N^{3 }due to inversion of H^{H}H. This makes the ZF receiver for oversampled uplink MIMO computationally prohibitive when the block length in a data packet goes high. One can propose using MRC receiver instead of ZF receiver, but it has been shown that MRC receiver suffers significantly from an error floor and performs worse in terms of error rate when oversampling is performed compared to the SR sampling case for 1bit quantized case in prior art. Therefore, we seek to construct a sequential receiver that will provide the advantages that come with oversampling as in the linear ZF filter case and has a complexity that grows linearly with the block length N.
To derive a sequential linear receiver, we make some modifications in the signal model that we present in the system model section such that the derived receiver does not wait for the whole quantized observation vector r, which is of size βMN, to be obtained to update the estimate for the transmitted data symbol vector x. In (9), the quantized receive vector r is expressed as a function of the data symbol vector x. At this point, we define the observation vector at the time instant n, for which only the first nP elements of the quantized receive vector r are observed, while the remaining βMN−nP elements are not observed yet. We denote this vector by r[n]. In this case, the observation model can be expressed as
r[n]=Q(H[n]x+w[n]), (11)
where
In (14), H_{p}[1]^{H }represents the matrix formed by taking the first P rows of matrix H. Similarly H_{p}[1]^{H }and H_{p}[n]^{H}, represents the matrices formed by taking the second and the n^{th }P rows of the matrix H, respectively. Moreover, in (12) and (13), r_{i }and w_{i }are the i^{th }element of the vectors r and w, respectively. Denoting the soft estimate of vector x at the time instant n−1 as x′[n−1], which is calculated based on the observation vector at the time instant n−1, namely r[n−1]the aim is to update the estimate x′[n−1] to x′[n] using r[n]. Such an estimator can be defined with the following update equations performed at time instant n.
K[n] can be denoted as the Kalman gain matrix, M[n] as the MMSE matrix and is the matrix formed by taking the n^{th }P rows of matrix Ĥ, which is the estimated version of matrix H. The execution of the update equations in (15)(17) will also be referred to as the “n^{th }iteration step of the sequential receiver”. The size of the Kalman gain matrix K[n] is NK×P, whereas the size of the MMSE matrix M[n] is NK×NK. When no data is observed yet, the symbol estimate {circumflex over (x)}[n] and the MMSE matrix M[n] should be initialized using the prior information of the symbol estimates as follows.
The equations (15)(17) are the application of block Kalman filtering derived for unquantized observation model in prior art to the case of oversampled MIMO structure with quantization. The receiver characterized by the equations (15)(17) will be referred to as block sequential LMMSE (BSLMMSE) receiver. When P=1, the equations (15)(17) correspond to the update equations for the sequential LMMSE for the unquantized observation model in prior art. We propose this estimation technique to be directly used with the quantized observations. With such a sequential estimation scheme, the matrix inversion in the ZF receiver is avoided.
An important advantage of the proposed sequential estimator is its ability to provide estimates for the data vector without having to wait for all observations taken for the whole data processing block (total number of observations for data processing block is βMN). For example, let the vector for the hard symbol estimates for the symbols transmitted at symbol interval be denoted as {circumflex over (x)}^{p}. It can be expressed as
where {circumflex over (x)}_{i }corresponds to the i^{th }element of the hard symbol estimate vector {circumflex over (x)} for the transmitted symbol vector x defined in (4). Let the soft estimates for the symbols transmitted in the symbol interval at the n^{th }iteration step of the sequential estimation algorithm be denoted as x′[n,p]. It can be written as
where x′_{i}[n] corresponds to the i^{th }element of the vector x′[n]. Assuming that employed pulse shape decays to insignificant levels after L′ symbol durations, the hard symbol estimate vector for the symbols transmitted at symbol interval {circumflex over (x)}^{p }can be found by mapping the elements in the soft estimate vector for the transmitted symbols at symbol interval at the (Mβ(p+L″)/P)^{th }iteration step, namely x′[Mβ(p+L″)/P,p], where L″=L+L′−1, to the minimum distance constellation point. In short, we make the hard decisions for the symbols transmitted at the n^{th }symbol interval, whenever the observation for the (N+L″)^{th }symbol interval r_{(n+L″)βM/P }is taken. With this scheme, the maximum delay for the symbol decisions is L″T for all transmitted symbols, while the delay for ZF receiver can be up to NT, which is in general significantly larger than L″T.
