SINR (signal-to-interference-and-noise ratio) is a general quality metric that can be computed for any array.

Consider a general “memoryless” array with M elements.  Then the signal received at the beamformer input can be modeled as Mx1 vector

x(n) = i(n) + sum_{q=1}^Q a(q) s(n;q)

at time "n", where s(n;q) is the qth transmitted signal received by the array (along with observed delay and frequency shift added by the channel), a(q) is the Mx1 spatial signature for that signal, and i(n) is the Mx1 background interference vector received by the array.  Also assume that the transmitted signals are uncorrelated and have received power levels {Rss(q)} (typically subsumed into the spatial signatures), and the MxM interference autocorrelation matrix Rii is known.

Further assume that signal “s(n;q)” is estimated by linearly combining the M antenna elements using Mx1 beamforming vector w(q), resulting in beamformer output signal 

y(n;q) = w(q)’ * x(n),

where ()’ denotes the conjugate-transpose (Hermitian) operation.  Then the SINR of y(n;q) is given by

SINR(q) = SNR(q,q) / (1 + sum_{p\=q} SNR(q,p) )

where SNR(q,p) is the signal-to-noise ratio (SNR) of signal “p” at the output of beamformer “q”,

SNR(q,p) = abs(w(q)’ * a(p))^2 Rss(p) / w(q)’ * Rii w(q).

It should be noted that SINR(q) is **always** lower than SNR(q) = SNR(q,q), hence its not surprising that you get a “better” result for SNR.  In fact, its not a “better” result, as much as an inaccurately high result, as it does not account for contributions from the interferers in the environment.

A better metric is misadjustment from maximum attainable SINR, given by

maxSINR(q) = maxcorr(q) / (1 - maxcorr(q)),

maxcorr(q) = a(q)’ * inv(Rxx) a(q),

where Rxx is the full data autocorrelation matrix,

Rxx = Rii + sum_{q=1}^Q a(q)*a(q)’ * Rss(q).

The spatial signatures should model direct and reflection paths for each signal, and the interference vector should model the composite receiver noise, background noise received at the antenna, and background interference received by the array.  Definition of “background interference” is loosely defined, could be signals **not** intended for the receiver, could be just “weak” signals.  In a careful full-network simulation, there are no “interferers," that is **all** of the signals received by the array are modeled inside the summation.

 Note, this is a simplified model.  In an OFDM(A) format, it would be more appropriate to replace “time n” with "(slot,subcarrier) (n,k)," in which case SINR could vary from subcarrier to subcarrier.  This would typically happen in presence of frequency-dependent multipath, which is highly likely for WiFi.  Can also vary between slots in time-varying multipath.

In re one other responders comments, just “assuming” that the interferers are nulled is very dangerous, as they will of course **not** be fully nulled and will lead to erroneous results.  Moreover, in a full network, the actual number of received signals is likely to be much higher than the number of elements in the array, and they **cannot** all be fully nulled.

In an actual system, various means can be contrived to estimate the true SINR, usually based on the mean-squared-error of the signal at the beamformer output.  In practice, this also requires estimation of the observed delay and frequency shift between the transmitted and received signals, for a pilot component of the signal, after demodulation and remodulation of the received signal.

Thank you Lauris and Brian.

You are welcome.  BTW, a typo at the end of my response.  I meant you can estimate SINR from monitoring pilots OR from quality estimates provided from the demodulated and remodulated received (information-bearing) signal.

Matlab offers an excellent simulink based platform to model beamforming very easily.

Hopefully the link will help.

https://www.mathworks.com/discovery/beamforming.html

When simulating the performance of a wireless system, the choice of performance metric and simulation methodology depends on the specific research question and system design. In general, the SINR or SNR is used as a performance metric for wireless systems, and the methodology to calculate it varies depending on the system design.

In the case of conformal beamforming, the focus is on improving the received signal power for a single user by using a dedicated beam. However, the interference from other base stations can still affect the received signal power and the SINR of the user. Therefore, it may not be appropriate to ignore the interference from other base stations when computing the SINR of the user under conformal beamforming.

One possible approach is to use a multi-user beamforming technique that optimizes the beamforming vectors to minimize the interference from other base stations while maximizing the received signal power at the user. This can be done by solving an optimization problem that takes into account the channel matrix, transmit power, and noise power, and outputs the optimal beamforming vector. The resulting SINR can then be calculated as the ratio of the received signal power to the noise and interference power.

In summary, when simulating the performance of conformal beamforming, it is important to take into account the interference from other base stations and use an appropriate methodology to calculate the SINR of the user.