Although the proposed sequential receiver characterized by (15)(17) has the mentioned advantages, its complexity is still not low. For example, in (15), the complexity of the multiplication of matrix M[n−1], whose size is NK×NK, with Ĥ_{p}[n], which is a matrix of size NK×P, grows with N^{2}. Repeating this multiplication for all iteration steps means that the complexity of the multiplications to estimate vector x at the end of all iterations grows with N^{3}, since the total number of iterations is βMN/P. Therefore, with the presented sequential receiver, the total number of multiplications still grows with N^{3 }similar to the ZF filter case. To reduce the complexity of the sequential receiver, we exploit the fact that the pulse shape decays to insignificant levels after a certain number of symbol durations (L′) and the length of the channel impulse response is finite, thus it is not necessary to update all symbol estimates for every observation. The low complexity version of the sequential receiver is characterized by the following update equations that are performed at each iteration step.
In (26) and (27), x′[n]_{i }corresponds to the i^{th }element of the vector x′[n] and ĥ[n]_{i }refers to the i^{th }row of matrix Ĥ_{p}[n] and M_{l}[n]_{i,j }corresponds to the element of matrix M_{l}[n] at its i^{th }row and j^{th }column. Moreover, the indexes n_{b}=(n_{i}−L)N_{t }and n_{s}=(n_{i}+L)N_{t}, where index n_{i }specifies the current symbol interval that the observations are being taken from at the n^{th }iteration of the sequential receiver and is equal to └(nP−1)/M/β+1┘, where └.┘ is the floor function that gives the largest integer less than its operand. In this setting for the sequential receiver, the size of the Kalman gain matrix K_{l}[n] and the MMSE matrix M_{l}[n] becomes (2LN_{t}+1)×P and (2LN_{t}+1)×(2LN_{t}+1) and they can be initialized as in (19) and (20). For the low complexity version of the sequential receiver characterized by (23)(25), the number of complex multiplications in the update equations (23)(25) do not change with the block length N since the sizes of H_{p}_{l}[n−1], x′_{l}[n−1] and M_{l}[n−1] are (2LN_{t}+1)×P, (2LN_{t}+1)×P and (2LN_{t}+1)×(2LN_{t}+1), respectively, which are all independent of N. Since there are βMN/P iterations, the number of complex multiplications grows with N compared to N^{3 }for the ZF receiver and the high complexity version of the sequential characterized by (15)(17). Moreover, for the low complexity sequential receiver, the number of complex multiplications per estimated symbol of each user does not change with N since each user transmits N symbols in the whole data block.
Simulation Results:
Number of users (K) and receive antennas (M) are taken to be 20 and 400, respectively. The block length N) is selected to be 10 symbols and the oversampling rate (β) is chosen between 1 and 4. The rolloff factor (ρ) for the rootraised cosine (RRC) pulse shape is taken to be 0.22. For narrowband channel scenario plots L=1 and L″=4. For frequency selective channel simulations, t_{l}=lT, L=3 and L″=6. Modulation type is selected to be QPSK. The solid curves in all figures represent the perfect CSI cases, whereas the dashed curves correspond to the imperfect CSI cases. Moreover, while the curves with markers with triangular shape indicate the performance of ZF receiver, the curves with other type of markers correspond to the performance of BSLMMSE receiver. The SNR values on the plots are equal to 1/σ_{n}^{2}.
The error rate performances of BSLMMSE receiver and ZF receiver are obtained by simulations and plotted in
As can be noted in
We also present SER versus the number of receive antennas when SNR is fixed as −12 dB in
In
To demonstrate the advantage of oversampling in terms of the necessary number of receive antennas for frequency selective channel case, SER versus the number of receive antennas when SNR is fixed as −7 dB is presented in in
The detectors utilizing temporal oversampling in uplink quantized MIMO systems reduce the necessary number of receive antennas to maintain a certain error rate performance significantly.
From the above detailed description, a receiver scheme comprising; the method of a quantized detection in uplink mimo with oversampling which takes samples faster than the symbol rate for uplink MIMO with 1bit ADC and comprising the steps of;

 obtaining the relation between the transmitted data symbols x and the quantized temporally oversampled observation vector r in a simple form y=Hx+n, by deriving matrix H,
 providing an estimate for the transmitted data symbols x based on the quantized observation vector r, matrix H and the derived simple relation between them r=Q(Hx+n) by detectors (receivers).